Eisenstein type series for Calabi-Yau varieties

Energy Technology Data Exchange (ETDEWEB)

Movasati, Hossein [Instituto de Matematica Pura e Aplicada, IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, RJ (Brazil)

2011-06-11

In this article we introduce an ordinary differential equation associated to the one parameter family of Calabi-Yau varieties which is mirror dual to the universal family of smooth quintic three folds. It is satisfied by seven functions written in the q-expansion form and the Yukawa coupling turns out to be rational in these functions. We prove that these functions are algebraically independent over the field of complex numbers, and hence, the algebra generated by such functions can be interpreted as the theory of (quasi) modular forms attached to the one parameter family of Calabi-Yau varieties. Our result is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures. It is a generalization of the Ramanujan differential equation satisfied by three Eisenstein series.

Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications

Energy Technology Data Exchange (ETDEWEB)

Cicoli, Michele [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Mayrhofer, Christoph [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Kreuzer, Maximilian

2011-06-15

We analyse several explicit toric examples of compact K3-fibred Calabi-Yau three-folds which can be used for the study of string dualities and are crucial ingredients for the construction of LARGE Volume type IIB vacua with promising applications to cosmology and particle phenomenology. In order to build a phenomenologically viable model, on top of the two moduli corresponding to the base and the K3 fibre, we demand also the existence of two additional rigid divisors: the first supporting the non-perturbative effects needed to achieve moduli stabilisation, and the second allowing the presence of chiral matter on wrapped D-branes. We clarify the topology of these rigid divisors by discussing the interplay between a diagonal structure of the Calabi-Yau volume and D-terms. Del Pezzo divisors appearing in the volume form in a completely diagonal way are natural candidates for supporting non-perturbative effects and for quiver constructions, while 'non-diagonal' del Pezzo and rigid but not del Pezzo divisors are particularly interesting for model building in the geometric regime. Searching through the existing list of four dimensional reflexive lattice polytopes, we find 158 examples admitting a Calabi-Yau hypersurface which is a K3 fibration with four Kaehler moduli where at least one of them is a 'diagonal' del Pezzo. We work out explicitly the topological details of a few examples showing how, in the case of simplicial polytopes, all the del Pezzo divisors are 'diagonal', while 'non-diagonal' ones appear only in the case of non-simplicial polytopes. A companion paper will use these results in the study of moduli stabilisation for globally consistent explicit Calabi-Yau compactifications with the local presence of chirality. (orig.)

Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications

International Nuclear Information System (INIS)

Cicoli, Michele; Mayrhofer, Christoph; Kreuzer, Maximilian

2011-06-01

We analyse several explicit toric examples of compact K3-fibred Calabi-Yau three-folds which can be used for the study of string dualities and are crucial ingredients for the construction of LARGE Volume type IIB vacua with promising applications to cosmology and particle phenomenology. In order to build a phenomenologically viable model, on top of the two moduli corresponding to the base and the K3 fibre, we demand also the existence of two additional rigid divisors: the first supporting the non-perturbative effects needed to achieve moduli stabilisation, and the second allowing the presence of chiral matter on wrapped D-branes. We clarify the topology of these rigid divisors by discussing the interplay between a diagonal structure of the Calabi-Yau volume and D-terms. Del Pezzo divisors appearing in the volume form in a completely diagonal way are natural candidates for supporting non-perturbative effects and for quiver constructions, while 'non-diagonal' del Pezzo and rigid but not del Pezzo divisors are particularly interesting for model building in the geometric regime. Searching through the existing list of four dimensional reflexive lattice polytopes, we find 158 examples admitting a Calabi-Yau hypersurface which is a K3 fibration with four Kaehler moduli where at least one of them is a 'diagonal' del Pezzo. We work out explicitly the topological details of a few examples showing how, in the case of simplicial polytopes, all the del Pezzo divisors are 'diagonal', while 'non-diagonal' ones appear only in the case of non-simplicial polytopes. A companion paper will use these results in the study of moduli stabilisation for globally consistent explicit Calabi-Yau compactifications with the local presence of chirality. (orig.)

One-dimensional super Calabi-Yau manifolds and their mirrors

Energy Technology Data Exchange (ETDEWEB)

Noja, S. [Dipartimento di Matematica, Università degli Studi di Milano,Via Saldini 50, I-20133 Milano (Italy); Cacciatori, S.L. [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy); Piazza, F. Dalla [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); Marrani, A. [Centro Studi e Ricerche ‘Enrico Fermi’,Via Panisperna 89A, I-00184 Roma (Italy); Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova,and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy); Re, R. [Dipartimento di Matematica e Informatica, Università degli Studi di Catania,Viale Andrea Doria 6, 95125 Catania (Italy)

2017-04-18

We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY’s having reduced manifold equal to ℙ{sup 1}, namely the projective super space ℙ{sup 1|2} and the weighted projective super space Wℙ{sub (2)}{sup 1|1}. Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces ℙ{sup n|m}. We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of ℙ{sup 1|2}, whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of ℙ{sup 1|m}, discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that ℙ{sup 1|2} is self-mirror, whereas Wℙ{sub (2)}{sup 1|1} has a zero dimensional mirror. Also, the mirror map for ℙ{sup 1|2} naturally endows it with a structure of N=2 super Riemann surface.

Topological strings on compact Calabi-Yau's

Energy Technology Data Exchange (ETDEWEB)

Hollands, Lotte, E-mail: lhollands@science.uva.nl

2007-09-15

Some steps towards solving topological string amplitudes on Calabi-Yau spaces have been taken lately: all-genus amplitudes have been computed for non-compact toric Calabi-Yau threefolds, local Riemann surfaces and K3-fibrations, while progression has been made for the Fermat quintic threefold. However, the building blocks of all-genus topological string amplitudes for general compact Calabi-Yau's remain unknown. We study some aspects of the underlying geometry and discuss difficulties.

On Mirror Symmetry for Calabi-Yau Fourfolds with Three-Form Cohomology

NARCIS (Netherlands)

Greiner, Sebastian; Grimm, Thomas W.

2016-01-01

We study the action of mirror symmetry on two-dimensional N=(2,2) effective theories obtained by compactifying Type IIA string theory on Calabi-Yau fourfolds. Our focus is on fourfold geometries with non-trivial three-form cohomology. The couplings of the massless zero-modes arising by expanding in

Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds

Science.gov (United States)

Alim, Murad; Movasati, Hossein; Scheidegger, Emanuel; Yau, Shing-Tung

2016-06-01

We describe a Lie Algebra on the moduli space of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions {{F}g^alg, g ≥ 1}, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.

The complete matter sector in a three-generation compactification

International Nuclear Information System (INIS)

Berglund, P.; Parkes, L.; Huebsch, T.

1992-01-01

We consider a Calabi-Yau compactification paradigm with three light generations and an R-symmetry. From a special form of the Tian-Yau manifold, we also construct a new three-generation model with markedly different phenomenology. The complete spectrum of all light matter fields is obtained in a universal way and moreover in a physically suitable basis, allowing a straightforward analysis of all their couplings. Here we discuss all the renormalizable Yukawa couplings. This computation can equally well be repeated for all compactification models based on Calabi-Yau complete intersections in products of homogeneous spaces. (orig.)

Hermitian Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds

International Nuclear Information System (INIS)

Popov, Alexander D.

2010-01-01

We consider the Hermitian Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle E over an almost complex manifold X 6 which is the twistor space of an oriented Riemannian manifold M 4 . Each solution of the HYM equations on such X 6 defines a pseudo-holomorphic structure on the bundle E. It is shown that the pull-back to X 6 of any anti-self-dual gauge field on M 4 is a solution of the HYM equations on X 6 . This correspondence allows us to introduce new twistor actions for bosonic and supersymmetric Yang-Mills theories. As examples of X 6 we consider homogeneous nearly Kaehler and nearly Calabi-Yau manifolds which are twistor spaces of S 4 , CP 2 and B 4 , CB 2 (real 4-ball and complex 2-ball), respectively. Various explicit examples of solutions to the HYM equations on these spaces are provided. Applications in flux compactifications of heterotic strings are briefly discussed.

A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list

Energy Technology Data Exchange (ETDEWEB)

Altman, Ross [Department of Physics, Northeastern University,360 Huntington Avenue, Boston, MA 02115 (United States); Gray, James [Physics Department, Robeson Hall, Virginia Tech,850 West Campus Drive, Blacksburg, VA 24061 (United States); He, Yang-Hui [Department of Mathematics, City University,Northampton Square, London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford, OX1 4JD (United Kingdom); Jejjala, Vishnu [Centre for Theoretical Physics, NITheP, andSchool of Physics, University of the Witwatersrand,1 Jan Smuts Avenue, Johannesburg, WITS 2050 (South Africa); Nelson, Brent D. [Department of Physics, Northeastern University,360 Huntington Avenue, Boston, MA 02115 (United States); International Center for Theoretical Physics,Strada Costiera 11, Trieste 34014 (Italy)

2015-02-25

Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions http://arxiv.org/abs/hep-th/0002240. These polyhedra describe the singular limits of ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. In this paper, we review how to extract topological and geometric information about Calabi-Yau threefolds using the toric construction, and we provide, in a companion online database (see http://nuweb1.neu.edu/cydatabase), a detailed inventory of these quantities which are of interest to physicists. Many of the singular ambient spaces described by the Kreuzer-Skarke list can be smoothed out into multiple distinct toric ambient spaces describing different Calabi-Yau threefolds. We provide a list of the different Calabi-Yau threefolds which can be obtained from each polytope, up to current computational limits. We then give the details of a variety of quantities associated to each of these Calabi-Yau such as Chern classes, intersection numbers, and the Kähler and Mori cones, in addition to the Hodge data. This data forms a useful starting point for a number of physical applications of the Kreuzer-Skarke list.

D-brane superpotentials and Ooguri-Vafa invariants of compact Calabi-Yau threefolds

Science.gov (United States)

Xu, Feng-Jun; Yang, Fu-Zhong

2015-04-01

We calculate the D-brane superpotentials for two compact Calabi-Yau manifolds X14(1,1,2,3,7) and X8(1,1,1,2,3) which are of non-Fermat type in the type II string theory. By constructing the open mirror symmetry, we also compute the Ooguri-Vafa invariants, which are related to the open Gromov-Witten invariants. Supported by NSFC (11075204, 11475178)

New large volume Calabi-Yau threefolds

Science.gov (United States)

Altman, Ross; He, Yang-Hui; Jejjala, Vishnu; Nelson, Brent D.

2018-02-01

In previous work, we have commenced the task of unpacking the 473 800 776 reflexive polyhedra by Kreuzer and Skarke into a database of Calabi-Yau threefolds [R. Altman et al. J. High Energy Phys. 02 (2015) 158., 10.1007/JHEP02(2015)158] (see www.rossealtman.com). In this paper, following a pedagogical introduction, we present a new algorithm to isolate Swiss cheese solutions characterized by "holes," or small 4-cycles, descending from the toric divisors inherent to the original four dimensional reflexive polyhedra. Implementing these methods, we find 2268 explicit Swiss cheese manifolds, over half of which have h1 ,1=6 . Many of our solutions have multiple large cycles. Such Swiss cheese geometries facilitate moduli stabilization in string compactifications and provide flat directions for cosmological inflation.

Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau

Science.gov (United States)

Aleshkin, Konstantin; Belavin, Alexander

2018-01-01

We clarify the recently proposed method for computing a special Kähler metric on a Calabi-Yau complex structure moduli space using the fact that the moduli space is a subspace of a particular Frobenius manifold. We use this method to compute a previously unknown special Kähler metric in a two-moduli non-Fermat model.

Heterotic model building: 16 special manifolds

International Nuclear Information System (INIS)

He, Yang-Hui; Lee, Seung-Joo; Lukas, Andre; Sun, Chuang

2014-01-01

We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html.

Energy functionals for Calabi-Yau metrics

International Nuclear Information System (INIS)

Headrick, M; Nassar, A

2013-01-01

We identify a set of ''energy'' functionals on the space of metrics in a given Kähler class on a Calabi-Yau manifold, which are bounded below and minimized uniquely on the Ricci-flat metric in that class. Using these functionals, we recast the problem of numerically solving the Einstein equation as an optimization problem. We apply this strategy, using the ''algebraic'' metrics (metrics for which the Kähler potential is given in terms of a polynomial in the projective coordinates), to the Fermat quartic and to a one-parameter family of quintics that includes the Fermat and conifold quintics. We show that this method yields approximations to the Ricci-flat metric that are exponentially accurate in the degree of the polynomial (except at the conifold point, where the convergence is polynomial), and therefore orders of magnitude more accurate than the balanced metrics, previously studied as approximations to the Ricci-flat metric. The method is relatively fast and easy to implement. On the theoretical side, we also show that the functionals can be used to give a heuristic proof of Yau's theorem

Numerical Calabi-Yau metrics

International Nuclear Information System (INIS)

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

2008-01-01

We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results

Distribution of flux vacua around singular points in Calabi-Yau moduli space

International Nuclear Information System (INIS)

Eguchi, Tohru; Tachikawa, Yuji

2006-01-01

We study the distribution of type-IIB flux vacua in the moduli space near various singular loci, e.g. conifolds, ADE singularities on P 1 , Argyres-Douglas point etc, using the Ashok-Douglas density det (R+ω). We find that the vacuum density is integrable around each of them, irrespective of the type of the singularities. We study in detail an explicit example of an Argyres-Douglas point embedded in a compact Calabi-Yau manifold

String theory of Calabi-Yau compactifications

International Nuclear Information System (INIS)

Luetken, C.A.

1989-01-01

The conformal field theory description of Calabi-Yau compactifications of the heterotic superstring from 10 to 4 dimensions is outlined. The basic ideas of ordinary (bosonic) conformal field theory are explained before describing the exactly solvable N=2 superconformal minimal models which are needed in the tensor construction of certain particularly simple string vacua. Using a simple sigma-model construction of algebraic varieties and drawing on insight gained from the Landau-Ginzburg description of critical phenomena, it is explained how the critical behaviour of these 2-dimensional solvable quantum field theories with complex supersymmetry may be regarded as string compactification on a Calabi-Yau background. The virtue of this is to provide a tool for computing exact (tree level) results for strings in these highly non-trivial vacua, including all the Yukawa couplings needed in the construction of the low-energy effective field theory. (orig.)

On (orientifold of) type IIA on a compact Calabi-Yau

International Nuclear Information System (INIS)

Misra, A.

2004-01-01

We study the gauged sigma model and its mirror Landau-Ginsburg model corresponding to type IIA on the Fermat degree-24 hypersurface in WCP 4 [1,1,2,8,12] (whose blow-up gives the smooth CY 3 (3,243)) away from the orbifold singularities, and its orientifold by a freely-acting antiholomorphic involution. We derive the Picard-Fuchs equation obeyed a period integral of a parent N=2 type IIA theory. We obtain the Meijer's basis of solutions to the equation in the large and small complex structure limits (on the mirror Landau-Ginsburg side) of the abovementioned Calabi-Yau, and make some remarks about the monodromy properties associated at the same and another MATHEMATICAlly interesting point. Based on a recently shown N=1 four-dimensional triality between Heterotic on the self-mirror Calabi-Yau CY 3 (11,11), M theory on CY 3 (3,243) x S 1 /(Z 2 ) and F-theory on an elliptically fibered CY 4 with the base given by CP 1 x Enriques surface, we first give a heuristic argument that there can be no superpotential generated in the orientifold of of CY 3 (3,243), and then explicitly verify the same using a mirror symmetry formulation for the abovementioned hypersurface away from its orbifold singularities. We then discuss briefly the sigma model and the mirror Landau-Ginsburg model corresponding to the resolved Calabi-Yau as well. (Abstract Copyright [2004], Wiley Periodicals, Inc.)

On four-derivative terms in IIB Calabi-Yau orientifold reductions

Energy Technology Data Exchange (ETDEWEB)

Weissenbacher, Matthias [Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa-no-ha 5-1-5, 277-8583 (Japan)

2017-04-11

We perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational α{sup ′3}-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of O3/O7-planes. We consider infinitesimal Kähler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the Kähler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inflation.

Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

DEFF Research Database (Denmark)

Andreas, Björn; Garcia Fernandez, Mario

2012-01-01

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(......) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain....

Microscopic Calabi-Yau black holes in string theory

Energy Technology Data Exchange (ETDEWEB)

Ansari, Saeid

2011-07-22

In this thesis we study microscopic aspects of Calabi-Yau black holes in string theory. We compute the absorption cross-section of the space-time massless scalars by the worldvolume of D2-branes, wrapped on the S{sup 2} of an AdS{sub 2} x S{sup 2} x CY{sub 3} geometry of a fourdimensional D4-D0 Calabi-Yau black hole. The D2-brane can also have a generic D0 probe-brane charge. However, we restrict ourselves to D2-branes with small D0-charge so that the perturbation theory is applicable. According to the proposed AdS{sub 2}/QM correspondence the candidate for the dual theory is the quantum mechanics of a set of probe D0-branes in the AdS{sub 2} geometry. For small but non-zero probe D0-charge we find the quantum mechanical absorption cross-section seen by an asymptotic anti-de Sitter observer. We repeat the calculations for vanishing probe D0-charge as well and discuss our result by comparing with the classical absorption cross-section. In other project, for a given fourdimensional Calabi-Yau black hole with generic D6-D4-D2-D0 charges we identify a set of supersymmetric branes, which are static or stationary in the global coordinates, of the corresponding eleven-dimensional near horizon geometry. The set of these BPS states, which include the branes partially or fully wrap the horizon, should play a role in understanding the partition function of black holes with D6-charge. (orig.)

Microscopic Calabi-Yau black holes in string theory

International Nuclear Information System (INIS)

Ansari, Saeid

2011-01-01

In this thesis we study microscopic aspects of Calabi-Yau black holes in string theory. We compute the absorption cross-section of the space-time massless scalars by the worldvolume of D2-branes, wrapped on the S 2 of an AdS 2 x S 2 x CY 3 geometry of a fourdimensional D4-D0 Calabi-Yau black hole. The D2-brane can also have a generic D0 probe-brane charge. However, we restrict ourselves to D2-branes with small D0-charge so that the perturbation theory is applicable. According to the proposed AdS 2 /QM correspondence the candidate for the dual theory is the quantum mechanics of a set of probe D0-branes in the AdS 2 geometry. For small but non-zero probe D0-charge we find the quantum mechanical absorption cross-section seen by an asymptotic anti-de Sitter observer. We repeat the calculations for vanishing probe D0-charge as well and discuss our result by comparing with the classical absorption cross-section. In other project, for a given fourdimensional Calabi-Yau black hole with generic D6-D4-D2-D0 charges we identify a set of supersymmetric branes, which are static or stationary in the global coordinates, of the corresponding eleven-dimensional near horizon geometry. The set of these BPS states, which include the branes partially or fully wrap the horizon, should play a role in understanding the partition function of black holes with D6-charge. (orig.)

Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

International Nuclear Information System (INIS)

Bao, L; Kleinschmidt, A; Nilsson, B E W; Persson, D; Pioline, B

2013-01-01

Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2, 1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers O_d, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; O_d). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers O_1 = Z[i].

Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

Science.gov (United States)

Bao, L.; Kleinschmidt, A.; Nilsson, B. E. W.; Persson, D.; Pioline, B.

2013-12-01

Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2, 1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers d, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; d). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers 1 = Bbb Z[i].

Compactification de la Supergravite 10-D Sur les Varietes de Calabi-Yau

Science.gov (United States)

Gagnon, Michel

Les varietes de Calabi-Yau permettent une description relativement simple et assez juste de la realite. Recemment, de nombreuses equipes de recherche s'y sont interessees, en particulier P. Candelas, A. M. Dale, C. A. Lutken et R. Schimmrigk (13) qui ont propose une liste de 7868 configurations distinctes. Toutefois, nous croyons que certaines des techniques qui sont exploitees pour construire cette liste ne sont pas suffisamment justifiees et ont pour effet de soustraire a nos investigations bon nombre de configurations potentiellement interessantes. Ainsi, nous produisons, sans utiliser ces techniques simplificatrices, une liste de 97360 configurations. Ensuite, dans le cadre des modeles a 4 generations, nous appliquons un ensemble de criteres, fondes sur les symetries discretes, pour delimiter le domaine des configurations phenomenologiquement viables. Finalement, apres avoir fixe notre choix sur une configuration particuliere, nous essayons de montrer tout l'interet physique des varietes de Calabi-Yau en exposant certains aspects de la phenomenologie a basse energie, notamment les nombres quantiques, les spectres fermioniques, la brisure intermediaire du groupe de jauge et la duree de vie du proton.

The Ising model: from elliptic curves to modular forms and Calabi-Yau equations

International Nuclear Information System (INIS)

Bostan, A; Boukraa, S; Hassani, S; Zenine, N; Van Hoeij, M; Maillard, J-M; Weil, J-A

2011-01-01

We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributions of the susceptibility of the Ising model for n ≤ 6 are linear differential operators associated with elliptic curves. Beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators Z 2 , F 2 , F 3 , L-tilde 3 can actually be interpreted as modular forms of the elliptic curve of the Ising model. A last order-4 globally nilpotent linear differential operator is not reducible to this elliptic curve, modular form scheme. This operator is shown to actually correspond to a natural generalization of this elliptic curve, modular form scheme, with the emergence of a Calabi-Yau equation, corresponding to a selected 4 F 3 hypergeometric function. This hypergeometric function can also be seen as a Hadamard product of the complete elliptic integral K, with a remarkably simple algebraic pull-back (square root extension), the corresponding Calabi-Yau fourth order differential operator having a symplectic differential Galois group SP(4,C). The mirror maps and higher order Schwarzian ODEs, associated with this Calabi-Yau ODE, present all the nice physical and mathematical ingredients we had with elliptic curves and modular forms, in particular an exact (isogenies) representation of the generators of the renormalization group, extending the modular group SL(2,Z) to a GL(2,Z) symmetry group.

Calabi-Yau structures on categories of matrix factorizations

Science.gov (United States)

Shklyarov, Dmytro

2017-09-01

Using tools of complex geometry, we construct explicit proper Calabi-Yau structures, that is, non-degenerate cyclic cocycles on differential graded categories of matrix factorizations of regular functions with isolated critical points. The formulas involve the Kapustin-Li trace and its higher corrections. From the physics perspective, our result yields explicit 'off-shell' models for categories of topological D-branes in B-twisted Landau-Ginzburg models.

6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces

Energy Technology Data Exchange (ETDEWEB)

Martini, Gabriella; Taylor, Washington [Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA 02139 (United States)

2015-06-10

We carry out a systematic study of a class of 6D F-theory models and associated Calabi-Yau threefolds that are constructed using base surfaces with a generalization of toric structure. In particular, we determine all smooth surfaces with a structure invariant under a single ℂ{sup ∗} action (sometimes called “T-varieties” in the mathematical literature) that can act as bases for an elliptic fibration with section of a Calabi-Yau threefold. We identify 162,404 distinct bases, which include as a subset the previously studied set of strictly toric bases. Calabi-Yau threefolds constructed in this fashion include examples with previously unknown Hodge numbers. There are also bases over which the generic elliptic fibration has a Mordell-Weil group of sections with nonzero rank, corresponding to non-Higgsable U(1) factors in the 6D supergravity model; this type of structure does not arise for generic elliptic fibrations in the purely toric context.

6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces

International Nuclear Information System (INIS)

Martini, Gabriella; Taylor, Washington

2015-01-01

We carry out a systematic study of a class of 6D F-theory models and associated Calabi-Yau threefolds that are constructed using base surfaces with a generalization of toric structure. In particular, we determine all smooth surfaces with a structure invariant under a single ℂ ∗ action (sometimes called “T-varieties” in the mathematical literature) that can act as bases for an elliptic fibration with section of a Calabi-Yau threefold. We identify 162,404 distinct bases, which include as a subset the previously studied set of strictly toric bases. Calabi-Yau threefolds constructed in this fashion include examples with previously unknown Hodge numbers. There are also bases over which the generic elliptic fibration has a Mordell-Weil group of sections with nonzero rank, corresponding to non-Higgsable U(1) factors in the 6D supergravity model; this type of structure does not arise for generic elliptic fibrations in the purely toric context.

Three-form periods on Calabi-Yau fourfolds: toric hypersurfaces and F-theory applications

Energy Technology Data Exchange (ETDEWEB)

Greiner, Sebastian; Grimm, Thomas W. [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University,Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 Munich (Germany)

2017-05-30

The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. This work introduces the mathematical machinery to derive the complete moduli dependence of the periods of non-trivial three-forms for fourfolds realized as hypersurfaces in toric ambient spaces. It sets the stage to determine Picard-Fuchs-type differential equations and integral expressions for these forms. The key tool is the observation that non-trivial three-forms on fourfold hypersurfaces in toric ambient spaces always stem from divisors that are build out of trees of toric surfaces fibered over Riemann surfaces. The three-form periods are then non-trivially related to the one-form periods of these Riemann surfaces. In general, the three-form periods are known to vary holomorphically over the complex structure moduli space and play an important role in the effective actions arising in fourfold compactifications. We discuss two explicit example fourfolds for F-theory compactifications in which the three-form periods determine axion decay constants.

The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications

Energy Technology Data Exchange (ETDEWEB)

Braun, A.P. [Department of Mathematics, King’s College,London WC2R 2LS (United Kingdom); Watari, T. [Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwano-ha 5-1-5, 277-8583 (Japan)

2015-01-12

The four-form field strength in F-theory compactifications on Calabi-Yau fourfolds takes its value in the middle cohomology group H{sup 4}. The middle cohomology is decomposed into a vertical, a horizontal and a remaining component, all three of which are present in general. We argue that a flux along the remaining or vertical component may break some symmetry, while a purely horizontal flux does not influence the unbroken part of the gauge group or the net chirality of charged matter fields. This makes the decomposition crucial to the counting of flux vacua in the context of F-theory GUTs. We use mirror symmetry to derive a combinatorial formula for the dimensions of these components applicable to any toric Calabi-Yau hypersurface, and also make a partial attempt at providing a geometric characterization of the four-cycles Poincaré dual to the remaining component of H{sup 4}. It is also found in general elliptic Calabi-Yau fourfolds supporting SU(5) gauge symmetry that a remaining component can be present, for example, in a form crucial to the symmetry breaking SU(5)⟶SU(3){sub C}×SU(2){sub L}×U(1){sub Y}. The dimension of the horizontal component is used to derive an estimate of the statistical distribution of the number of generations and the rank of 7-brane gauge groups in the landscape of F-theory flux vacua.

Algebraic Structure of tt * Equations for Calabi-Yau Sigma Models

Science.gov (United States)

Alim, Murad

2017-08-01

The tt * equations define a flat connection on the moduli spaces of {2d, \\mathcal{N}=2} quantum field theories. For conformal theories with c = 3 d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. We show that the non-holomorphic content of the tt * equations, restricted to the conformal directions, in the cases d = 1, 2, 3 is captured in terms of finitely many generators of special functions, which close under derivatives. The generators are understood as coordinates on a larger moduli space. This space parameterizes a freedom in choosing representatives of the chiral ring while preserving a constant topological metric. Geometrically, the freedom corresponds to a choice of forms on the target space respecting the Hodge filtration and having a constant pairing. Linear combinations of vector fields on that space are identified with the generators of a Lie algebra. This Lie algebra replaces the non-holomorphic derivatives of tt * and provides these with a finer and algebraic meaning. For sigma models into lattice polarized K3 manifolds, the differential ring of special functions on the moduli space is constructed, extending known structures for d = 1 and 3. The generators of the differential rings of special functions are given by quasi-modular forms for d = 1 and their generalizations in d = 2, 3. Some explicit examples are worked out including the case of the mirror of the quartic in {\\mathbbm{P}^3}, where due to further algebraic constraints, the differential ring coincides with quasi modular forms.

Type IIA on a compact Calabi-Yau and D=11 supergravity uplift of its orientifold

International Nuclear Information System (INIS)

Misra, A.

2004-01-01

Using the prescription of K. Hori and C. Vafa for defining period integrals in the Landau-Ginsburg theory for compact Calabi-Yau's, we obtain the Picard-Fuchs equation and the Meijer basis of solutions for the compact Calabi-Yau CY 3 (3,243) expressed as a degree-24 Fermat hypersurface after resolution of the orbifold singularities. The importance of the method lies in the ease with which one can consider the large and small complex structure limits, as well as the ability to get the ''ln''-terms in the periods without having to parametrically differentiate infinite series. We consider in detail the evaluation of the monodromy matrix in the large and small complex structure limits. We also consider the action of the freely acting antiholomorphic involution on D=11 supergravity compactified on CY 3 (3,243) x S 1 and obtain the Kaehler potential for the same in the limit of large volume of the Calabi-Yau. As a by-product, we also give a conjecture for the action of the orientation-reversing antiholomorphic involution on the periods, given its action on the cohomology, using a canonical (co)homology basis. Finally, we also consider showing a null superpotential on the orientifold of type IIA on CY 3 (3,243), having taken care of the orbifold singularities. (Abstract Copyright [2004], Wiley Periodicals, Inc.)

Heterotic Non-Kähler Geometries via Polystable Bundles on Calabi-Yau Threefolds

DEFF Research Database (Denmark)

Andreas, Bjorn; Garcia Fernandez, Mario

2012-01-01

In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi-Yau threefold X which satisfies c_2(X) = c_2(V ) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case...

Non-Kaehler attracting manifolds

International Nuclear Information System (INIS)

Dall'Agata, Gianguido

2006-01-01

We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski 'attractor points' for 3-form fluxes are special-hermitian manifolds

The Real Topological String on a local Calabi-Yau

CERN Document Server

Krefl, Daniel

2009-01-01

We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by the anti-holomorphic involution. This leads to a computation of open and unoriented Gromov-Witten invariants that can be applied to any toric Calabi-Yau with involution. We then show that the full topological string amplitudes can be reproduced within the topological vertex formalism. We obtain the real topological vertex with trivial fixed leg. Finally, we verify that the same results derive in the B-model from the extended holomorphic anomaly equation, together with appropriate boundary conditions. The expansion at the conifold exhibits a gap structure that belongs to a so far unidentified universality class.

Yukawa couplings between (2,1)-forms

International Nuclear Information System (INIS)

Candelas, P.

1988-01-01

The compactification of superstrings leads to an effective field theory for which the space-time manifold is the product of a four-dimensional Minkowski space with a six-dimensional Calabi-Yau space. The particles that are massless in the four-dimensional world correspond to differential forms of type (1,1) and of type (2,1) on the Calabi-Yau space. The Yukawa couplings between the families correspond to certain integrals involving three differential forms. For an important class of Calabi-Yau manifolds, which includes the cases for which the manifold may be realized as a complete intersection of polynomial equations in a projective space, the families correspond to (2,1)-forms. The relation between (2,1)-forms and the geometrical deformations of the Calabi-Yau space is explained and it is shown, for those cases for which the manifold may be realized as the complete intersection of polynomial equations in a single projective space or for many cases when the manifold may be realized as the transverse intersection of polynomial equations in a product of projective spaces, that the calculation of the Yukawa coupling reduces to a purely algebraic problem involving the defining polynomials. The generalization of this process is presented for a general Calabi-Yau manifold. (orig.)

Calabi-Yau compactifications of non-supersymmetric heterotic string theory

International Nuclear Information System (INIS)

Blaszczyk, Michael; Groot Nibbelink, Stefan

2015-07-01

Phenomenological explorations of heterotic strings have conventionally focused primarily on the E 8 x E 8 theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric SO(16) x SO(16) theory and the related supersymmetric E 8 x E 8 and SO(32) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the nonsupersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion-couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five branes in the SO(16) x SO(16) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.

A generalized construction of mirror manifolds

International Nuclear Information System (INIS)

Berglund, P.; Huebsch, T.

1993-01-01

We generalize the known method for explicit construction of mirror pairs of (2,2)-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known. (orig.)

Global embedding of fibre inflation models

Energy Technology Data Exchange (ETDEWEB)

Cicoli, Michele [Dipartimento di Fisica e Astronomia, Università di Bologna,via Irnerio 46, 40126 Bologna (Italy); INFN - Sezione di Bologna,viale Berti Pichat 6/2, 40127 Bologna (Italy); Abdus Salam ICTP,Strada Costiera 11, Trieste 34151 (Italy); Muia, Francesco [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Rd., Oxford OX1 3NP (United Kingdom); Shukla, Pramod [Abdus Salam ICTP,Strada Costiera 11, Trieste 34151 (Italy)

2016-11-30

We present concrete embeddings of fibre inflation models in globally consistent type IIB Calabi-Yau orientifolds with closed string moduli stabilisation. After performing a systematic search through the existing list of toric Calabi-Yau manifolds, we find several examples that reproduce the minimal setup to embed fibre inflation models. This involves Calabi-Yau manifolds with h{sup 1,1}=3 which are K3 fibrations over a ℙ{sup 1} base with an additional shrinkable rigid divisor. We then provide different consistent choices of the underlying brane set-up which generate a non-perturbative superpotential suitable for moduli stabilisation and string loop corrections with the correct form to drive inflation. For each Calabi-Yau orientifold setting, we also compute the effect of higher derivative contributions and study their influence on the inflationary dynamics.

Multiverse Space-Antispace Dual Calabi-Yau `Exciplex-Zitterbewegung' Particle Creation

Science.gov (United States)

Amoroso, Richard L.

Modeling the `creation/emergence' of matter from spacetime is as old as modern cosmology itself and not without controversy within each model such as Static, Steady-state, Big Bang or Multiverse Continuous-State. In this paper we present only a brief primitive introduction to a new form of `Exciplex-Zitterbewegung' dual space-antispace vacuum Particle Creation applicable especially to Big Bang alternatives which are well-known but ignored; Hubble discovered `Redshift' not a Doppler expansion of the universe which remains the currently popular interpretation. Holographic Anthropic Multiverse cosmology provides viable alternatives to all seemingly sacrosanct pillars of the Big Bang. A model for Multiverse Space-Antispace Dual Calabi-Yau `Exciplex-Zitterbewegung' particle creation has only become possible by incorporating the additional degrees of freedom provided by the capacity complex dimensional extended Yang-Mills Kaluza-Klein correspondence provides.

Special Lagrangian torus fibrations of complete intersection Calabi–Yau manifolds: A geometric conjecture

Energy Technology Data Exchange (ETDEWEB)

Morrison, David R., E-mail: drm@physics.ucsb.edu [Departments of Mathematics and Physics, U.C. Santa Barbara, Santa Barbara, CA 93106 (United States); Ronen Plesser, M. [Center for Geometry and Theoretical Physics, Duke University, Durham NC 27708 (United States)

2015-09-15

For complete intersection Calabi–Yau manifolds in toric varieties, Gross and Haase–Zharkov have given a conjectural combinatorial description of the special Lagrangian torus fibrations whose existence was predicted by Strominger, Yau and Zaslow. We present a geometric version of this construction, generalizing an earlier conjecture of the first author.

Compactifications of heterotic strings on non-Kaehler complex manifolds II

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; Dasgupta, Keshav; Green, Paul S.; Sharpe, Eric

2004-01-01

We continue our study of heterotic compactifications on non-Kaehler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and possible supergravity description for a generic non-Kaehler complex manifold using the newly proposed superpotential. The manifolds studied in our earlier papers had zero Euler characteristics. We construct new examples of non-Kaehler complex manifolds with torsion in lower dimensions, that have nonzero Euler characteristics. Some of these examples are constructed from consistent backgrounds in F-theory and therefore are solutions to the string equations of motion. We discuss consistency conditions for compactifications of the heterotic string on smooth non-Kaehler manifolds and illustrate how some results well known for Calabi-Yau compactifications, including counting the number of generations, apply to the non-Kaehler case. We briefly address various issues regarding possible phenomenological applications

Classification of stationary compact homogeneous special pseudo K\\"ahler manifolds of semisimple groups

OpenAIRE

Alekseevsky, D. V.; Cortes, V.

1997-01-01

The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K\\"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K\\"ahler manifolds correspond to certain (abstract) variations of Hodge structure which generalize the above example. We give the classification of homogeneous special pseudo K\\"ahler manifolds of semisimple groups with compact stabilizer.

Non-perturbative effects and the refined topological string

Energy Technology Data Exchange (ETDEWEB)

Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematiques; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

2013-06-15

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P{sup 1} x P{sup 1}, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

Tops as building blocks for G 2 manifolds

Science.gov (United States)

Braun, Andreas P.

2017-10-01

A large number of examples of compact G 2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two building blocks times a circle. These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.

Systematics of axion inflation in Calabi-Yau hypersurfaces

Energy Technology Data Exchange (ETDEWEB)

Long, Cody; McAllister, Liam; Stout, John [Department of Physics, Cornell University,Ithaca, NY 14853 (United States)

2017-02-03

We initiate a comprehensive survey of axion inflation in compactifications of type IIB string theory on Calabi-Yau hypersurfaces in toric varieties. For every threefold with h{sup 1,1}≤4 in the Kreuzer-Skarke database, we compute the metric on Kähler moduli space, as well as the matrix of four-form axion charges of Euclidean D3-branes on rigid divisors. These charges encode the possibility of enlarging the field range via alignment. We then determine an upper bound on the inflationary field range Δϕ that results from the leading instanton potential, in the absence of monodromy. The bound on the field range in this ensemble is Δϕ≲0.3M{sub pl}, in a compactification where the smallest curve volume is (2π){sup 2}α{sup ′}, and we argue that the sigma model expansion is adequately controlled. The largest increase resulting from alignment is a factor ≈2.6. We also examine a set of threefolds with h{sup 1,1} up to 100 and characterize their axion charge matrices. While we find modest alignment in this ensemble, the maximum field range is ultimately suppressed by the volume of the internal space, which typically grows quickly with h{sup 1,1}. Furthermore, we find that many toric divisors are rigid — and the corresponding charge matrices are relatively trivial — at large h{sup 1,1}. It is therefore challenging to realize alignment via superpotentials generated only by Euclidean D3-branes, without taking into account the effects of flux, D7-branes, and orientifolding.

Multiple fibrations in Calabi-Yau geometry and string dualities

Energy Technology Data Exchange (ETDEWEB)

Anderson, Lara B.; Gao, Xin; Gray, James; Lee, Seung-Joo [Physics Department, Virginia Tech,Robeson Hall, Blacksburg, VA 24061 (United States)

2016-10-19

In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA, and heterotic string theories. Our results include many M-/F-theory correspondences in which distinct F-theory vacua — associated to different elliptic fibrations of the same CY n-fold — give rise to the same M-theory limit in one dimension lower. Examples include 5-dimensional correspondences between 6-dimensional theories with Abelian, non-Abelian and superconformal structure, as well as examples of higher rank Mordell-Weil geometries. In addition, in the context of heterotic/F-theory duality, we investigate the role played by multiple K3- and elliptic fibrations in known and novel string dualities in 8-, 6- and 4-dimensional theories. Here we systematically summarize nested fibration structures and comment on the roles they play in T-duality, mirror symmetry, and 4-dimensional compactifications of F-theory with G-flux. This investigation of duality structures is made possible by geometric tools developed in a companion paper http://arxiv.org/abs/1608.07554.

Topological Strings and Integrable Hierarchies

CERN Document Server

Aganagic, M; Klemm, A D; Marino, M; Vafa, C; Aganagic, Mina; Dijkgraaf, Robbert; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

2006-01-01

We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue that topological strings on Calabi-Yau geometries provide a unifying picture connecting non-critical (super)strings, integrable hierarchies, and various matrix models. In particular we show how the ordinary matrix model, the double scaling limit of matrix models, and Kontsevich-like matrix model are all related and arise from studying branes in specific local Calabi-Yau three-folds. We also show how A-model topological string on P^1 and local toric threefolds (and in particular the topological vertex) can be realized and solved as B-model topological string amplitudes on a Calabi-Yau manifold.

T4 fibrations over Calabi–Yau two-folds and non-Kähler manifolds in string theory

Directory of Open Access Journals (Sweden)

Hai Lin

2016-08-01

Full Text Available We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial T4 fibrations over Calabi–Yau two-folds. These give rise to eight-dimensional non-Kähler Hermitian manifolds with SU(4 structure. The eight-manifold is also a circle fibration over a seven-dimensional G2 manifold with skew torsion. The eight-manifolds of this type appear as internal manifolds with SU(4 structure in type IIB string theory with F3 and F7 fluxes. These manifolds have generalized calibrated cycles in the presence of fluxes.

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

Science.gov (United States)

Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten

2018-01-01

We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

Mirror symmetry in the presence of branes

Energy Technology Data Exchange (ETDEWEB)

Mertens, Adrian

2011-10-11

This work deals with mirror symmetry for N=1 compactifications on compact Calabi-Yau threefolds with branes. The mayor tool is a combined deformation space for the Calabi-Yau and a hypersurface within it. Periods of this deformation space contain information about B-type branes within the hypersurface in addition to the usual closed string data. To study these periods we generalize techniques used in closed string mirror symmetry. We derive the Picard-Fuchs system and encode the information in extended toric polytopes. Solutions of the Picard-Fuchs equations give superpotentials for certain brane configurations. This is an efficient way to calculate superpotentials. The deformations we consider are massive for all branes with non trivial superpotential. Depending on a choice of a family of hypersurfaces, the superpotential of the effective low energy theory depends on different massive fields. A priori there is no reason for these fields to be lighter then other fields that are not included. We find however examples where the superpotential is nearly at. In these examples we use the Gauss-Manin connection on the combined deformation space to define an open string mirror map. We find instanton generated superpotentials of A-type branes. This gives predictions for Ooguri-Vafa invariants counting holomorphic disks that end on a Lagrangian brane on the Quintic. A second class of examples does not have preferred nearly massless deformations and different families of hypersurfaces can be used to calculate the same on-shell superpotential. We calculate examples of superpotentials for branes in Calabi-Yau manifolds with several moduli. The on-shell superpotentials are mapped to the mirror A-model to study the instanton expansion and to obtain predictions for disk invariants. The combined deformation spaces are equivalent to the quantum corrected Kaehler deformation spaces of certain non compact Calabi-Yau fourfolds. These fourfolds are fibrations of Calabi-Yau threefolds

Mirror symmetry in the presence of branes

International Nuclear Information System (INIS)

Mertens, Adrian

2011-01-01

This work deals with mirror symmetry for N=1 compactifications on compact Calabi-Yau threefolds with branes. The mayor tool is a combined deformation space for the Calabi-Yau and a hypersurface within it. Periods of this deformation space contain information about B-type branes within the hypersurface in addition to the usual closed string data. To study these periods we generalize techniques used in closed string mirror symmetry. We derive the Picard-Fuchs system and encode the information in extended toric polytopes. Solutions of the Picard-Fuchs equations give superpotentials for certain brane configurations. This is an efficient way to calculate superpotentials. The deformations we consider are massive for all branes with non trivial superpotential. Depending on a choice of a family of hypersurfaces, the superpotential of the effective low energy theory depends on different massive fields. A priori there is no reason for these fields to be lighter then other fields that are not included. We find however examples where the superpotential is nearly at. In these examples we use the Gauss-Manin connection on the combined deformation space to define an open string mirror map. We find instanton generated superpotentials of A-type branes. This gives predictions for Ooguri-Vafa invariants counting holomorphic disks that end on a Lagrangian brane on the Quintic. A second class of examples does not have preferred nearly massless deformations and different families of hypersurfaces can be used to calculate the same on-shell superpotential. We calculate examples of superpotentials for branes in Calabi-Yau manifolds with several moduli. The on-shell superpotentials are mapped to the mirror A-model to study the instanton expansion and to obtain predictions for disk invariants. The combined deformation spaces are equivalent to the quantum corrected Kaehler deformation spaces of certain non compact Calabi-Yau fourfolds. These fourfolds are fibrations of Calabi-Yau threefolds

GUTs in type IIB orientifold compactifications

International Nuclear Information System (INIS)

Blumenhagen, Ralph; Braun, Volker; Grimm, Thomas W.; Weigand, Timo

2009-01-01

We systematically analyse globally consistent SU(5) GUT models on intersecting D7-branes in genuine Calabi-Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realisation of SU(5) GUTs with gauge symmetry breaking via U(1) Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P 1,1,1,6,9 [18] and of the Quintic P 1,1,1,1,1 [5], respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of these geometries and present five globally consistent string GUT models in detail, including a 3-generation SU(5) model with no exotics whatsoever. We also realise other phenomenological features such as the 10105 H Yukawa coupling and comment on the possibility of moduli stabilisation, where we find an entire new set of so-called swiss-cheese type Calabi-Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi-Yau fourfolds.

GUTs on Compact Type IIB Orientifolds

Energy Technology Data Exchange (ETDEWEB)

Blumenhagen, Ralph; /Munich, Max Planck Inst.; Braun, Volker; /Dublin Inst.; Grimm, Thomas W.; /Bonn U.; Weigand, Timo; /SLAC

2008-12-01

We systematically analyze globally consistent SU(5) GUT models on intersecting D7-branes in genuine Calabi-Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realization of SU(5) GUTs with gauge symmetry breaking via U(1)Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P{sub 1,1,1,6,9}[18] and of the Quintic P{sub 1,1,1,1,1}[5], respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of these geometries and present five globally consistent string GUT models in detail, including a 3-generation SU(5) model with no exotics whatsoever. We also realize other phenomenological features such as the 10 10 5{sub H} Yukawa coupling and comment on the possibility of moduli stabilization, where we find an entire new set of so-called swiss-cheese type Calabi-Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi-Yau fourfolds.

K-theory and phase transitions at high energies

Directory of Open Access Journals (Sweden)

T. V. Obikhod

2016-06-01

Full Text Available The duality between E8xE8 heteritic string on manifold K3xT2 and Type IIA string compactified on a Calabi-Yau manifold induces a correspondence between vector bundles on K3xT2 and Calabi-Yau manifolds. Vector bundles over compact base space K3xT2 form the set of isomorphism classes, which is a semi-ring under the operation of Whitney sum and tensor product. The construction of semi-ring V ect X of isomorphism classes of complex vector bundles over X leads to the ring KX = K(V ect X, called Grothendieck group. As K3 has no isometries and no non-trivial one-cycles, so vector bundle winding modes arise from the T2 compactification. Since we have focused on supergravity in d = 11, there exist solutions in d = 10 for which space-time is Minkowski space and extra dimensions are K3xT2. The complete set of soliton solutions of supergravity theory is characterized by RR charges, identified by K-theory. Toric presentation of Calabi-Yau through Batyrev's toric approximation enables us to connect transitions between Calabi-Yau manifolds, classified by enhanced symmetry group, with K-theory classification.

Higher derivatives in Type II and M-theory on Calabi-Yau threefolds

Science.gov (United States)

Grimm, Thomas W.; Mayer, Kilian; Weissenbacher, Matthias

2018-02-01

The four- and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten- and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kähler structure of the compact space and the form-field back-ground are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten- and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kähler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kähler modulus case is presented for both Type II theories and M-theory.

Mirror symmetry for G{sub 2}-manifolds: twisted connected sums and dual tops

Energy Technology Data Exchange (ETDEWEB)

Braun, Andreas P. [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Zotto, Michele Del [Simons Center for Geometry and Physics, State University of New York at Stony Brook,Stony Brook, NY, 11794-3636 (United States)

2017-05-15

Recently, at least 50 million of novel examples of compact G{sub 2} holonomy manifolds have been constructed as twisted connected sums of asymptotically cylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror symmetry for compactifications of Type II superstrings in this context. We focus on G{sub 2} manifolds obtained from building blocks constructed from dual pairs of tops, which are the closest to toric CY hypersurfaces, and formulate the analogue of the Batyrev mirror map for this class of G{sub 2} holonomy manifolds, thus obtaining several millions of novel dual superstring backgrounds. In particular, this leads us to conjecture a plethora of novel exact dualities among the corresponding 2d N=1 sigma models.

Complex Structure of the Four-Dimensional Kerr Geometry: Stringy System, Kerr Theorem, and Calabi-Yau Twofold

Directory of Open Access Journals (Sweden)

Alexander Burinskii

2013-01-01

Full Text Available The 4D Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Newman. Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the structure of M-theory. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the critical N = 2 superstring.

Five-brane superpotentials and heterotic/F-theory duality

International Nuclear Information System (INIS)

Grimm, Thomas W.; Ha, Tae-Won; Klemm, Albrecht; Klevers, Denis

2010-01-01

Under heterotic/F-theory duality it was argued that a wide class of heterotic five-branes is mapped into the geometry of an F-theory compactification manifold. In four-dimensional compactifications this identifies a five-brane wrapped on a curve in the base of an elliptically fibered Calabi-Yau threefold with a specific F-theory Calabi-Yau fourfold containing the blow-up of the five-brane curve. We argue that this duality can be reformulated by first constructing a non-Calabi-Yau heterotic threefold by blowing up the curve of the five-brane into a divisor with five-brane flux. Employing heterotic/F-theory duality this leads us to the construction of a Calabi-Yau fourfold and four-form flux. Moreover, we obtain an explicit map between the five-brane superpotential and an F-theory flux superpotential. The map of the open-closed deformation problem of a five-brane in a compact Calabi-Yau threefold into a deformation problem of complex structures on a dual Calabi-Yau fourfold with four-form flux provides a powerful tool to explicitly compute the five-brane superpotential.

Mathematical Sciences Research Institute Workshop

CERN Document Server

Mirror Symmetry I

1998-01-01

This volume is an updated edition of ""Essays on Mirror Manifolds"", the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here. Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hubsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and $N=2$ supergravity. Rocek proposed possible mirrors for Calabi-Yau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics.

Supersymmetric gauge theories from string theory

International Nuclear Information System (INIS)

Metzger, St.

2005-12-01

This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G 2 -manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G 2 -manifold is known. Here we construct families of metrics on compact weak G 2 -manifolds, which contain two conical singularities. Weak G 2 -manifolds have properties that are similar to the ones of proper G 2 -manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E 8 x E 8 -heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the classical action. (author)

Moduli Potentials in Type IIA Compactifications with RR and NS Flux

Energy Technology Data Exchange (ETDEWEB)

Kachru, S.

2004-12-01

We describe a simple class of type IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the Kaehler moduli. This class of models corresponds to gauged {Nu} = 2 supergravities, and the potential is completely determined by a choice of gauging and by data of the {Nu} = 2 Calabi-Yau model--the prepotential for vector multiplets and the quaternionic metric on the hypermultiplet moduli space. Using mirror symmetry, one can determine many (though not all) of the quantum corrections which are relevant in these models.

Sasaki-Einstein Manifolds and Volume Minimisation

CERN Document Server

Martelli, D; Yau, S T; Martelli, Dario; Sparks, James; Yau, Shing-Tung

2006-01-01

We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi-Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat-Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theo...

Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string

Energy Technology Data Exchange (ETDEWEB)

Sun, Kaiwen [Department of Mathematics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China); Wang, Xin; Huang, Min-xin [Interdisciplinary Center for Theoretical Study,Department of Modern Physics, University of Science and Technology of China,96 Jinzhai Road, Hefei, Anhui 230026 (China)

2017-01-16

We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mariño conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g, the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant ℏ and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and topological string, another quantization scheme was proposed by Grassi-Hatsuda-Mariño, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. The equivalence for mirror curves of genus one has been verified for some local del Pezzo surfaces. In this paper, we generalize the correspondence to higher genus, and analyze in detail the resolved ℂ{sup 3}/ℤ{sub 5} orbifold and several SU(N) geometries. We also give a proof for some models at ℏ=2π/k.

Elliptically fibered Calabi–Yau manifolds and the ring of Jacobi forms

Directory of Open Access Journals (Sweden)

Min-xin Huang

2015-09-01

Full Text Available We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi–Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows quadratically with the base degree. The denominators of these forms have a simple universal form with the property that the poles of the meromorphic form lie only at torsion points. The modular parameter corresponds to the fibre class while the role of the string coupling is played by the elliptic parameter. This leads to very strong all genus results on these geometries, which are checked against results from curve counting.

Heterotic and type II orientifold compactifications on SU(3) structure manifolds

International Nuclear Information System (INIS)

Benmachiche, I.

2006-07-01

We study the four-dimensional N=1 effective theories of generic SU(3) structure compactifications in the presence of background fluxes. For heterotic and type IIA/B orientifold theories, the N=1 characteristic data are determined by a Kaluza-Klein reduction of the fermionic actions. The Kaehler potentials, superpotentials and the D-terms are entirely encoded by geometrical data of the internal manifold. The background flux and the intrinsic torsion of the SU(3) structure manifold, gives rise to contributions to the four-dimensional F-terms. The corresponding superpotentials generalize the Gukov-Vafa-Witten superpotential. For the heterotic compactification, the four-dimensional fermionic supersymmetry variations, as well as the conditions on supersymmetric vacua, are determined. The Yukawa couplings of the theory turn out to be similar to their Calabi-Yau counterparts. (Orig.)

Relating double field theory to the scalar potential of N=2 gauged supergravity

Energy Technology Data Exchange (ETDEWEB)

Blumenhagen, Ralph [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, München, 80805 (Germany); Font, Anamaria [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, München, 80805 (Germany); Arnold Sommerfeld Center for Theoretical Physics, LMU,Theresienstr. 37, München, 80333 (Germany); Plauschinn, Erik [Arnold Sommerfeld Center for Theoretical Physics, LMU,Theresienstr. 37, München, 80333 (Germany)

2015-12-18

The double field theory action in the flux formulation is dimensionally reduced on a Calabi-Yau three-fold equipped with non-vanishing type IIB geometric and non-geometric fluxes. First, we rewrite the metric-dependent reduced DFT action in terms of quantities that can be evaluated without explicitly knowing the metric on the Calabi-Yau manifold. Second, using properties of special geometry we obtain the scalar potential of N=2 gauged supergravity. After an orientifold projection, this potential is consistent with the scalar potential arising from the flux-induced superpotential, plus an additional D-term contribution.

Matrix model as a mirror of Chern-Simons theory

International Nuclear Information System (INIS)

Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

2004-01-01

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators. (author)

Hyperconifold transitions, mirror symmetry, and string theory

Science.gov (United States)

Davies, Rhys

2011-09-01

Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli space) is an isolated singularity which is a finite cyclic quotient of the conifold; these were called hyperconifolds. It was also shown that if the order of the quotient group is even, such singular varieties have projective crepant resolutions, which are therefore smooth Calabi-Yau manifolds. The resulting topological transitions were called hyperconifold transitions, and change the fundamental group as well as the Hodge numbers. Here Batyrev's construction of Calabi-Yau hypersurfaces in toric fourfolds is used to demonstrate that certain compact examples containing the remaining hyperconifolds — the Z and Z cases — also have Calabi-Yau resolutions. The mirrors of the resulting transitions are studied and it is found, surprisingly, that they are ordinary conifold transitions. These are the first examples of conifold transitions with mirrors which are more exotic extremal transitions. The new hyperconifold transitions are also used to construct a small number of new Calabi-Yau manifolds, with small Hodge numbers and fundamental group Z or Z. Finally, it is demonstrated that a hyperconifold is a physically sensible background in Type IIB string theory. In analogy to the conifold case, non-perturbative dynamics smooth the physical moduli space, such that hyperconifold transitions correspond to non-singular processes in the full theory.

Hyperconifold transitions, mirror symmetry, and string theory

International Nuclear Information System (INIS)

Davies, Rhys

2011-01-01

Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli space) is an isolated singularity which is a finite cyclic quotient of the conifold; these were called hyperconifolds. It was also shown that if the order of the quotient group is even, such singular varieties have projective crepant resolutions, which are therefore smooth Calabi-Yau manifolds. The resulting topological transitions were called hyperconifold transitions, and change the fundamental group as well as the Hodge numbers. Here Batyrev's construction of Calabi-Yau hypersurfaces in toric fourfolds is used to demonstrate that certain compact examples containing the remaining hyperconifolds - the Z 3 and Z 5 cases - also have Calabi-Yau resolutions. The mirrors of the resulting transitions are studied and it is found, surprisingly, that they are ordinary conifold transitions. These are the first examples of conifold transitions with mirrors which are more exotic extremal transitions. The new hyperconifold transitions are also used to construct a small number of new Calabi-Yau manifolds, with small Hodge numbers and fundamental group Z 3 or Z 5 . Finally, it is demonstrated that a hyperconifold is a physically sensible background in Type IIB string theory. In analogy to the conifold case, non-perturbative dynamics smooth the physical moduli space, such that hyperconifold transitions correspond to non-singular processes in the full theory.

F-theory and the landscape of intersecting D7-branes

Energy Technology Data Exchange (ETDEWEB)

Braun, Andreas

2010-02-05

In this work, the moduli of D7-branes in type IIB orientifold compactifications and their stabilization by fluxes is studied from the perspective of F-theory. In F-theory, the moduli of the D7-branes and the moduli of the orientifold are unified in the moduli space of an elliptic Calabi-Yau manifold. This makes it possible to study flux the stabilization of D7-branes in an elegant manner. To answer phenomenological questions, one has to translate the deformations of the elliptic Calabi-Yau manifold of F-theory back to the positions and the shape of the D7-branes. We address this problem by constructing the homology cycles that are relevant for the deformations of the elliptic Calabi-Yau manifold.We show the viability of our approach for the case of elliptic two- and three-folds. Furthermore, we discuss a consistency conditions related to the intersections between D7-branes and orientifold planes which is automatically fulfilled in F-theory. Finally, we use our results to study the flux stabilization of D7-branes on the orientifold K3 x T{sup 2}/Z{sub 2} using F-theory on K3 x K3. In this context, we derive conditions on the fluxes to stabilize a given configuration of D7-branes. (orig.)

F-theory and the landscape of intersecting D7-branes

International Nuclear Information System (INIS)

Braun, Andreas

2010-01-01

In this work, the moduli of D7-branes in type IIB orientifold compactifications and their stabilization by fluxes is studied from the perspective of F-theory. In F-theory, the moduli of the D7-branes and the moduli of the orientifold are unified in the moduli space of an elliptic Calabi-Yau manifold. This makes it possible to study flux the stabilization of D7-branes in an elegant manner. To answer phenomenological questions, one has to translate the deformations of the elliptic Calabi-Yau manifold of F-theory back to the positions and the shape of the D7-branes. We address this problem by constructing the homology cycles that are relevant for the deformations of the elliptic Calabi-Yau manifold.We show the viability of our approach for the case of elliptic two- and three-folds. Furthermore, we discuss a consistency conditions related to the intersections between D7-branes and orientifold planes which is automatically fulfilled in F-theory. Finally, we use our results to study the flux stabilization of D7-branes on the orientifold K3 x T 2 /Z 2 using F-theory on K3 x K3. In this context, we derive conditions on the fluxes to stabilize a given configuration of D7-branes. (orig.)

Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

Science.gov (United States)

Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

2018-03-01

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

Supersymmetric gauge theories from string theory; Theorie de jauge supersymetrique de la theorie des cordes

Energy Technology Data Exchange (ETDEWEB)

Metzger, St

2005-12-15

This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G{sub 2}-manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G{sub 2}-manifold is known. Here we construct families of metrics on compact weak G{sub 2}-manifolds, which contain two conical singularities. Weak G{sub 2}-manifolds have properties that are similar to the ones of proper G{sub 2}-manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E{sub 8} x E{sub 8}-heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the

Heterotic String/F-theory Duality from Mirror Symmetry

CERN Document Server

Berglund, Per

1998-01-01

We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds $X_{n+1}$ to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of these data as valid classical solutions of the heterotic string compactified on Z_n proves F-theory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n+1-fold $X_{n+1}$ a toric n fold Z_n together with a specific family of sheafs on it. This allows for a systematic construction of phenomenologically interesting d=4 N=1 heterotic vacua, e.g. on deformations of the tangent bundle, with grand unified and SU(3)\\times SU(2) gauge groups. As another application we find non-perturbative gauge enhancements of the heterotic string on singular Calabi-Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds.

Geometry of mirror manifolds

International Nuclear Information System (INIS)

Aspinwall, P.S.; Luetken, C.A.

1991-01-01

We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kaehler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifolds are fixed, but the intersection numbes are highly ambiguous, presumably reflected a rich structure of multicritical points in the moduli space of the field theory. (orig.)

Hyperconifold transitions, mirror symmetry, and string theory

Energy Technology Data Exchange (ETDEWEB)

Davies, Rhys, E-mail: daviesr@maths.ox.ac.uk [Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB (United Kingdom)

2011-09-01

Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli space) is an isolated singularity which is a finite cyclic quotient of the conifold; these were called hyperconifolds. It was also shown that if the order of the quotient group is even, such singular varieties have projective crepant resolutions, which are therefore smooth Calabi-Yau manifolds. The resulting topological transitions were called hyperconifold transitions, and change the fundamental group as well as the Hodge numbers. Here Batyrev's construction of Calabi-Yau hypersurfaces in toric fourfolds is used to demonstrate that certain compact examples containing the remaining hyperconifolds - the Z{sub 3} and Z{sub 5} cases - also have Calabi-Yau resolutions. The mirrors of the resulting transitions are studied and it is found, surprisingly, that they are ordinary conifold transitions. These are the first examples of conifold transitions with mirrors which are more exotic extremal transitions. The new hyperconifold transitions are also used to construct a small number of new Calabi-Yau manifolds, with small Hodge numbers and fundamental group Z{sub 3} or Z{sub 5}. Finally, it is demonstrated that a hyperconifold is a physically sensible background in Type IIB string theory. In analogy to the conifold case, non-perturbative dynamics smooth the physical moduli space, such that hyperconifold transitions correspond to non-singular processes in the full theory.

Blown-up orbifolds

International Nuclear Information System (INIS)

Cvetic, M.

1987-05-01

A method to repair - ''blow-up'' - the singularities of the Abelian (2,2) orbifolds to obtain the corresponding (2,2) Calabi-Yau manifolds is presented. This approach makes use of the fact that with each orbifold singularity there are associated massless scalar fields - blowing-up modes - whose potential is flat to all orders in the string perturbation theory. The zero vacuum expectation values (VEV's) of the blowing-up modes correspond to the orbifold limit, while nonzero VEV's yield the corresponding Calabi-Yau manifold. One can then calculate explicitly, for such Calabi-Yau manifolds, the mass spectrum, Yukawa couplings, and all the other parameters of the effective Lagrangian by inserting successively all the background blowing-up modes with nonzero vacuum expectation value into the corresponding orbifold amplitudes. The results are exact at the string tree-level; however, they are perturbative in the blowing-up procedure. Mass spectra and Yukawa couplings for the blown-up Z 3 and Z 4 orbifolds are explicitly calculated. In particular all the E 6 singlets except the ones associated with the moduli-space of the blown-up orbifolds receive the mass; while the 27's and anti 27's do not pair up

F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches

CERN Document Server

Klevers, Denis; Oehlmann, Paul-Konstantin; Piragua, Hernan; Reuter, Jonas

2015-01-01

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in P^2, P^1x P^1 and the recently studied ...

Geometrically induced metastability and holography

Energy Technology Data Exchange (ETDEWEB)

Aganagic, Mina; Aganagic, Mina; Beem, Christopher; Seo, Jihye; Vafa, Cumrun

2006-10-23

We construct metastable configurations of branes and anti-branes wrapping 2-spheres inside local Calabi-Yau manifolds and study their large N duals. These duals are Calabi-Yau manifolds in which the wrapped 2-spheres have been replaced by 3-spheres with flux through them, and supersymmetry is spontaneously broken. The geometry of the non-supersymmetric vacuum is exactly calculable to all orders of the't Hooft parameter, and to the leading order in 1/N. The computation utilizes the same matrix model techniques that were used in the supersymmetric context. This provides a novel mechanism for breaking supersymmetry in the context of flux compactifications.

Quivers, YBE and 3-manifolds

Science.gov (United States)

Yamazaki, Masahito

2012-05-01

We study 4d superconformal indices for a large class of {N} = 1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T 2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T 2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in {{H}^3} , each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph. The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results [1].

K3-fibered Calabi-Yau threefolds II, singular fibers

OpenAIRE

Hunt, Bruce

1999-01-01

In part I of this paper we constructed certain fibered Calabi-Yaus by a quotient construction in the context of weighted hypersurfaces. In this paper look at the case of K3 fibrations more closely and study the singular fibers which occur. This differs from previous work since the fibrations we discuss have constant modulus, and the singular fibers have torsion monodromy.

Supersymmetry breaking and α'-corrections to flux induced potentials

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; Haack, Michael; Louis, Jan

2002-01-01

We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant.We show that in the context of type-IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources α'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that α'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications. (author)

Vertex algebras and mirror symmetry

International Nuclear Information System (INIS)

Borisov, L.A.

2001-01-01

Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)

Bipartite field theories: from D-brane probes to scattering amplitudes

Science.gov (United States)

Franco, Sebastián

2012-11-01

We introduce and initiate the investigation of a general class of 4d, {N}=1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories (BFTs). BFTs underlie a wide spectrum of interesting physical systems, including: D3-branes probing toric Calabi-Yau 3-folds, their mirror configurations of D6-branes, cluster integrable systems in (0 + 1) dimensions and leading singularities in scattering amplitudes for {N}=4 SYM. While our discussion is fully general, we focus on models that are relevant for scattering amplitudes. We investigate the BFT perspective on graph modifications, the emergence of Calabi-Yau manifolds (which arise as the master and moduli spaces of BFTs), the translation between square moves in the graph and Seiberg duality and the identification of dual theories by means of the underlying Calabi-Yaus, the phenomenon of loop reduction and the interpretation of the boundary operator for cells in the positive Grassmannian as higgsing in the BFT. We develop a technique based on generalized Kasteleyn matrices that permits an efficient determination of the Calabi-Yau geometries associated to arbitrary graphs. Our techniques allow us to go beyond the planar limit by both increasing the number of boundaries of the graphs and the genus of the underlying Riemann surface. Our investigation suggests a central role for Calabi-Yau manifolds in the context of leading singularities, whose full scope is yet to be uncovered.

Global embeddings for branes at toric singularities

CERN Document Server

Balasubramanian, Vijay; Braun, Volker; García-Etxebarria, Iñaki

2012-01-01

We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.

F-theory on all toric hypersurface fibrations and its Higgs branches

Energy Technology Data Exchange (ETDEWEB)

Klevers, Denis [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104-6396 (United States); Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland); Peña, Damián Kaloni Mayorga; Oehlmann, Paul-Konstantin [Bethe Center for Theoretical Physics, Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany); Piragua, Hernan [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104-6396 (United States); Reuter, Jonas [Bethe Center for Theoretical Physics, Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany)

2015-01-27

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in ℙ{sup 2}, ℙ{sup 1}×ℙ{sup 1} and the recently studied ℙ{sup 2}(1,1,2), yield F-theory realizations of SUGRA theories with discrete gauge groups ℤ{sub 3}, ℤ{sub 2} and ℤ{sub 4}. This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I{sub 2}-fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. We also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP{sub 1} has a U(1)-gauge field induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q=3.

Calabi-Yau varieties: arithmetic, geometry and physics lecture notes on concentrated graduate courses

CERN Document Server

Schütt, Matthias; Yui, Noriko

2015-01-01

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Generalized N=1 orientifold compactifications and the Hitchin functionals

International Nuclear Information System (INIS)

Benmachiche, Iman; Grimm, Thomas W.

2006-01-01

The four-dimensional N=1 supergravity theories arising in compactifications of type IIA and type IIB on generalized orientifold backgrounds with background fluxes are discussed. The Kahler potentials are derived for reductions on SU(3) structure orientifolds and shown to consist of the logarithm of the two Hitchin functionals. These are functions of even and odd forms parameterizing the geometry of the internal manifold, the B-field and the dilaton. The superpotentials induced by background fluxes and the non-Calabi-Yau geometry are determined by a reduction of the type IIA and type IIB fermionic actions on SU(3) and generalized SU(3)xSU(3) manifolds. Mirror spaces of Calabi-Yau orientifolds with electric and part of the magnetic NS-NS fluxes are conjectured to be certain SU(3)xSU(3) structure manifolds. Evidence for this identification is provided by comparing the generalized type IIA and type IIB superpotentials

A stringy origin of M2 brane Chern-Simons theories

International Nuclear Information System (INIS)

Aganagic, Mina

2010-01-01

We show that string duality relates M-theory on a local Calabi-Yau fourfold singularity X 4 to type IIA string theory on a Calabi-Yau threefold X 3 fibered over a real line, with RR 2-form fluxes turned on. The RR flux encodes how the M-theory circle is fibered over the IIA geometry. The theories on N D2 branes probing X 3 are the well-known quiver theories with N=2 supersymmetry in three dimensions. We show that turning on fluxes, and fibering the X 3 over a direction transverse to the branes, corresponds to turning on N=2 Chern-Simons couplings. String duality implies that, in the strong coupling limit, the N D2 branes on X 3 in this background become N M2 branes on X 4 . This provides a string theory derivation for the recently conjectured description of the M2 brane theories on Calabi-Yau fourfolds in terms of N=2 quiver Chern-Simons theories. We also provide a new N=2 Chern-Simons theory dual to AdS 4 xQ 1,1,1 . Type IIA/M-theory duality also relates IIA string theory on X 3 with only the RR fluxes turned on, to M-theory on a G 2 holonomy manifold. We show that this implies that the N M2 branes probing the G 2 manifold are described by the quiver Chern-Simons theory originating from the D2 branes probing X 3 , except that now Chern-Simons terms preserve only N=1 supersymmetry in three dimensions.

A large class of new gravitational and axionic backgrounds for four-dimensional superstrings

CERN Document Server

Kiritsis, Elias B; Lüst, Dieter

1994-01-01

A large class of new 4-D superstring vacua with non-trivial/singular geometries, spacetime supersymmetry and other background fields (axion, dilaton) are found. Killing symmetries are generic and are associated with non-trivial dilaton and antisymmetric tensor fields. Duality symmetries preserving N=2 superconformal invariance are employed to generate a large class of explicit metrics for non-compact 4-D Calabi-Yau manifolds with Killing symmetries.

On D-branes from gauged linear sigma models

International Nuclear Information System (INIS)

Govindarajan, S.; Jayaraman, T.; Sarkar, T.

2001-01-01

We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields are first considered in the large-volume phase/non-linear sigma model limit of the corresponding Calabi-Yau manifold, where we find that we need to add a contact term on the boundary. These considerations enable to us to derive the boundary conditions in the full gauged linear sigma model, including the addition of the appropriate boundary contact terms, such that these boundary conditions have the correct non-linear sigma model limit. Most of the analysis is for the case of Calabi-Yau manifolds with one Kaehler modulus (including those corresponding to hypersurfaces in weighted projective space), though we comment on possible generalisations

A note on flux induced superpotentials in string theory

Energy Technology Data Exchange (ETDEWEB)

Becker, Melanie [Department of Physics, University of Maryland, College Park, MD 20742-4111 (United States)]. E-mail: melanieb@physics.umd.edu; Constantin, Dragos [Department of Physics, University of Maryland, College Park, MD 20742-4111 (United States)

2003-08-01

Non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory. Gukov has conjectured the explicit form of this superpotential. We check this conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well as for warped M-theory compactifications on Spin(7) holonomy manifolds, by performing a Kaluza-Klein reduction. (author)

A note on flux induced superpotentials in string theory

International Nuclear Information System (INIS)

Becker, Melanie; Constantin, Dragos

2003-01-01

Non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory. Gukov has conjectured the explicit form of this superpotential. We check this conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well as for warped M-theory compactifications on Spin(7) holonomy manifolds, by performing a Kaluza-Klein reduction. (author)

Generalized N=1 orientifold compactifications and the Hitchin functionals

International Nuclear Information System (INIS)

Benmachiche, I.; Hamburg Univ.; Grimm, T.W.

2006-02-01

The four-dimensional N=1 supergravity theories arising in compactifications of type IIA and type IIB on generalized orientifold backgrounds with background fluxes are discussed. The Kaehler potentials are derived for reductions on SU(3) structure orientifolds and shown to consist of the logarithm of the two Hitchin functionals. These are functions of even and odd forms parameterizing the geometry of the internal manifold, the B-field and the dilaton. The superpotentials induced by background fluxes and the non-Calabi-Yau geometry are determined by a reduction of the type IIA and type IIB fermionic actions on SU(3) and generalized SU(3) x SU(3) manifolds. Mirror spaces of Calabi-Yau orientifolds with electric and part of the magnetic NS-NS fluxes are conjectured to be certain SU(3) x SU(3) structure manifolds. Evidence for this identification is provided by comparing the generalized type IIA and type IIB superpotentials. (orig.)

Flux compactification of M-theory on compact manifolds with Spin(7) holonomy

International Nuclear Information System (INIS)

Constantin, D.

2005-01-01

At the leading order, M-theory admits minimal supersymmetric compactifications if the internal manifold has exceptional holonomy. The inclusion of non-vanishing fluxes in M-theory and string theory compactifications induce a superpotential in the lower dimensional theory, which depends on the fluxes. In this work, we check the conjectured form of this superpotential in the case of warped M-theory compactifications on Spin(7) holonomy manifolds. We perform a Kaluza-Klein reduction of the eleven-dimensional supersymmetry transformation for the gravitino and we find by direct comparison the superpotential expression. We check the conjecture for the heterotic string compactified on a Calabi-Yau three-fold as well. The conjecture can be checked indirectly by inspecting the scalar potential obtained after the compactification of M-theory on Spin(7) holonomy manifolds with non-vanishing fluxes. The scalar potential can be written in terms of the superpotential and we show that this potential stabilizes all the moduli fields describing deformations of the metric except for the radial modulus. All the above analyses require the knowledge of the minimal supergravity action in three dimensions. Therefore we calculate the most general causal N =1 three-dimensional, gauge invariant action coupled to matter in superspace and derive its component form using Ectoplasmic integration theory. We also show that the three-dimensional theory which results from the compactification is in agreement with the more general supergravity construction. The compactification procedure takes into account higher order quantum correction terms in the low energy effective action. We analyze the properties of these terms on a Spin(7) background. We derive a perturbative set of solutions which emerges from a warped compactification on a Spin(7) holonomy manifold with non-vanishing flux for the M-theory field strength and we show that in general the Ricci flatness of the internal manifold is lost, which

G-fluxes and non-perturbative stabilisation of heterotic M-theory

International Nuclear Information System (INIS)

Curio, Gottfried; Krause, Axel

2002-01-01

We examine heterotic M-theory compactified on a Calabi-Yau manifold with an additional parallel M5-brane. The dominant non-perturbative effect stems from open membrane instantons connecting the M5 with the boundaries. We derive the four-dimensional low-energy supergravity potential for this situation including subleading contributions as it turns out that the leading term vanishes after minimisation. At the minimum of the potential the M5 gets stabilised at the middle of the orbifold interval while the vacuum energy is shown to be manifestly positive. Moreover, induced by the non-trivial running of the Calabi-Yau volume along the orbifold which is driven by the G-fluxes, we find that the orbifold-length and the Calabi-Yau volume modulus are stabilised at values which are related by the G-flux of the visible boundary. Finally we determine the supersymmetry-breaking scale and the gravitino mass for this open membrane vacuum

Black hole attractors and pure spinors

International Nuclear Information System (INIS)

Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro

2006-01-01

We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to Σf k = Im(CΦ), where Φ is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, Φ = Ω and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation

Black Hole Attractors and Pure Spinors

International Nuclear Information System (INIS)

Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro

2006-01-01

We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to Σf k = Im(CΦ), where Φ is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, Φ = (Omega) and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation

Picard-Fuchs uniformization and modularity of the mirror map

International Nuclear Information System (INIS)

Doran, C.F.

2000-01-01

Arithmetic properties of mirror symmetry (type IIA-IIB string duality) are studied. We give criteria for the mirror map q-series of certain families of Calabi-Yau manifolds to be automorphic functions. For families of elliptic curves and lattice polarized K3 surfaces with surjective period mappings, global Torelli theorems allow one to present these criteria in terms of the ramification behavior of natural algebraic invariants - the functional and generalized functional invariants respectively. In particular, when applied to one parameter families of rank 19 lattice polarized K3 surfaces, our criterion demystifies the mirror-Moonshine phenomenon of Lian and Yau and highlights its non-monstrous nature. The lack of global Torelli theorems and presence of instanton corrections makes Calabi-Yau threefold families more complicated. Via the constraints of special geometry, the Picard-Fuchs equations for one parameter families of Calabi-Yau threefolds imply a differential equation criterion for automorphicity of the mirror map in terms of the Yukawa coupling. In the absence of instanton corrections, the projective periods map to a twisted cubic space curve. A hierarchy of ''algebraic'' instanton corrections correlated with the differential Galois group of the Picard-Fuchs equation is proposed. (orig.)

On discrete symmetries and torsion homology in F-theory

Energy Technology Data Exchange (ETDEWEB)

Mayrhofer, Christoph [Arnold-Sommerfeld-Center, Ludwig-Maximilians-Universität München,München (Germany); Palti, Eran; Till, Oskar; Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg,Heidelberg (Germany)

2015-06-04

We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a ℤ{sub 2} symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a ℤ{sub 2} gauge symmetry. We show that the resulting five-dimensional theories do not have a ℤ{sub 2} symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit torsion in homology. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a ℤ{sub 2} symmetry in five dimensions and, accordingly, we find explicitly an associated torsion cycle. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.

Superconformal compactifications in weighted projective space

International Nuclear Information System (INIS)

Greene, B.R.

1990-01-01

We discuss some aspects of string vacua constructed from orbifolded nonminimal Landau-Ginzburg theories which correspond to Calabi-Yau manifolds in weighted projective space. In contrast to previous expectations, we find that these theories allow for the construction of numerous stable (2, 0) Calabi-Yau vacua (most of which are not simply deformations of an underlying (2, 2) theory) thus indicating that this phenomenologically promising sector of the space of classical vacua is quite robust. We briefly discuss methods for extracting the phenomenology of these models and show, for example, that the full renormalizable superpotential of our SU(5) theories is not corrected by world sheet instantons and is thus given exactly by its tree-level value. (orig.)

New Higgs transitions between dual N=2 string models

International Nuclear Information System (INIS)

Berglund, P.; Katz, S.; Klemm, A.; Mayr, P.

1997-01-01

We describe a new kind of transition between topologically distinct N=2 type II Calabi-Yau vacua through points with enhanced non-abelian gauge symmetries together with fundamental charged matter hyper multiplets. We connect the appearance of matter to the local geometry of the singularity and discuss the relation between the instanton numbers of the Calabi-Yau manifolds taking part in the transition. In a dual heterotic string theory on K3 x T 2 the process corresponds to Higgsing a semi-classical gauge group or equivalently to a variation of the gauge bundle. In special cases the situation reduces to simple conifold transitions in the Coulomb phase of the non-abelian gauge symmetries. (orig.)

Exploring the web of heterotic string theories using anomalies

International Nuclear Information System (INIS)

Ruehle, Fabian

2013-07-01

We investigate how anomalies can be used to infer relations among different descriptions of heterotic string theory. Starting from the observation that the construction mechanism of heterotic orbifold compactifications considered up to now prevents them from being resolved into fully smooth Calabi-Yau compactification manifolds, we use a new mechanism to obtain an orbifold which does not suffer from the aforementioned limitations. We explain in general how to resolve orbifolds into smooth Calabi-Yau using toric geometry and gauged linear sigma models. The latter allow for studying the theory in various other regions of the string moduli space as well, which unveils interesting intermediate geometries. By following anomalies through the different regimes, we can match the orbifold theories to their smooth Calabi-Yau counterparts. In the process, we investigate discrete R and non-R orbifold symmetries and propose a mechanism for studying their fate in other regions of the moduli space. Finally, we introduce a novel anomaly cancelation mechanism in gauged linear sigma models, which manifests itself in target space as a description of compactification geometries with torsion and Neveu-Schwarz five branes.

Phase transitions, double-scaling limit, and topological strings

International Nuclear Information System (INIS)

Caporaso, Nicola; Griguolo, Luca; Pasquetti, Sara; Marino, Marcos; Seminara, Domenico

2007-01-01

Topological strings on Calabi-Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi-Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q-deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q-deformed 2D Yang-Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2D gravity. We give strong evidence that there is a double-scaled theory at the critical point whose all-genus free energy is governed by the Painleve I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2D supergravity, and we comment on possible implications for nonperturbative 2D gravity. We also give evidence for a new open/closed duality relating these Calabi-Yau backgrounds to open strings with framing

Exploring the web of heterotic string theories using anomalies

Energy Technology Data Exchange (ETDEWEB)

Ruehle, Fabian

2013-07-15

We investigate how anomalies can be used to infer relations among different descriptions of heterotic string theory. Starting from the observation that the construction mechanism of heterotic orbifold compactifications considered up to now prevents them from being resolved into fully smooth Calabi-Yau compactification manifolds, we use a new mechanism to obtain an orbifold which does not suffer from the aforementioned limitations. We explain in general how to resolve orbifolds into smooth Calabi-Yau using toric geometry and gauged linear sigma models. The latter allow for studying the theory in various other regions of the string moduli space as well, which unveils interesting intermediate geometries. By following anomalies through the different regimes, we can match the orbifold theories to their smooth Calabi-Yau counterparts. In the process, we investigate discrete R and non-R orbifold symmetries and propose a mechanism for studying their fate in other regions of the moduli space. Finally, we introduce a novel anomaly cancelation mechanism in gauged linear sigma models, which manifests itself in target space as a description of compactification geometries with torsion and Neveu-Schwarz five branes.

String theory flux vacua on twisted tori and generalized complex geometry

International Nuclear Information System (INIS)

Andriot, David

2010-01-01

This thesis is devoted to the study of flux vacua of string theory, with the ten-dimensional space-time split into a four-dimensional maximally symmetric space-time, and a six-dimensional internal manifold M, taken to be a solv-manifold (twisted torus). Such vacua are of particular interest when trying to relate string theory to supersymmetric (SUSY) extensions of the standard model of particles, or to cosmological models. For SUSY solutions of type II supergravities, allowing for fluxes on M helps to solve the moduli problem. Then, a broader class of manifolds than just the Calabi-Yau can be considered for M, and a general characterization is given in terms of Generalized Complex Geometry: M has to be a Generalized Calabi-Yau (GCY). A subclass of solv-manifolds have been proven to be GCY, so we look for solutions with such M. To do so, we use an algorithmic resolution method. Then we focus on specific new solutions: those admitting an intermediate SU(2) structure. A transformation named the twist is then discussed. It relates solutions on torus to solutions on solv-manifolds. Working out constraints on the twist to generate solutions, we can relate known solutions, and find a new one. We also use the twist to relate flux vacua of heterotic string. Finally we consider ten-dimensional de Sitter solutions. Looking for such solutions is difficult, because of several problems among which the breaking of SUSY. We propose an Ansatz for SUSY breaking sources which helps to overcome these difficulties. We give an explicit solution on a solv-manifold, and discuss partially its four-dimensional stability. (author)

Moduli stabilization, large-volume dS minimum without D3-bar branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi-Yau's

CERN Document Server

Misra, Aalok

2008-01-01

We consider issues of moduli stabilization and "area codes" for type II flux compactifications, and the "Inverse Problem" and "Fake Superpotentials" for extremal (non)supersymmetric black holes in type II compactifications on (orientifold of) a compact two-parameter Calabi-Yau expressed as a degree-18 hypersurface in WCP^4[1,1,1,6,9] which has multiple singular loci in its moduli space. We argue the existence of extended "area codes" [1] wherein for the same set of large NS-NS and RR fluxes, one can stabilize all the complex structure moduli and the axion-dilaton modulus (to different sets of values) for points in the moduli space away as well as near the different singular conifold loci leading to the existence of domain walls. By including non-perturbative alpha' and instanton corrections in the Kaehler potential and superpotential [2], we show the possibility of getting a large-volume non-supersymmetric (A)dS minimum. Further, using techniques of [3] we explicitly show that given a set of moduli and choice...

Towards mirror symmetry a la SYZ for generalized Calabi-Yau manifolds

Energy Technology Data Exchange (ETDEWEB)

Grange, P. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Schaefer-Nameki, S. [California Inst. of Tech., Pasadena, CA (United States)

2007-10-15

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal sixmanifold M with static SU(2) structure and mirror M, it is argued that the product M x M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and M. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3) x SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry. (orig.)

Aspects of superstring model-building

International Nuclear Information System (INIS)

Ellis, J.

1989-01-01

Several approaches to model-building with strings are discussed, including Calabi-Yau manifolds and fermionic formulations of strings directly in four dimensions. Ideas about supersymmetry breaking are reviewed. Flipped SU(5)xU(1) is touted as the theory of everything below the Planck scale (perhaps). (author). 64 refs, 7 figs

Constrained CPn models

International Nuclear Information System (INIS)

Latorre, J.I.; Luetken, C.A.

1988-11-01

We construct a large new class of two dimensional sigma models with Kaehler target spaces which are algebraic manifolds realized as complete interactions in weighted CP n spaces. They are N=2 superconformally symmetric and particular choices of constraints give Calabi-Yau target spaces which are nontrivial string vacua. (orig.)

Extended no-scale structure and {alpha}'{sup 2} corrections to the type IIB action

Energy Technology Data Exchange (ETDEWEB)

Pedro, F.G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Rummel, M. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Hong Kong Univ. of Science and Technology (China). Inst. for Advanced Study; Westphal, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kavali Institute for Theoretical Physics, Santa Barbara, CA (United States)

2013-06-15

We analyse a new N=1 string tree level correction at O({alpha}'{sup 2}) to the Kaehler potential of the volume moduli of type IIB Calabi-Yau flux compactification found recently by T. W. Grimm, R. Savelli and M. Weissenbacher (arXiv:1303.3317 [hep-th]) and its impact on the moduli potential. We find that it imposes a strong lower bound the Calabi-Yau volume in the Large Volume Scenario of moduli stabilisation. For KKLT-like scenarios we find that consistency of the action imposes an upper bound on the flux superpotential vertical stroke W{sub 0} vertical stroke Calabi-Yau manifolds where the new correction is present and dominated by the 4-cycle controlling the overall volume if the volume is stabilised at values V>or similar 10{sup 3}. We discuss the phenomenological implication of these bounds on V in the various scenarios.

Gauge theories from toric geometry and brane tilings

International Nuclear Information System (INIS)

Franco, Sebastian; Hanany, Amihay; Martelli, Dario; Sparks, James; Vegh, David; Wecht, Brian

2006-01-01

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds L a,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily L a,b,a , whose smallest member is the Suspended Pinch Point

Picard-Fuchs equations and the moduli space of superconformal field theories

International Nuclear Information System (INIS)

Cadavid, A.C.; Ferrara, S.

1991-01-01

We derive simple techniques which allow us to relate Picard-Fuchs differential equations for the periods of holomorphic p-forms on certain complex manifolds, to their moduli space and its modular group (target space duality). For Calabi-Yau manifolds the special geometry of moduli space gives the Zamolodchikov metric and the Yukawa couplings in terms of the periods. For general N=2 superconformal theories these equations exactly determine perturbed correlation functions of the chiral rings of primary fields. (orig.)

Topological sigma B model in 4-dimensions

International Nuclear Information System (INIS)

Jun, Hyun-Keun; Park, Jae-Suk

2008-01-01

We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensional topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.

Periods for Calabi-Yau and Landau-Ginzburg vacua

CERN Document Server

Berglund, P; De la Ossa, X C; Font, A; Hübsch, T; Jancic, D; Quevedo, Fernando; Berglund, Per; Candelas, Philip; Ossa, Xenia de la; Font, Anamaria; Hubsch, Tristan; Jancic, Dubravka; Quevedo, Fernando

1994-01-01

The complete structure of the moduli space of \\cys\\ and the associated Landau-Ginzburg theories, and hence also of the corresponding low-energy effective theory that results from (2,2) superstring compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calculable for a great many such models. We illustrate this by computing the periods explicitly for a number of classes of \\cys. We also point out that it is possible to read off from the periods certain important information relating to the mirror manifolds.

Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality

CERN Document Server

Cvetic, Mirjam; Klevers, Denis; Poretschkin, Maximilian; Song, Peng

2016-01-01

We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required ...

The N=1 effective actions of D-branes in Type IIA and IIB orientifolds

International Nuclear Information System (INIS)

Grimm, Thomas W.; Vieira Lopes, Daniel

2012-01-01

We discuss the four-dimensional N=1 effective actions of single space-time filling Dp-branes in general Type IIA and Type IIB Calabi-Yau orientifold compactifications. The effective actions depend on an infinite number of normal deformations and gauge connection modes. For D6-branes the N=1 Kähler potential, the gauge-coupling function, the superpotential and the D-terms are determined as functions of these fields. They can be expressed as integrals over chains which end on the D-brane cycle and a reference cycle. The infinite deformation space will reduce to a finite dimensional moduli space of special Lagrangian submanifolds upon imposing F- and D-term supersymmetry conditions. We show that the Type IIA moduli space geometry is captured by three real functionals encoding the deformations of special Lagrangian submanifolds, holomorphic three-forms and Kähler two-forms of Calabi-Yau manifolds. These elegantly combine in the N=1 Kähler potential, which reduces after applying mirror symmetry to the results previously determined for space-time filling D3-, D5- and D7-branes. We also propose general chain integral expressions for the Kähler potentials of Type IIB D-branes.

Tools for CICYs in F-theory

Energy Technology Data Exchange (ETDEWEB)

Anderson, Lara B.; Gao, Xin; Gray, James; Lee, Seung-Joo [Physics Department, Virginia Tech,Robeson Hall, Blacksburg, VA 24061 (United States)

2016-11-02

We provide a set of tools for analyzing the geometry of elliptically fibered Calabi-Yau manifolds, starting with a description of the total space rather than with a Weierstrass model or a specified type of fiber/base. Such an approach to the subject of F-theory compactification makes certain geometric properties, which are usually hidden, manifest. Specifically, we review how to isolate genus-one fibrations in such geometries and then describe how to find their sections explicitly. This includes a full parameterization of the Mordell-Weil group where non-trivial. We then describe how to analyze the associated Weierstrass models, Jacobians and resolved geometries. We illustrate our discussion with concrete examples which are complete intersections in products of projective spaces (CICYs). The examples presented include cases exhibiting non-abelian symmetries and higher rank Mordell-Weil group. We also make some comments on non-flat fibrations in this context. In a companion paper http://arxiv.org/abs/1608.07555 to this one, these results will be used to analyze the consequences for string dualities of the ubiquity of multiple fibrations in known constructions of Calabi-Yau manifolds.

New Supersymmetric String Compactifications

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Kachru, Shamit

2002-11-25

We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR fluxes. The simplest examples have descriptions as cosets, generalizing the three-dimensional nilmanifold. They can also be thought of as twisted tori. We derive a formula for the (super)potential governing the light fields, which is generated by the fluxes and certain ''twists'' in the geometry. Detailed consideration of an example also gives strong evidence that in some cases, these exotic geometries are related by smooth transitions to standard Calabi-Yau or G2 compactifications of M-theory.

On natural inflation and moduli stabilisation in string theory

Energy Technology Data Exchange (ETDEWEB)

Palti, Eran [Institut für Theoretische Physik, Ruprecht-Karls-Universität, Philosophenweg 19, Heidelberg, 69120 (Germany)

2015-10-28

Natural inflation relies on the existence of an axion decay constant which is super-Planckian. In string theory only sub-Planckian axion decay constants have been found in any controlled regime. However in field theory it is possible to generate an enhanced super-Planckian decay constant by an appropriate aligned mixing between axions with individual sub-Planckian decay constants. We study the possibility of such a mechanism in string theory. In particular we construct a new realisation of an alignment scenario in type IIA string theory compactifications on a Calabi-Yau where the alignment is induced through fluxes. Within field theory the original decay constants are taken to be independent of the parameters which induce the alignment. In string theory however they are moduli dependent quantities and so interact gravitationally with the physics responsible for the mixing. We show that this gravitational effect of the fluxes on the moduli can precisely cancel any enhancement of the effective decay constant. This censorship of an effective super-Planckian decay constant depends on detailed properties of Calabi-Yau moduli spaces and occurs for all the examples and classes that we study. We expand these results to a general superpotential assuming only that the axion superpartners are fixed supersymmetrically and are able to show for a large class of Calabi-Yau manifolds, but not all, that the cancellation effect occurs and is independent of the superpotential. We also study simple models where the moduli are fixed non-supersymmetrically and find that similar cancellation behaviour can emerge. Finally we make some comments on a possible generalisation to axion monodromy inflation models.

Anomaly, fluxes and (2,0) heterotic-string compactifications

Energy Technology Data Exchange (ETDEWEB)

Gillard, Joe; Papadopoulos, George; Tsimpis, Dimitrios [Department of Mathematics, King' s College London, Strand, London WC2R 2LS (United Kingdom)]. E-mail: tsimpis@fy.chalmers.se

2003-06-01

We compute the corrections to heterotic-string backgrounds with (2,0) world-sheet supersymmetry, up to two loops in sigma-model perturbation theory. We investigate the conditions for these backgrounds to preserve spacetime supersymmetry and we find that a sufficient requirement for consistency is the applicability of the {partial_derivative} {partial_derivative}-bar-lemma. In particular, we investigate the {alpha}' corrections to (2,0) heterotic-string compactifications and we find that the Calabi-Yau geometry of the internal space is deformed to a hermitean one. We show that at first order in {alpha}', the heterotic anomaly-cancellation mechanism does not induce any lifting of moduli. We explicitly compute the corrections to the conifold and to the U(n)-invariant Calabi-Yau metric at first order in {alpha}'. We also find a generalization of the gauge-field equations, compatible with the Donaldson equations on conformally-balanced hermitean manifolds. (author)

Anomaly, fluxes and (2,0) heterotic-string compactifications

International Nuclear Information System (INIS)

Gillard, Joe; Papadopoulos, George; Tsimpis, Dimitrios

2003-01-01

We compute the corrections to heterotic-string backgrounds with (2,0) world-sheet supersymmetry, up to two loops in sigma-model perturbation theory. We investigate the conditions for these backgrounds to preserve spacetime supersymmetry and we find that a sufficient requirement for consistency is the applicability of the ∂ ∂-bar-lemma. In particular, we investigate the α' corrections to (2,0) heterotic-string compactifications and we find that the Calabi-Yau geometry of the internal space is deformed to a hermitean one. We show that at first order in α', the heterotic anomaly-cancellation mechanism does not induce any lifting of moduli. We explicitly compute the corrections to the conifold and to the U(n)-invariant Calabi-Yau metric at first order in α'. We also find a generalization of the gauge-field equations, compatible with the Donaldson equations on conformally-balanced hermitean manifolds. (author)

Coset spaces as alternatives to Calabi-Yau spaces in the presence of Gaugino condensation

International Nuclear Information System (INIS)

Govindarajan, T.R.; Joshipura, A.S.; Rindani, S.D.; Sarkar, U.

1986-12-01

Compactification of the field-theory limit of the E 8 xE' 8 heterotic string on six-dimensional coset manifolds is discussed, with specific reference to maintaining four-dimensional supersymmetry. By choosing a torsion proportional to the background value of the three-index field H mnp occurring in the theory it is possible to satisfy the condition of SU(3) holonbmy necessary for supersymmetry. However, in all cases considered, it is found impossible to satisfy all the remaining conditions for supersymmetry. If gaugino condensation is assumed to occur, it is possible to preserve supersymmetry satisfying all the modified requirements of supersymmetry for the spaces SU(3)/U(1)xU(1), G 2 /SU(3) and SO(5)/SU(2)xU(1). The question of chiral fermions is examined in these cases using the Atiyah-Singer index theorem. Background gauge fields, which correspond to different numbers of generations of chiral fermions, are constructed explicitly. In all these cases the low-energy symmetry group is E 6 xE' 8 . (author)

Hurwitz numbers, matrix models and enumerative geometry

CERN Document Server

Bouchard, Vincent

2007-01-01

We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi-Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topological vertex, leads to a recursion relation for Hodge integrals with three Hodge class insertions. Our conjecture in Hurwitz theory follows from this recursion for the framed vertex in the limit of infinite framing.

Hodge numbers for all CICY quotients

International Nuclear Information System (INIS)

Constantin, Andrei; Gray, James; Lukas, Andre

2017-01-01

We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.

Hodge numbers for all CICY quotients

Energy Technology Data Exchange (ETDEWEB)

Constantin, Andrei [Department of Physics and Astronomy, Uppsala University, SE-751 20, Uppsala (Sweden); Gray, James [Physics Department, Robeson Hall, Virginia Tech,Blacksburg, VA 24061 (United States); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)

2017-01-02

We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.

Brane brick models in the mirror

Energy Technology Data Exchange (ETDEWEB)

Franco, Sebastián [Physics Department, The City College of the CUNY,160 Convent Avenue, New York, NY 10031 (United States); The Graduate School and University Center, The City University of New York,365 Fifth Avenue, New York NY 10016 (United States); Lee, Sangmin [Center for Theoretical Physics, Seoul National University,Seoul 08826 (Korea, Republic of); Department of Physics and Astronomy, Seoul National University,Seoul 08826 (Korea, Republic of); College of Liberal Studies, Seoul National University,Seoul 08826 (Korea, Republic of); Seong, Rak-Kyeong [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of); Vafa, Cumrun [Jefferson Physical Laboratory, Harvard University,Cambridge, MA 02138 (United States)

2017-02-21

Brane brick models are Type IIA brane configurations that encode the 2dN=(0,2) gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect. We also explain how 2d(0,2) triality is realized in terms of geometric transitions in the mirror geometry. Mirror symmetry leads to a geometric unification of dualities in different dimensions, where the order of duality is n−1 for a Calabi-Yau n-fold. This makes us conjecture the existence of a quadrality symmetry in 0d. Finally, we comment on how the M-theory lift of brane brick models connects to the classification of 2d(0,2) theories in terms of 4-manifolds.

Mirror symmetry

CERN Document Server

Voisin, Claire

1999-01-01

This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...

Higher-Derivative Supergravity and Moduli Stabilization

International Nuclear Information System (INIS)

Ciupke, David; Westphal, Alexander; Louis, Jan; Hamburg Univ.

2015-05-01

We review the ghost-free four-derivative terms for chiral superfields in N=1 supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar potential. We discuss the different solutions and argue that only one of them is consistent with the principles of effective field theory. Special attention is paid to the corrections along flat directions which can be stabilized or destabilized by the higher-derivative terms. We then compute these higher-derivative terms explicitly for the type IIB string compactified on a Calabi-Yau orientifold with fluxes via Kaluza-Klein reducing the (α') 3 R 4 corrections in ten dimensions for the respective N=1 Kaehler moduli sector. We prove that together with flux and the known (α') 3 -corrections the higher-derivative term stabilizes all Calabi-Yau manifolds with positive Euler number, provided the sign of the new correction is negative.

Moduli stabilization in type IIB orientifolds

International Nuclear Information System (INIS)

Schulgin, W.

2007-01-01

This thesis deals with the stabilization of the moduli fields in the compactifications of the type IIB string theory on orientifolds. A concrete procedure for the construction of solutions, in which all moduli fields are fixed, yields the KKLT scenario. We study, on which models the scenario can be applied, if approximations of the original KKLT work are abandoned. We find that in a series of models, namely such without complex-structure moduli the construction of the consistent solutions in the framework of the KKLT scenario is not possible. The nonperturbative effects, like D3 instantons and gaugino condensates are a further component of the KKLT scenario. They lead to the stabilization of the Kaehler moduli. We present criteria for the generation of the superpotential due to the D3 instantons at a Calaby-Yau manifold in presence of fluxes. Furthermore we show that although the presence of the nonperturbative superpotential in the equations of motions is correlated with the switching on of all ISD and IASD fluxes, the deciding criterium for the generation of the nonperturbative superpotential depends only on the fluxes of the type (2,1). Thereafter we discuss two models, in which we stabilize all moduli fields. Thereby it deals with Calabi-Yau orientifolds which have been obtained by a blow-up procedure from the Z 6-II and Z 2 x Z 4 orientifolds

Holomorphic couplings in non-perturbative string compactifications

International Nuclear Information System (INIS)

Klevers, Denis Marco

2011-06-01

In this thesis we present an analysis of several aspects of four-dimensional, non-perturbative N = 1 compactifications of string theory. Our focus is on the study of brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N=1 effective action, most prominently the superpotential W. The thesis is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we demonstrate exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefold Z 3 , that is canonically constructed from the original five-brane and Calabi-Yau threefold Z 3 via a blow-up. We exploit the use of the blow-up threefold Z 3 as a tool to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpret Z 3 as a flux compactification dual to the original five-brane by defining an SU(3)-structure on Z 3 , that is generated dynamically by the five-brane backreaction. (orig.)

Three-forms in supergravity and flux compactifications

Energy Technology Data Exchange (ETDEWEB)

Farakos, Fotis; Lanza, Stefano; Martucci, Luca; Sorokin, Dmitri [Univ. degli Studi di Padova (Italy). Dipt. di Fisica e Astronomia ' ' Galileo Galilei' ' ; I.N.F.N., Sezione di Padova (Italy)

2017-09-15

We present a duality procedure that relates conventional four-dimensional matter-coupled N = 1 supergravities to dual formulations in which auxiliary fields are replaced by field strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the superpotential to vacuum expectation values of the field strengths. We then apply this general duality to type IIA string compactifications on Calabi-Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms. (orig.)

Quantum periods of Calabi–Yau fourfolds

Energy Technology Data Exchange (ETDEWEB)

Gerhardus, Andreas, E-mail: gerhardus@th.physik.uni-bonn.de; Jockers, Hans, E-mail: jockers@uni-bonn.de

2016-12-15

In this work we study the quantum periods together with their Picard–Fuchs differential equations of Calabi–Yau fourfolds. In contrast to Calabi–Yau threefolds, we argue that the large volume points of Calabi–Yau fourfolds generically are regular singular points of the Picard–Fuchs operators of non-maximally unipotent monodromy. We demonstrate this property in explicit examples of Calabi–Yau fourfolds with a single Kähler modulus. For these examples we construct integral quantum periods and study their global properties in the quantum Kähler moduli space with the help of numerical analytic continuation techniques. Furthermore, we determine their genus zero Gromov–Witten invariants, their Klemm–Pandharipande meeting invariants, and their genus one BPS invariants. In our computations we emphasize the features attributed to the non-maximally unipotent monodromy property. For instance, it implies the existence of integral quantum periods that at large volume are purely worldsheet instanton generated. To verify our results, we also present intersection theory techniques to enumerate lines with a marked point on complete intersection Calabi–Yau fourfolds in Grassmannian varieties.

Special geometry

International Nuclear Information System (INIS)

Strominger, A.

1990-01-01

A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

Homological mirror symmetry and tropical geometry

CERN Document Server

Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia

2014-01-01

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...

Holomorphic couplings in non-perturbative string compactifications

Energy Technology Data Exchange (ETDEWEB)

Klevers, Denis Marco

2011-06-15

In this thesis we present an analysis of several aspects of four-dimensional, non-perturbative N = 1 compactifications of string theory. Our focus is on the study of brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N=1 effective action, most prominently the superpotential W. The thesis is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we demonstrate exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefold Z{sub 3}, that is canonically constructed from the original five-brane and Calabi-Yau threefold Z{sub 3} via a blow-up. We exploit the use of the blow-up threefold Z{sub 3} as a tool to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpret Z{sub 3} as a flux compactification dual to the original five-brane by defining an SU(3)-structure on Z{sub 3}, that is generated dynamically by the five-brane backreaction. (orig.)

On the elliptic genus of three E-strings and heterotic strings

International Nuclear Information System (INIS)

Cai, Wenhe; Huang, Min-xin; Sun, Kaiwen

2015-01-01

A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n=3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings.

Special geometry on the moduli space for the two-moduli non-Fermat Calabi–Yau

Directory of Open Access Journals (Sweden)

Konstantin Aleshkin

2018-01-01

Full Text Available We clarify the recently proposed method for computing a special Kähler metric on a Calabi–Yau complex structure moduli space using the fact that the moduli space is a subspace of a particular Frobenius manifold. We use this method to compute a previously unknown special Kähler metric in a two-moduli non-Fermat model.

Global D-brane models with stabilised moduli and light axions

Science.gov (United States)

Cicoli, Michele

2014-03-01

We review recent attempts to try to combine global issues of string compactifications, like moduli stabilisation, with local issues, like semi-realistic D-brane constructions. We list the main problems encountered, and outline a possible solution which allows globally consistent embeddings of chiral models. We also argue that this stabilisation mechanism leads to an axiverse. We finally illustrate our general claims in a concrete example where the Calabi-Yau manifold is explicitly described by toric geometry.

Voisin-Borcea manifolds and heterotic orbifold models

Energy Technology Data Exchange (ETDEWEB)

Buchmuller, W.; Schmidt, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Louis, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Valandro, R. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2012-08-15

We study the relation between a heterotic T{sup 6}/Z{sub 6} orbifold model and a compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with non-trivial line bundles. This orbifold can be seen as a Z{sub 2} quotient of T{sup 4}/Z{sub 3} x T{sup 2}. We consider a two-step resolution, whose intermediate step is (K3 x T{sup 2})/Z{sub 2}. This allows us to identify the massless twisted states which correspond to the geometric Kaehler and complex structure moduli. We work out the match of the two models when non-zero expectation values are given to all twisted geometric moduli. We find that even though the orbifold gauge group contains an SO(10) factor, a possible GUT group, the subgroup after Higgsing does not even include the standard model gauge group. Moreover, after Higgsing, the massless spectrum is non-chiral under the surviving gauge group.

Yukawa couplings in superstring compactification. [in quantum gravity theory

Science.gov (United States)

Strominger, A.

1985-01-01

A topological formula is given for the entire tree-level contribution to the low-energy effective action of a Calabi-Yau superstring compactification. The constraints on proton lifetime in the Calabi-Yau compactification are discussed in detail.

Effective actions and topological strings. Off-shell mirror symmetry and mock modularity of multiple M5-branes

Energy Technology Data Exchange (ETDEWEB)

Hecht, Michael

2011-10-20

This thesis addresses two different topics within the field of string theory. In the first part it is shown how Hodge-theoretic methods in conjunction with open string mirror symmetry can be used to compute non-perturbative effective superpotential couplings for type II/F-theory compactifications with D-branes and fluxes on compact Calabi-Yau manifolds. This is achieved by studying the at structure of operators which derives from the open/closed {beta}-model geometry. We analyze the variation of mixed Hodge structure of the relative cohomology induced by a family of divisors, which is wrapped by a D7-brane. This leads to a Picard-Fuchs system of differential operators, which can be used to compute the moduli dependence of the superpotential couplings as well as the mirror maps at various points in the open/closed deformation space. These techniques are used to obtain predictions for genuine A-model Ooguri-Vafa invariants of special Lagrangian submanifolds in compact Calabi-Yau geometries and real enumerative invariants of on-shell domain wall tensions. By an open/closed duality the system of differential equations can also be obtained from a gauged linear {sigma}-model, which describes a non-compact Calabi-Yau four-fold compactification without branes. This is used in the examples of multi-parameter models to study the various phases of the combined open/closed deformation space. It is furthermore shown how the brane geometry can be related to a F-theory compactification on a compact Calabi-Yau four-fold, where the Hodge-theoretic techniques can be used to compute the G-flux induced Gukov-Vafa-Witten potential. The dual F-theory picture also allows to conjecture the form of the Kaehler potential on the full open/closed deformation space. In the second part we analyze the background dependence of theories which derive from multiple wrapped M5-branes. Using the Kontsevich-Soibelman wall-crossing formula and the theory of mock modular forms we derive a holomorphic

Effective actions and topological strings. Off-shell mirror symmetry and mock modularity of multiple M5-branes

International Nuclear Information System (INIS)

Hecht, Michael

2011-01-01

This thesis addresses two different topics within the field of string theory. In the first part it is shown how Hodge-theoretic methods in conjunction with open string mirror symmetry can be used to compute non-perturbative effective superpotential couplings for type II/F-theory compactifications with D-branes and fluxes on compact Calabi-Yau manifolds. This is achieved by studying the at structure of operators which derives from the open/closed Β-model geometry. We analyze the variation of mixed Hodge structure of the relative cohomology induced by a family of divisors, which is wrapped by a D7-brane. This leads to a Picard-Fuchs system of differential operators, which can be used to compute the moduli dependence of the superpotential couplings as well as the mirror maps at various points in the open/closed deformation space. These techniques are used to obtain predictions for genuine A-model Ooguri-Vafa invariants of special Lagrangian submanifolds in compact Calabi-Yau geometries and real enumerative invariants of on-shell domain wall tensions. By an open/closed duality the system of differential equations can also be obtained from a gauged linear σ-model, which describes a non-compact Calabi-Yau four-fold compactification without branes. This is used in the examples of multi-parameter models to study the various phases of the combined open/closed deformation space. It is furthermore shown how the brane geometry can be related to a F-theory compactification on a compact Calabi-Yau four-fold, where the Hodge-theoretic techniques can be used to compute the G-flux induced Gukov-Vafa-Witten potential. The dual F-theory picture also allows to conjecture the form of the Kaehler potential on the full open/closed deformation space. In the second part we analyze the background dependence of theories which derive from multiple wrapped M5-branes. Using the Kontsevich-Soibelman wall-crossing formula and the theory of mock modular forms we derive a holomorphic anomaly

N=1 domain wall solutions of massive type II supergravity as generalized geometries

International Nuclear Information System (INIS)

Louis, J.

2006-05-01

We study N=1 domain wall solutions of type IIB supergravity compactified on a Calabi-Yau manifold in the presence of RR and NS electric and magnetic fluxes. We show that the dynamics of the scalar fields along the direction transverse to the domain wall is described by gradient flow equations controlled by a superpotential W. We then provide a geometrical interpretation of the gradient flow equations in terms of the mirror symmetric compactification of type IIA. They correspond to a set of generalized Hitchin flow equations of a manifold with SU(3) x SU(3)structure which is fibered over the direction transverse to the domain wall. (Orig.)

Topological strings from quantum mechanics

International Nuclear Information System (INIS)

Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki

2014-12-01

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

D-Branes in Curved Space

Energy Technology Data Exchange (ETDEWEB)

McGreevy, John Austen; /Stanford U., Phys. Dept.

2005-07-06

This thesis is a study of D-branes in string compactifications. In this context, D-branes are relevant as an important component of the nonperturbative spectrum, as an incisive probe of these backgrounds, and as a natural stringy tool for localizing gauge interactions. In the first part of the thesis, we discuss half-BPS D-branes in compactifications of type II string theory on Calabi-Yau threefolds. The results we describe for these objects are pertinent both in their role as stringy brane-worlds, and in their role as solitonic objects. In particular, we determine couplings of these branes to the moduli determining the closed-string geometry, both perturbatively and non-perturbatively in the worldsheet expansion. We provide a local model for transitions in moduli space where the BPS spectrum jumps, and discuss the extension of mirror symmetry between Calabi-Yau manifolds to the case when D-branes are present. The next section is an interlude which provides some applications of D-branes to other curved backgrounds of string theory. In particular, we discuss a surprising phenomenon in which fundamental strings moving through background Ramond-Ramond fields dissolve into large spherical D3-branes. This mechanism is used to explain a previously-mysterious fact discovered via the AdS-CFT correspondence. Next, we make a connection between type IIA string vacua of the type discussed in the first section and M-theory compactifications on manifolds of G{sub 2} holonomy. Finally we discuss constructions of string vacua which do not have large radius limits. In the final part of the thesis, we develop techniques for studying the worldsheets of open strings ending on the curved D-branes studied in the first section. More precisely, we formulate a large class of massive two-dimensional gauge theories coupled to boundary matter, which flow in the infrared to the relevant boundary conformal field theories. Along with many other applications, these techniques are used to describe

Geometric Transitions, Topological Strings, and Generalized Complex Geometry

International Nuclear Information System (INIS)

Chuang, Wu-yen

2007-01-01

Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism

Geometric Transitions, Topological Strings, and Generalized Complex Geometry

Energy Technology Data Exchange (ETDEWEB)

Chuang, Wu-yen; /SLAC /Stanford U., Phys. Dept.

2007-06-29

Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.

Integrable mappings via rational elliptic surfaces

International Nuclear Information System (INIS)

Tsuda, Teruhisa

2004-01-01

We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi-Yau manifolds, is also presented

Multidimensional flamelet-generated manifolds for partially premixed combustion

Energy Technology Data Exchange (ETDEWEB)

Nguyen, Phuc-Danh; Vervisch, Luc; Subramanian, Vallinayagam; Domingo, Pascale [CORIA - CNRS and INSA de Rouen, Technopole du Madrillet, BP 8, 76801 Saint-Etienne-du-Rouvray (France)

2010-01-15

Flamelet-generated manifolds have been restricted so far to premixed or diffusion flame archetypes, even though the resulting tables have been applied to nonpremixed and partially premixed flame simulations. By using a projection of the full set of mass conservation species balance equations into a restricted subset of the composition space, unsteady multidimensional flamelet governing equations are derived from first principles, under given hypotheses. During the projection, as in usual one-dimensional flamelets, the tangential strain rate of scalar isosurfaces is expressed in the form of the scalar dissipation rates of the control parameters of the multidimensional flamelet-generated manifold (MFM), which is tested in its five-dimensional form for partially premixed combustion, with two composition space directions and three scalar dissipation rates. It is shown that strain-rate-induced effects can hardly be fully neglected in chemistry tabulation of partially premixed combustion, because of fluxes across iso-equivalence-ratio and iso-progress-of-reaction surfaces. This is illustrated by comparing the 5D flamelet-generated manifold with one-dimensional premixed flame and unsteady strained diffusion flame composition space trajectories. The formal links between the asymptotic behavior of MFM and stratified flame, weakly varying partially premixed front, triple-flame, premixed and nonpremixed edge flames are also evidenced. (author)

Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals

CERN Document Server

Martelli, D; Martelli, Dario; Sparks, James

2006-01-01

Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on S^2 x S^3 has been discovered, where p and q are two coprime positive integers, with qCalabi-Yau cones, which moreover are toric. Aided by several recent results in toric geometry, we show that these are Kahler quotients C^4//U(1), namely the vacua of gauged linear sigma models with charges (p,p,-p+q,-p-q), thereby generalising the conifold, which is p=1,q=0. We present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold C^3/Z_{p+1}xZ_{p+1} for all q

manifolds are AdS/CFT dual to an infinite class of N=1 superconformal field theories arising as infra-red (IR) fixed points of toric quiver gauge theories with gauge group SU(N)^{2p}. As a non-trivial example, we show that Y^{2,1} is an explicit irregular Sasaki-Einstein metric on the horizon of the complex cone over the first del Pezz...

Higher-dimensional analogues of Donaldson-Witten theory

International Nuclear Information System (INIS)

Acharya, B.S.; Spence, B.

1997-01-01

We present a Donaldson-Witten-type field theory in eight dimensions on manifolds with Spin(7) holonomy. We prove that the stress tensor is BRST exact for metric variations preserving the holonomy and we give the invariants for this class of variations. In six and seven dimensions we propose similar theories on Calabi-Yau threefolds and manifolds of G 2 holonomy, respectively. We point out that these theories arise by considering supersymmetric Yang-Mills theory defined on such manifolds. The theories are invariant under metric variations preserving the holonomy structure without the need for twisting. This statement is a higher-dimensional analogue of the fact that Donaldson-Witten field theory on hyper-Kaehler 4-manifolds is topological without twisting. Higher-dimensional analogues of Floer cohomology are briefly outlined. All of these theories arise naturally within the context of string theory. (orig.)

The geometry and physics of Abelian gauge groups in F-theory

Energy Technology Data Exchange (ETDEWEB)

Keitel, Jan

2015-07-14

In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

The geometry and physics of Abelian gauge groups in F-theory

International Nuclear Information System (INIS)

Keitel, Jan

2015-01-01

In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

On the trace-manifold generated by the deformations of a body-manifold

Directory of Open Access Journals (Sweden)

Boja Nicolae

2003-01-01

Full Text Available In this paper, concerned to the study of continuous deformations of material media using some tools of modem differential geometry, a moving frame of Frenet type along the orbits of an one-parameter group acting on a so-called "trace-manifold", M, associated to the deformations, is constructed. The manifold M is defined as an infinite union of non-disjoint compact manifolds, generated by the consecutive positions in the Euclidean affine 3-space of a body-manifold under deformations in a closed time interval. We put in evidence a skew-symmetric band tensor of second order, ω, which describes the deformation in a small neighborhood of any point along the orbits. The non-null components ωi,i+i, (i =1,2, of ω are assimilated as like curvatures at each point of an orbit in the planes generated by the pairs of vectors (ĕi,ĕi+i of a moving frame in M associated to the orbit in a similar way as the Frenet's frame is. Also a formula for the energy of the orbits is given and its relationship with some stiffness matrices is established.

D-Branes on K3-Fibrations

CERN Document Server

Kaste, P.; Lutken, C.A.; Walcher, Johannes

2000-01-01

B-type D-branes are constructed on two different K3-fibrations over IP_1 using boundary conformal field theory at the rational Gepner points of these models. The microscopic CFT charges are compared with the Ramond charges of D-branes wrapped on holomorphic cycles of the corresponding Calabi-Yau manifold. We study in particular D4-branes and bundles localized on the K3 fibers, and find agreement with expectations. This provides a further test of the boundary CFT approach to $D$-brane physics.

Topological field theory and surgery on three-manifolds

International Nuclear Information System (INIS)

Guadagnini, E.; Panicucci, S.

1992-01-01

The solution of the SU(2) quantum Chern-Simons field theory defined on a closed, connected and orientable three-manifold is presented. The vacuum expectation values of Wilson line operators, associated with framed links in a generic manifold, are computed in terms of the expectation values of the three-sphere. The method consists of using an operator realization of Dehn surgery. The rules, corresponding to the surgery instructions in the three-sphere, are derived and the three-manifold invariant defined by the Chern-Simons theory is constructed. Several examples are considered and explicit results are reported. (orig.)

Hamilton's gradient estimate for the heat kernel on complete manifolds

OpenAIRE

Kotschwar, Brett

2007-01-01

In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \\geq -Kg$. We accomplish this extension via a maximum principle of L. Karp and P. Li and a Bernstein-type estimate on the gradient of the solution. An application of our result, together with the bounds of P. Li and S.T. Yau, yields an estimate on the gradient of the heat kernel for complete manifol...

Nonperturbative flipped SU(5) vacua in heterotic M-theory

Energy Technology Data Exchange (ETDEWEB)

Faraggi, Alon E. E-mail: faraggi@thphys.ox.ac.uk; Garavuso, Richard E-mail: garavuso@thphys.ox.ac.uk; Isidro, Jose M. E-mail: isidro@thphys.ox.ac.uk

2002-10-07

The evidence for neutrino masses in atmospheric and solar neutrino experiments provides further support for the embedding of the Standard Model fermions in the chiral 16 SO(10) representation. Such an embedding is afforded by the realistic free fermionic heterotic-string models. In this paper we advance the study of these string models toward a nonperturbative analysis by generalizing the work of Donagi, Pantev, Ovrut and Waldram from the case of G=SU(2n+1) to G=SU(2n) stable holomorphic vector bundles on elliptically fibered Calabi-Yau manifolds with fundamental group Z{sub 2}. We demonstrate existence of G=SU(4) solutions with three generations and SO(10) observable gauge group over Hirzebruch base surface, whereas we show that certain classes of del Pezzo base surface do not admit such solutions. The SO(10) symmetry is broken to SU(5)xU(1) by a Wilson line. The overlap with the realistic free fermionic heterotic-string models is discussed.

Global F-theory GUTs

Energy Technology Data Exchange (ETDEWEB)

Blumenhagen, Ralph; /Munich, Max Planck Inst.; Grimm, Thomas W.; /Bonn U.; Jurke, Benjamin; /Munich, Max Planck Inst.; Weigand, Timo; /SLAC

2010-08-26

We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi-Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge flux are described by the spectral cover construction. We consider a split S[U(4) x U(1){sub X}] spectral cover, which allows for the phenomenologically relevant Yukawa couplings and GUT breaking to the MSSM via hypercharge flux while preventing dimension-4 proton decay. General expressions for the massless spectrum, consistency conditions and a new method for the computation of curvature-induced tadpoles are presented. We also provide a geometric toolkit for further model searches in the framework of toric geometry. Finally, an explicit global model with three chiral generations and all required Yukawa couplings is defined on a Calabi-Yau fourfold which is fibered over the del Pezzo transition of the Fano threefold P{sup 4}.

Global F-theory GUTs

International Nuclear Information System (INIS)

Blumenhagen, Ralph; Grimm, Thomas W.; Jurke, Benjamin; Weigand, Timo

2010-01-01

We construct global F-theory GUT models on del Pezzo surfaces in compact Calabi-Yau fourfolds realized as complete intersections of two hypersurface constraints. The intersections of the GUT brane and the flavour branes as well as the gauge flux are described by the spectral cover construction. We consider a split S[U(4)xU(1) X ] spectral cover, which allows for the phenomenologically relevant Yukawa couplings and GUT breaking to the MSSM via hypercharge flux while preventing dimension-4 proton decay. General expressions for the massless spectrum, consistency conditions and a new method for the computation of curvature-induced tadpoles are presented. We also provide a geometric toolkit for further model searches in the framework of toric geometry. Finally, an explicit global model with three chiral generations and all required Yukawa couplings is defined on a Calabi-Yau fourfold which is fibered over the del Pezzo transition of the Fano threefold P 4 [4].

Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results

Directory of Open Access Journals (Sweden)

James Carlson

2009-09-01

Full Text Available This paper is a survey of the subject of variations of Hodge structure (VHS considered as exterior differential systems (EDS. We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate section we present some new results on the characteristic cohomology of a homogeneous Pfaffian system. In the last section we discuss how the integrability conditions of an EDS affect the expected dimension of an integral submanifold. The paper ends with some speculation on EDS and Hodge conjecture for Calabi-Yau manifolds.

The Topological Vertex

CERN Document Server

Aganagic, M; Marino, M; Vafa, C; Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

2005-01-01

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of Calabi-Yau. We interpret this result as an operator computation of the amplitudes in the B-model mirror which is the Kodaira-Spencer quantum theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

Geometry of (0,2) Landau-Ginzburg orbifolds

International Nuclear Information System (INIS)

Kawai, Toshiya; Mohri, Kenji

1994-01-01

Several aspects of (0,2) Landau-Ginzburg orbifolds are investigated. Especially the elliptic genera are computed in general and, for a class of models recently invented by Distler and Kachru, they are compared with the ones from (0,2) sigma models. Our formalism gives an easy way to calculate the generation numbers for lots of Distler-Kachru models even if they are based on singular Calabi-Yau spaces. We also make some general remarks on the Born-Oppenheimer calculation of the ground states elucidating its mathematical meaning in the untwisted sector. For Distler-Kachru models based on non-singular Calabi-Yau spaces we show that there exist ''residue'' type formulas of the elliptic genera as well. ((orig.))

Squashed Toric Sigma Models and Mock Modular Forms

Science.gov (United States)

Gupta, Rajesh Kumar; Murthy, Sameer

2018-05-01

We study a class of two-dimensional N}=(2,2)} sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global {U(1)} symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold in which the torus fibration maintains a constant size in the interior of the manifold, thus producing a neck-like region. We compute the elliptic genus of these models, using localization, in the case when the unsquashed vacuum manifolds obey the Calabi-Yau condition. The elliptic genera have a non-holomorphic dependence on the modular parameter {τ} coming from the continuum produced by the neck. In the simplest case corresponding to squashed {C / Z_{2 the elliptic genus is a mixed mock Jacobi form which coincides with the elliptic genus of the {N=(2,2)} {SL(2,R) / U(1)} cigar coset.

Deformations of Geometric Structures in Topological Sigma Models

International Nuclear Information System (INIS)

Bytsenko, A. A.

2010-01-01

We study a Lie algebra of formal vector fields W n with it application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent classes of deformations are described by a Hochschild cohomology of the DG-algebra A = (A,Q), Q = ∂-bar+∂ deform, which is defined to be the cohomology of (-1) n Q+d Hoch . Here ∂-bar is the initial non-deformed BRST operator while ∂ deform is the deformed part whose algebra is a Lie algebra of linear vector fields gl n .

Exact quantization conditions for the relativistic Toda lattice

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki; Mariño, Marcos

2016-01-01

Inspired by recent connections between spectral theory and topological string theory, we propose exact quantization conditions for the relativistic Toda lattice of N particles. These conditions involve the Nekrasov-Shatashvili free energy, which resums the perturbative WKB expansion, but they require in addition a non-perturbative contribution, which is related to the perturbative result by an S-duality transformation of the Planck constant. We test the quantization conditions against explicit calculations of the spectrum for N=3. Our proposal can be generalized to arbitrary toric Calabi-Yau manifolds and might solve the corresponding quantum integrable system of Goncharov and Kenyon.

Anomaly cancellation and smooth non-Kahler solutions in heterotic string theory

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; Fu Jixiang; Tseng, L.-S.; Yau, S.-T.

2006-01-01

We show that six-dimensional backgrounds that are T 2 bundle over a Calabi-Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can only be satisfied if the base is K3 while a T 4 base is excluded. The conditions imposed by anomaly cancellation for the T 2 bundle structure, the dilaton field, and the holomorphic stable bundles are analyzed and the solutions determined. Applying duality, we check the consistency of the anomaly cancellation constraints with those for flux backgrounds of M-theory on eight-manifolds

Supergravity and supersymmetry breaking in four and five dimensions

International Nuclear Information System (INIS)

Ellis, John; Lalak, Zygmunt; Pokorski, Stefan; Thomas, Steven

1999-01-01

We discuss supersymmetry breaking in the field-theoretical limit of the strongly coupled heterotic string compactified on a Calabi-Yau manifold, from the different perspectives of four and five dimensions. The former applies to light degrees of freedom below the threshold for five-dimensional Kaluza-Klein excitations, whereas the five-dimensional perspective is also valid up to the Calabi-Yau scale. We show how, in the latter case, two gauge sectors separated in the fifth dimension are combined to form a consistent four-dimensional supergravity. In the lowest order of the κ 2/3 expansion, we show how a four-dimensional supergravity with gauge kinetic function f 1,2 =S is reproduced, and we show how higher-order terms give rise to four-dimensional operators that differ in the two gauge sectors. In the four-dimensional approach, supersymmetry is seen to be broken when condensates form on one or both walls, and the goldstino may have a non-zero dilatino component. As in the five-dimensional approach, the Lagrangian is not a perfect square, and we have not identified a vacuum with broken supersymmetry and zero vacuum energy. We derive soft supersymmetry-breaking terms for non-standard perturbative embeddings, that are relevant in more general situations such as type I/type IIB orientifold models

Gromov-Witten invariants and localization

Science.gov (United States)

Morrison, David R.

2017-11-01

We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kähler potential on the conformal manifold. We show how the Kähler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves. This is a contribution to the review issue ‘Localization techniques in quantum field theories’ (ed V Pestun and M Zabzine) which contains 17 chapters, available at [1].

Group actions, non-Kähler complex manifolds and SKT structures

Directory of Open Access Journals (Sweden)

Poddar Mainak

2018-02-01

Full Text Available We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler complex structures on tangential frame bundles of complex orbifolds.

On symplectomorphisms of the symplectisation of a compact contact manifold

International Nuclear Information System (INIS)

Banyaga, A.

2004-03-01

Let (N, α) be a compact contact manifold and (N x R, d(e t α)) its symplectisation. We show that the group G which is the identity component in the group of symplectic diffeomorphisms Φ of (N x R, d(e t α)) that cover diffeomorphisms of Φ of N x S 1 is simple, by showing that G is isomorphic to the kernel of the Calabi homomorphism of the associated locally conformal symplectic structure. (author)

Moduli stabilisation for chiral global models

International Nuclear Information System (INIS)

Cicoli, Michele; Mayrhofer, Christoph; Valandro, Roberto

2011-10-01

We combine moduli stabilisation and (chiral) model building in a fully consistent global set-up in Type IIB/F-theory. We consider compactifications on Calabi-Yau orientifolds which admit an explicit description in terms of toric geometry. We build globally consistent compactifications with tadpole and Freed-Witten anomaly cancellation by choosing appropriate brane set-ups and world-volume fluxes which also give rise to SU(5)- or MSSM-like chiral models. We fix all the Kaehler moduli within the Kaehler cone and the regime of validity of the 4D effective field theory. This is achieved in a way compatible with the local presence of chirality. The hidden sector generating the non-perturbative effects is placed on a del Pezzo divisor that does not have any chiral intersections with any other brane. In general, the vanishing D-term condition implies the shrinking of the rigid divisor supporting the visible sector. However, we avoid this problem by generating r< n D-term conditions on a set of n intersecting divisors. The remaining (n-r) flat directions are fixed by perturbative corrections to the Kaehler potential. We illustrate our general claims in an explicit example. We consider a K3-fibred Calabi-Yau with four Kaehler moduli, that is an hypersurface in a toric ambient space and admits a simple F-theory up-lift. We present explicit choices of brane set-ups and fluxes which lead to three different phenomenological scenarios: the first with GUT-scale strings and TeV-scale SUSY by fine-tuning the background fluxes; the second with an exponentially large value of the volume and TeV-scale SUSY without fine-tuning the background fluxes; and the third with a very anisotropic configuration that leads to TeV-scale strings and two micron-sized extra dimensions. The K3 fibration structure of the Calabi-Yau three-fold is also particularly suitable for cosmological purposes. (orig.)

Moduli stabilisation for chiral global models

Energy Technology Data Exchange (ETDEWEB)

Cicoli, Michele [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Mayrhofer, Christoph [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Valandro, Roberto [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2011-10-15

We combine moduli stabilisation and (chiral) model building in a fully consistent global set-up in Type IIB/F-theory. We consider compactifications on Calabi-Yau orientifolds which admit an explicit description in terms of toric geometry. We build globally consistent compactifications with tadpole and Freed-Witten anomaly cancellation by choosing appropriate brane set-ups and world-volume fluxes which also give rise to SU(5)- or MSSM-like chiral models. We fix all the Kaehler moduli within the Kaehler cone and the regime of validity of the 4D effective field theory. This is achieved in a way compatible with the local presence of chirality. The hidden sector generating the non-perturbative effects is placed on a del Pezzo divisor that does not have any chiral intersections with any other brane. In general, the vanishing D-term condition implies the shrinking of the rigid divisor supporting the visible sector. However, we avoid this problem by generating rCalabi-Yau with four Kaehler moduli, that is an hypersurface in a toric ambient space and admits a simple F-theory up-lift. We present explicit choices of brane set-ups and fluxes which lead to three different phenomenological scenarios: the first with GUT-scale strings and TeV-scale SUSY by fine-tuning the background fluxes; the second with an exponentially large value of the volume and TeV-scale SUSY without fine-tuning the background fluxes; and the third with a very anisotropic configuration that leads to TeV-scale strings and two micron-sized extra dimensions. The K3 fibration structure of the Calabi-Yau three-fold is also particularly suitable for cosmological purposes. (orig.)

The topological B-model on fattened complex manifolds and subsectors of N=4 self-dual Yang-Mills theory

International Nuclear Information System (INIS)

Saemann, Christian

2005-01-01

In this paper, we propose so-called fattened complex manifolds as target spaces for the topological B-model. We naturally obtain these manifolds by restricting the structure sheaf of the N=4 supertwistor space, a process, which can be understood as a fermionic dimensional reduction. Using the twistorial description of these fattened complex manifolds, we construct Penrose-Ward transforms between solutions to the holomorphic Chern-Simons equations on these spaces and bosonic subsectors of solutions to the N=4 self-dual Yang-Mills equations on C 4 or R 4 . Furthermore, we comment on Yau's theorem for these spaces. (author)

The gravitational sector of 2d (0,2) F-theory vacua

International Nuclear Information System (INIS)

Lawrie, Craig; Schäfer-Nameki, Sakura; Weigand, Timo

2017-01-01

F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S 1 reduction of the dual F-theory.

The gravitational sector of 2d (0,2) F-theory vacua

Energy Technology Data Exchange (ETDEWEB)

Lawrie, Craig [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, Heidelberg, 69120 (Germany); Schäfer-Nameki, Sakura [Mathematical Institute, University of Oxford,Woodstock Road, Oxford, OX2 6GG (United Kingdom); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, Heidelberg, 69120 (Germany)

2017-05-19

F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S{sup 1} reduction of the dual F-theory.

On heterotic vacua with fermionic expectation values

Energy Technology Data Exchange (ETDEWEB)

Minasian, Ruben [Institut de Physique Theorique, Universite Paris Saclay, CEA, CNRS, Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Universites, CNRS, LPTHE, UPMC Paris 06, UMR 7589, Paris (France); Svanes, Eirik Eik [Sorbonne Universites, CNRS, LPTHE, UPMC Paris 06, UMR 7589, Paris (France); Sorbonne Universites, Institut Lagrange de Paris, Paris (France)

2017-03-15

We study heterotic backgrounds with non-trivial H-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear Σ{sub MNP} = tr anti χΓ{sub MNP}χ. For Calabi-Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three-form Σ{sub mnp} that must be a singlet of the holonomy group. This condition does not hold anymore when an internal H-flux is turned on and O(α{sup '}) effects are included. In this paper we study flux compactifications to three and four-dimensions on G-structure manifolds. We derive the generic conditions for supersymmetric solutions. We use integrability conditions and Lichnerowicz type arguments to derive a set of constraints whose solution, together with supersymmetry, is sufficient for finding backgrounds with gaugino condensate. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Non-perturbative scalar potential inspired by type IIA strings on rigid CY

Energy Technology Data Exchange (ETDEWEB)

Alexandrov, Sergei [Laboratoire Charles Coulomb (L2C), UMR 5221, CNRS-Université de Montpellier,F-34095, Montpellier (France); Ketov, Sergei V. [Department of Physics, Tokyo Metropolitan University,1-1 Minami-ohsawa, Hachioji-shi, Tokyo 192-0397 (Japan); Kavli Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo,Chiba 277-8568 (Japan); Institute of Physics and Technology, Tomsk Polytechnic University,30 Lenin Ave., Tomsk 634050 (Russian Federation); Wakimoto, Yuki [Department of Physics, Tokyo Metropolitan University,1-1 Minami-ohsawa, Hachioji-shi, Tokyo 192-0397 (Japan)

2016-11-10

Motivated by a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we derive a non-perturbative potential of all scalar fields from the exact D-instanton corrected metric on the hypermultiplet moduli space. Applying this potential to moduli stabilization, we find a discrete set of exact vacua for axions. At these critical points, the stability problem is decoupled into two subspaces spanned by the axions and the other fields (dilaton and Kähler moduli), respectively. Whereas the stability of the axions is easily achieved, numerical analysis shows instabilities in the second subspace.

D-branes on K3-fibrations

International Nuclear Information System (INIS)

Kaste, P.; Lerche, W.; Luetken, C.A.; Walcher, J.

2000-01-01

B-type D-branes are constructed on two different K3-fibrations over P 1 using boundary conformal field theory at the rational Gepner points of these models. The microscopic CFT charges are compared with the Ramond charges of D-branes wrapped on holomorphic cycles of the corresponding Calabi-Yau manifold. We study in particular D4-branes and bundles localized on the K3 fibers, and find from CFT that each irreducible component of a bundle on K3 gains one modulus upon fibration over P 1 . This is in agreement with expectations and so provides a further test of the boundary CFT approach to D-brane physics

Non-extremal instantons and wormholes in string theory

International Nuclear Information System (INIS)

Bergshoeff, E.; Collinucci, A.; Gran, U.; Roest, D.; Vandoren, S.

2005-01-01

We construct the most general non-extremal spherically symmetric instanton solution of a gravity-dilaton-axion system with SL(2,R) symmetry, for arbitrary euclidean spacetime dimension D≥3. A subclass of these solutions describe completely regular wormhole geometries, whose size is determined by an invariant combination of the SL(2,R) charges. Our results can be applied to four-dimensional effective actions of type II strings compactified on a Calabi-Yau manifold, and in particular to the universal hypermultiplet coupled to gravity. We show that these models contain regular wormhole solutions, supported by regular dilaton and RR scalar fields of the universal hypermultiplet. (Abstract Copyright [2005], Wiley Periodicals, Inc.)

Asymmetric Gepner models III. B-L lifting

Energy Technology Data Exchange (ETDEWEB)

Gato-Rivera, B. [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); Schellekens, A.N., E-mail: t58@nikhef.n [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); IMAPP, Radboud Universiteit, Nijmegen (Netherlands)

2011-06-21

In the same spirit as heterotic weight lifting, B-L lifting is a way of replacing the superfluous and ubiquitous U(1){sub B-L} with something else with the same modular properties, but different conformal weights and ground state dimensions. This method works in principle for all variants of (2,2) constructions, such as orbifolds, Calabi-Yau manifolds, free bosons and fermions and Gepner models, since it only modifies the universal SO(10)xE{sub 8} part of the CFT. However, it can only yield chiral spectra if the 'internal' sector of the theory provides a simple current of order 5. Here we apply this new method to Gepner models. Including exceptional invariants, 86 of them have the required order 5 simple current, and 69 of these yield chiral spectra. Three family spectra occur abundantly.

Heterotic/Type-II duality and its field theory avatars

International Nuclear Information System (INIS)

Kiritsis, Elias

1999-01-01

In these lecture notes, I will describe heterotic/type-II duality in six and four dimensions. When supersymmetry is the maximal N=4 it will be shown that the duality reduces in the field theory limit to the Montonen-Olive duality of N=4 Super Yang-Mills theory. We will consider further compactifications of type II theory on Calabi-Yau manifolds. We will understand the physical meaning of geometric conifold singularities and the dynamics of conifold transitions. When the CY manifold is a K3 fibration we will argue that the type-II ground-state is dual to the heterotic theory compactified on K3xT 2 . This allows an exact computation of the low effective action. Taking the field theory limit, α ' →0, we will recover the Seiberg-Witten non-perturbative solution of N=2 gauge theory

Testing R-parity with geometry

Energy Technology Data Exchange (ETDEWEB)

He, Yang-Hui [Department of Mathematics, City University, London,Northampton Square, London EC1V 0HB (United Kingdom); School of Physics, NanKai University,94 Weijin Road, Tianjin, 300071 (China); Merton College, University of Oxford,Merton Street, OX1 4JD (United Kingdom); Jejjala, Vishnu [Mandelstam Institute for Theoretical Physics, NITheP, and School of Physics,University of the Witwatersrand,1 Jan Smuts Avenue, Johannesburg, WITS 2050 (South Africa); Matti, Cyril [Department of Mathematics, City University, London,Northampton Square, London EC1V 0HB (United Kingdom); Mandelstam Institute for Theoretical Physics, NITheP, and School of Physics,University of the Witwatersrand,1 Jan Smuts Avenue, Johannesburg, WITS 2050 (South Africa); Nelson, Brent D. [Department of Physics, Northeastern University,360 Huntington Avenue, Boston, MA 02115 (United States)

2016-03-14

We present a complete classification of the vacuum geometries of all renormalizable superpotentials built from the fields of the electroweak sector of the MSSM. In addition to the Severi and affine Calabi-Yau varieties previously found, new vacuum manifolds are identified; we thereby investigate the geometrical implication of theories which display a manifest matter parity (or R-parity) via the distinction between leptonic and Higgs doublets, and of the lepton number assignment of the right-handed neutrino fields. We find that the traditional R-parity assignments of the MSSM more readily accommodate the neutrino see-saw mechanism with non-trivial geometry than those superpotentials that violate R-parity. However there appears to be no geometrical preference for a fundamental Higgs bilinear in the superpotential, with operators that violate lepton number, such as νHH̄, generating vacuum moduli spaces equivalent to those with a fundamental bilinear.

New F-theory lifts

International Nuclear Information System (INIS)

Collinucci, Andres

2009-01-01

In this note, a procedure is developed to explicitly construct non-trivial F-theory lifts of perturbative IIB orientifold models on Calabi-Yau complete intersections in toric varieties. This procedure works on Calabi-Yau orientifolds where the involution coordinate can have arbitrary projective weight, as opposed to the well-known hypersurface cases where it has half the weight of the equation defining the CY threefold. This opens up the possibility of lifting more general setups, such as models that have O3-planes.

Aspects of NT ≥ 2 topological gauge theories and D-branes

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1996-12-01

Recently, topological field theories with extended N T > 1 topological symmetries have appeared in various contexts, e.g. in the discussion of S-duality in supersymmetry gauge theories, as world volume theories of Dirichlet p-branes in string theory, and in a general discussion of 'balanced' or critical topological theories. Here we will comment on, explain, or expand on various aspects of these theories, thus complementing the already existing discussions of such models in the literature. We comment on various aspects of topological gauge theories possessing N T ≥ 2 topological symmetry: 1. We show that the construction of Vafa-Witten and Dijkgraaf-Moore of 'balanced' topological field theories is equivalent to an earlier construction in terms of N T = 2 superfields inspired by supersymmetric quantum mechanics. 2. We explain the relation between topological field theories calculating signed and unsigned sums of Euler numbers of moduli spaces. 3. We show that the topological twist of N = 4 d = 4 Yang-Mills theory recently constructed by Marcus is formally a deformation of four-dimensional super-BF theory. 4. We construct a novel N T = 2 topological twist of N = 4 d = 3 Yang-Mills theory, a 'mirror' of the Casson invariant model, with certain unusual features (e.g. no bosonic scalar field and hence no underlying equivariant cohomology). 5. We give a complete classification of the topological twists of N = 8 d = 3 Yang-Mills theory and show that they are realized as world-volume theories of Dirichlet two-brane instantons wrapping supersymmetric three-cycles of Calabi-Yau three-folds and G 2 -holonomy Joyce manifolds. 6. We describe the topological gauge theories associated to D-string instantons on holomorphic curves in K3s and Calabi-Yau 3-folds. 48 refs

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Science.gov (United States)

Boukraa, S.; Hassani, S.; Maillard, J.-M.

2012-12-01

Focusing on examples associated with holonomic functions, we try to bring new ideas on how to look at phase transitions, for which the critical manifolds are not points but curves depending on a spectral variable, or even fill higher dimensional submanifolds. Lattice statistical mechanics often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in the most general mathematical framework, be too complex, or simply could not be defined. In a learn-by-example approach, considering several Picard-Fuchs systems of two-variables ‘above’ Calabi-Yau ODEs, associated with double hypergeometric series, we show that D-finite (holonomic) functions are actually a good framework for finding properly the singular manifolds. The singular manifolds are found to be genus-zero curves. We then analyze the singular algebraic varieties of quite important holonomic functions of lattice statistical mechanics, the n-fold integrals χ(n), corresponding to the n-particle decomposition of the magnetic susceptibility of the anisotropic square Ising model. In this anisotropic case, we revisit a set of so-called Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find the first set of non-Nickelian singularities for χ(3) and χ(4), that also turns out to be rational or elliptic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model, or, equivalently, that they depend on the spectral parameter of the model. This has important consequences on the physical nature of the anisotropic χ(n)s which appear to be highly composite objects. We address, from a birational viewpoint, the emergence of families of elliptic curves, and that of Calabi-Yau manifolds on such problems. We also address the question of singularities of non-holonomic functions with a discussion on the accumulation of these singular curves for the non-holonomic anisotropic full

Heterotic cosmic strings

International Nuclear Information System (INIS)

Becker, Katrin; Becker, Melanie; Krause, Axel

2006-01-01

We show that all three conditions for the cosmological relevance of heterotic cosmic strings, the right tension, stability and a production mechanism at the end of inflation, can be met in the strongly coupled M-theory regime. Whereas cosmic strings generated from weakly coupled heterotic strings have the well-known problems posed by Witten in 1985, we show that strings arising from M5-branes wrapped around 4-cycles (divisors) of a Calabi-Yau in heterotic M-theory compactifications solve these problems in an elegant fashion

Large volume axionic Swiss cheese inflation

Science.gov (United States)

Misra, Aalok; Shukla, Pramod

2008-09-01

Continuing with the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi Yau's, arXiv: 0707.0105 [hep-th], Nucl. Phys. B, in press], after inclusion of perturbative and non-perturbative α corrections to the Kähler potential and (D1- and D3-) instanton generated superpotential, we show the possibility of slow roll axionic inflation in the large volume limit of Swiss cheese Calabi Yau orientifold compactifications of type IIB string theory. We also include one- and two-loop corrections to the Kähler potential but find the same to be subdominant to the (perturbative and non-perturbative) α corrections. The NS NS axions provide a flat direction for slow roll inflation to proceed from a saddle point to the nearest dS minimum.

Large volume axionic Swiss cheese inflation

International Nuclear Information System (INIS)

Misra, Aalok; Shukla, Pramod

2008-01-01

Continuing with the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi-Yau's, (arXiv: 0707.0105 [hep-th]), Nucl. Phys. B, in press], after inclusion of perturbative and non-perturbative α ' corrections to the Kaehler potential and (D1- and D3-) instanton generated superpotential, we show the possibility of slow roll axionic inflation in the large volume limit of Swiss cheese Calabi-Yau orientifold compactifications of type IIB string theory. We also include one- and two-loop corrections to the Kaehler potential but find the same to be subdominant to the (perturbative and non-perturbative) α ' corrections. The NS-NS axions provide a flat direction for slow roll inflation to proceed from a saddle point to the nearest dS minimum

Origin of Abelian gauge symmetries in heterotic/F-theory duality

International Nuclear Information System (INIS)

Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng

2016-01-01

We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m)×U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m)×ℤ_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)’s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)’s is found by taking into account a Stückelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.

ZNxZM orbifolds and discrete torsion

International Nuclear Information System (INIS)

Font, A.; Quevedo, F.

1989-01-01

We extend previous work on Z N -orbifolds to the general Z N xZ M abelian case for both (2, 2) and (0, 2) models. We classify the corresponding (2, 2) compactifications and show that a number of models obtained by tensoring minimal N = 2 superconformal theories can be constructed as Z N xZ M -orbifolds. Furthermore, Z N xZ M -orbifolds allow the addition of discrete torsion which leads to new (2, 2) compactifications not considered previously. Some of the latter have negative Euler characteristics and Betti numbers equal to those of some complete intersection Calabi-Yau (CICY) manifolds. This suggests the existence of a previously overlooked connection between CICY models and orbifolds. (orig.)

Kac-Moody algebras and controlled chaos

International Nuclear Information System (INIS)

Wesley, Daniel H

2007-01-01

Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac-Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi-Yau, or M theory on a manifold of G 2 holonomy. (fast track communication)

Holomorphic Yukawa couplings in heterotic string theory

Energy Technology Data Exchange (ETDEWEB)

Blesneag, Stefan [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom); Buchbinder, Evgeny I. [The University of Western Australia,35 Stirling Highway, Crawley WA 6009 (Australia); Candelas, Philip [Mathematical Institute, University of Oxford,Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)

2016-01-26

We develop techniques, based on differential geometry, to compute holomorphic Yukawa couplings for heterotic line bundle models on Calabi-Yau manifolds defined as complete intersections in projective spaces. It is shown explicitly how these techniques relate to algebraic methods for computing holomorphic Yukawa couplings. We apply our methods to various examples and evaluate the holomorphic Yukawa couplings explicitly as functions of the complex structure moduli. It is shown that the rank of the Yukawa matrix can decrease at specific loci in complex structure moduli space. In particular, we compute the up Yukawa coupling and the singlet-Higgs-lepton trilinear coupling in the heterotic standard model described in ref. http://dx.doi.org/10.1007/JHEP06(2014)100.

Quantum entanglement of baby universes

International Nuclear Information System (INIS)

Aganagic, Mina; Okuda, Takuya; Ooguri, Hirosi

2007-01-01

We study quantum entanglements of baby universes which appear in non-perturbative corrections to the OSV formula for the entropy of extremal black holes in type IIA string theory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle over an arbitrary genus G Riemann surface. This generalizes the result for G=1 in hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions from baby universes, and the total wave-function is their coherent superposition in the third quantized Hilbert space. We find that half of the universes preserve one set of supercharges while the other half preserve a different set, making the total universe stable but non-BPS. The parent universe generates baby universes by brane/anti-brane pair creation, and baby universes are correlated by conservation of non-normalizable D-brane charges under the process. There are no other source of entanglement of baby universes, and all possible states are superposed with the equal weight

Quantum entanglement of baby universes

International Nuclear Information System (INIS)

Essman, Eric P.; Aganagic, Mina; Okuda, Takuya; Ooguri, Hirosi

2006-01-01

We study quantum entanglements of baby universes which appear in non-perturbative corrections to the OSV formula for the entropy of extremal black holes in type IIA string theory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle over an arbitrary genus G Riemann surface. This generalizes the result for G=1 in hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions from baby universes, and the total wave-function is their coherent superposition in the third quantized Hilbert space. We find that half of the universes preserve one set of supercharges while the other half preserve a different set, making the total universe stable but non-BPS. The parent universe generates baby universes by brane/anti-brane pair creation, and baby universes are correlated by conservation of non-normalizable D-brane charges under the process. There are no other source of entanglement of baby universes, and all possible states are superposed with the equal weight

The master space of N = 1 gauge theories

International Nuclear Information System (INIS)

Forcella, Davide; Hanany, Amihay; He Yanghui; Zaffaroni, Alberto

2008-01-01

The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X, M is a combination of the mesonic and baryonic branches. In consonance with the mathematical literature, the single brane moduli space is called the master space F b . Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F b is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F b and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode 'hidden' global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for N number of branes.

Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2

CERN Document Server

Couso-Santamaría, Ricardo; Schiappa, Ricardo; Vonk, Marcel

2015-01-01

The holomorphic anomaly equations describe B-model closed topological strings in Calabi-Yau geometries. Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by making use of resurgent transseries. These yield formal nonperturbative solutions, showing integrability of the holomorphic anomaly equations at the nonperturbative level. This paper takes such constructions one step further by working out in great detail the specific example of topological strings in the mirror of the local CP2 toric Calabi-Yau background, and by addressing the associated (resurgent) large-order analysis of both perturbative and multi-instanton sectors. In particular, analyzing the asymptotic growth of the perturbative free energies, one finds contributions from three different instanton actions related by Z_3 symmetry, alongside another action related to the Kahler parameter. Resurgent transseries methods then compute, from the extended holomorphic anomal...

String dualities and superpotential

International Nuclear Information System (INIS)

Ha, Tae-Won

2010-09-01

The main objective of this thesis is the computation of the superpotential induced by D5- branes in the type IIB string theory and by five-branes in the heterotic string theory. Both superpotentials have the same functional form which is the chain integral of the holomorphic three-form. Using relative (co)homology we can unify the flux and brane superpotential. The chain integral can be seen as an example of the Abel-Jacobi map. We discuss many structures such as mixed Hodge structure which allows for the computation of Picard-Fuchs differential equations crucial for explicit computations. We blow up the Calabi-Yau threefold along the submanifold wrapped by the brane to obtain geometrically more appropriate configuration. The resulting geometry is non-Calabi-Yau and we have a canonically given divisor. This blown-up geometry makes it possible to restrict our attention to complex structure deformations. However, the direct computation is yet very difficult, thus the main tool for computation will be the lift of the brane configuration to a F-theory compactification. In F-theory, since complex structure, brane and, if present, bundlemoduli are all contained in the complex structure moduli space of the elliptic Calabi-Yau fourfold, the computation can be dramatically simplified. The heterotic/F-theory duality is extended to include the blow-up geometry and thereby used to give the blow-up geometry amore physical meaning. (orig.)

String dualities and superpotential

Energy Technology Data Exchange (ETDEWEB)

Ha, Tae-Won

2010-09-15

The main objective of this thesis is the computation of the superpotential induced by D5- branes in the type IIB string theory and by five-branes in the heterotic string theory. Both superpotentials have the same functional form which is the chain integral of the holomorphic three-form. Using relative (co)homology we can unify the flux and brane superpotential. The chain integral can be seen as an example of the Abel-Jacobi map. We discuss many structures such as mixed Hodge structure which allows for the computation of Picard-Fuchs differential equations crucial for explicit computations. We blow up the Calabi-Yau threefold along the submanifold wrapped by the brane to obtain geometrically more appropriate configuration. The resulting geometry is non-Calabi-Yau and we have a canonically given divisor. This blown-up geometry makes it possible to restrict our attention to complex structure deformations. However, the direct computation is yet very difficult, thus the main tool for computation will be the lift of the brane configuration to a F-theory compactification. In F-theory, since complex structure, brane and, if present, bundlemoduli are all contained in the complex structure moduli space of the elliptic Calabi-Yau fourfold, the computation can be dramatically simplified. The heterotic/F-theory duality is extended to include the blow-up geometry and thereby used to give the blow-up geometry amore physical meaning. (orig.)

Standard-model bundles

CERN Document Server

Donagi, Ron; Pantev, Tony; Waldram, Dan; Donagi, Ron; Ovrut, Burt; Pantev, Tony; Waldram, Dan

2002-01-01

We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group ${\\mathbb Z}/2$. On each Calabi-Yau $Z$ in the family we exhibit a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group $SU(3)\\times SU(2)\\times U(1)$ and which have $c_{3} = 6$. We also show that for each bundle $V$ in our family, $c_{2}(Z) - c_{2}(V)$ is the class of an effective curve on $Z$. These conditions ensure that $Z$ and $V$ can be used for a phenomenologically relevant compactification of Heterotic M-theory.

Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds

International Nuclear Information System (INIS)

Parkhomenko, S.E.

2014-01-01

In this note we calculate elliptic genus in various examples of twisted chiral de Rham complex on two-dimensional toric compact manifolds and Calabi–Yau hypersurfaces in toric manifolds. At first the elliptic genus is calculated for the line bundle twisted chiral de Rham complex on a compact smooth toric manifold and K3 hypersurface in P 3 . Then we twist chiral de Rham complex by sheaves localized on positive codimension submanifolds in P 2 and calculate in each case the elliptic genus. In the last example the elliptic genus of chiral de Rham complex on P 2 twisted by SL(N) vector bundle with instanton number k is calculated. In all the cases considered we find the infinite tower of open string oscillator contributions and identify directly the open string boundary conditions of the corresponding bound state of D-branes

U(1) mediation of flux supersymmetry breaking

Science.gov (United States)

Grimm, Thomas W.; Klemm, Albrecht

2008-10-01

We study the mediation of supersymmetry breaking triggered by background fluxes in Type II string compactifications with Script N = 1 supersymmetry. The mediation arises due to an U(1) vector multiplet coupling to both a hidden supersymmetry breaking flux sector and a visible D-brane sector. The required internal manifolds can be constructed by non-Kähler resolutions of singular Calabi-Yau manifolds. The effective action encoding the U(1) coupling is then determined in terms of the global topological properties of the internal space. We investigate suitable local geometries for the hidden and visible sector in detail. This includes a systematic study of orientifold symmetries of del Pezzo surfaces realized in compact geometries after geometric transition. We construct compact examples admitting the key properties to realize flux supersymmetry breaking and U(1) mediation. Their toric realization allows us to analyze the geometry of curve classes and confirm the topological connection between the hidden and visible sector.

U(1) mediation of flux supersymmetry breaking

International Nuclear Information System (INIS)

Grimm, Thomas W.; Klemm, Albrecht

2008-01-01

We study the mediation of supersymmetry breaking triggered by background fluxes in Type II string compactifications with N = 1 supersymmetry. The mediation arises due to an U(1) vector multiplet coupling to both a hidden supersymmetry breaking flux sector and a visible D-brane sector. The required internal manifolds can be constructed by non-Kaehler resolutions of singular Calabi-Yau manifolds. The effective action encoding the U(1) coupling is then determined in terms of the global topological properties of the internal space. We investigate suitable local geometries for the hidden and visible sector in detail. This includes a systematic study of orientifold symmetries of del Pezzo surfaces realized in compact geometries after geometric transition. We construct compact examples admitting the key properties to realize flux supersymmetry breaking and U(1) mediation. Their toric realization allows us to analyze the geometry of curve classes and confirm the topological connection between the hidden and visible sector.

A three-generation superstring model. Pt. 1

International Nuclear Information System (INIS)

Greene, B.R.; Kirklin, K.H.; Miron, P.J.; Ross, G.G.

1986-01-01

We present the preliminary analysis of a three-generation heterotic superstring-inspired model. A detailed mathematical description of the manifold of compactification is given, along with a determination of its Hodge numbers and of the associated light supermultiplet structure. For a particular choice of vacuum moduli we derive this manifold's symmetry and groups, and determine their action on the massless fields in the theory. These transformation properties shall be shown, in a companion paper, to give rise to a model with interesting phenomenological properties. (orig.)

On the standard model group in F-theory

International Nuclear Information System (INIS)

Choi, Kang-Sin

2014-01-01

We analyze the standard model gauge group SU(3) x SU(2) x U(1) constructed in F-theory. The non-Abelian part SU(3) x SU(2) is described by a surface singularity of Kodaira type. Blow-up analysis shows that the non-Abelian part is distinguished from the naive product of SU(3) and SU(2), but that it should be a rank three group along the chain of E n groups, because it has non-generic gauge symmetry enhancement structure responsible for desirablematter curves. The Abelian part U(1) is constructed from a globally valid two-form with the desired gauge quantum numbers, using a similar method to the decomposition (factorization) method of the spectral cover. This technique makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU(5) is achieved, without requiring a threshold correction from the flux along the hypercharge direction. (orig.)

Anomaly cancelation in field theory and F-theory on a circle

International Nuclear Information System (INIS)

Grimm, Thomas W.; Kapfer, Andreas

2016-01-01

We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.

Dual little strings and their partition functions

Science.gov (United States)

Bastian, Brice; Hohenegger, Stefan; Iqbal, Amer; Rey, Soo-Jong

2018-05-01

We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds XN ,M at a generic point in the Kähler moduli space. These manifolds engineer little string theories in five dimensions or lower and are dual to stacks of M5-branes probing a transverse orbifold singularity. Using the refined topological vertex formalism, we explicitly calculate a generic building block which allows us to compute the topological string partition function of XN ,M as a series expansion in different Kähler parameters. Using this result, we give further explicit proof for a duality found previously in the literature, which relates XN ,M˜XN',M' for N M =N'M' and gcd (N ,M )=gcd (N',M') .

On stability of Kummer surfaces' tangent bundle

International Nuclear Information System (INIS)

Bozhkov, Y.D.

1988-10-01

In this paper we propose an explicit approximation of the Kaehler-Einstein-Calabi-Yau metric on the Kummer surfaces, which are manifolds of type K3. It is constructed by gluing 16 pieces of the Eguchi-Hanson metric and 16 pieces of the Euclidean metric. Two estimates on its curvature are proved. Then we prove an estimate on the first eigenvalue of a covariant differential operator of second order. This enables us to apply Taubes' iteration procedure to obtain that there exists an anti-self-dual connection on the considered Kummer surface. In fact, it is a Hermitian-Einstein connection from which we conclude that Kummer surfaces' co-tangent bundle is stable and therefore their tangent bundle is stable too. (author). 40 refs

Computing the scalar field couplings in 6D supergravity

Science.gov (United States)

Saidi, El Hassan

2008-11-01

Using non-chiral supersymmetry in 6D space-time, we compute the explicit expression of the metric the scalar manifold SO(1,1)×{SO(4,20)}/{SO(4)×SO(20)} of the ten-dimensional type IIA superstring on generic K3. We consider as well the scalar field self-couplings in the general case where the non-chiral 6D supergravity multiplet is coupled to generic n vector supermultiplets with moduli space SO(1,1)×{SO(4,n)}/{SO(4)×SO(n)}. We also work out a dictionary giving a correspondence between hyper-Kähler geometry and the Kähler geometry of the Coulomb branch of 10D type IIA on Calabi-Yau threefolds. Others features are also discussed.

Gravity duals of supersymmetric gauge theories on three-manifolds

International Nuclear Information System (INIS)

Farquet, Daniel; Lorenzen, Jakob; Martelli, Dario; Sparks, James

2016-01-01

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1)×U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.

Machine-learning the string landscape

Science.gov (United States)

He, Yang-Hui

2017-11-01

We propose a paradigm to apply machine learning various databases which have emerged in the study of the string landscape. In particular, we establish neural networks as both classifiers and predictors and train them with a host of available data ranging from Calabi-Yau manifolds and vector bundles, to quiver representations for gauge theories, using a novel framework of recasting geometrical and physical data as pixelated images. We find that even a relatively simple neural network can learn many significant quantities to astounding accuracy in a matter of minutes and can also predict hithertofore unencountered results, whereby rendering the paradigm a valuable tool in physics as well as pure mathematics. Of course, this paradigm is useful not only to physicists but to also to mathematicians; for instance, could our NN be trained well enough to approximate bundle cohomology calculations? This, and a host of other examples, we will now examine.Methodology  Neural networks are known for their complexity, involving usually a complicated directed graph each node of which is a ;perceptron; (an activation function imitating a neuron) and amongst the multitude of which there are many arrows encoding input/output. Throughout this letter, we will use a rather simple multi-layer perceptron (MLP) consisting of 5 layers, three of which are hidden, with activation functions typically of the form of a logistic sigmoid or a hyperbolic tangent. The input layer is a linear layer of 100 to 1000 nodes, recognizing a tensor (as we will soon see, algebro-geometric objects such as Calabi-Yau manifolds or polytopes are generically configurations of integer tensors) and the output layer is a summation layer giving a number corresponding to a Hodge number, or to rank of a cohomology group, etc. Such an MLP can be implemented, for instance, on the latest versions of Wolfram Mathematica. With 500-1000 training rounds, the running time is merely about 5-20 minutes on an ordinary laptop. It

Geometric symmetries and topological terms in F-theory and field theory

Energy Technology Data Exchange (ETDEWEB)

Kapfer, Andreas

2016-08-25

In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory. The first part treats settings of supersymmetry breaking in five dimensions. We focus on an N=4 to N=2 breaking in gauged supergravity. For certain classes of embedding tensors we can analyze the theory around the vacuum to a great extent. Importantly, one-loop corrections to Chern-Simons terms are generically induced which are independent of the supersymmetry-breaking scale. We investigate concrete examples of consistent truncations of supergravity and M-theory which show this N=4 to N=2 breaking pattern in five dimensions. In particular, we analyze necessary conditions for these consistent truncations to be used as effective theories for phenomenology by demanding consistency of the scale-independent corrections to Chern-Simons couplings. The second part is devoted to the study of anomalies and large gauge transformations in circle-reduced gauge theories and F-theory. We consider four- and six-dimensional matter-coupled gauge theories on the circle and classify all large gauge transformations that preserve the boundary conditions of the matter fields. Enforcing that they act consistently on one-loop Chern-Simons couplings in three and five dimensions explicitly yields all higher-dimensional gauge anomaly cancelation conditions. In the context of F-theory compactifications we identify the classified large gauge transformations along the circle with arithmetic structures on elliptically fibered Calabi-Yau manifolds via the dual M-theory setting. Integer Abelian large gauge transformations correspond to free basis shifts in the Mordell-Weil lattice of rational sections while special fractional non-Abelian large gauge transformations are matched to torsional shifts in the Mordell-Weil group. For integer non-Abelian large gauge transformations we

The N=1 effective action of F-theory compactifications

International Nuclear Information System (INIS)

Grimm, Thomas W.

2011-01-01

The four-dimensional N=1 effective action of F-theory compactified on a Calabi-Yau fourfold is studied by lifting a three-dimensional M-theory compactification. The lift is performed by using T-duality realized via a Legendre transform on the level of the effective action, and the application of vector-scalar duality in three dimensions. The leading order Kaehler potential and gauge-kinetic coupling functions are determined. In these compactifications two sources of gauge theories are present. Space-time filling non-Abelian seven-branes arise at the singularities of the elliptic fibration of the fourfold. Their couplings are included by resolving the singular fourfold. Generically a U(1) r gauge theory arises from the R-R bulk sector if the base of the elliptically fibered Calabi-Yau fourfold supports 2r harmonic three-forms. The gauge coupling functions depend holomorphically on the complex structure moduli of the fourfold, comprising closed and open string degrees of freedom. The four-dimensional electro-magnetic duality is studied in the three-dimensional effective theory obtained after M-theory compactification. A discussion of matter couplings transforming in the adjoint of the seven-brane gauge group is included.

Holomorphic D7-branes and flavored N=1 gauge theories

International Nuclear Information System (INIS)

Ouyang, Peter

2004-01-01

We consider D7-branes in the gauge theory/string theory correspondence, using a probe approximation. The D7-branes have four directions embedded holomorphically in a non-compact Calabi-Yau 3-fold (which for specificity we take to be the conifold) and their remaining four directions are parallel to a stack of D3-branes transverse to the Calabi-Yau space. The dual gauge theory, which has N=1 supersymmetry, contains quarks which transform in the fundamental representation of the gauge group, and we identify the interactions of these quarks in terms of a superpotential. By activating three-form fluxes in the gravity background, we obtain a dual gauge theory with a cascade of Seiberg dualities. We find a supersymmetric supergravity solution for the leading backreaction effects of the D7-branes, valid for large radius. The cascading theory with flavors exhibits the interesting phenomenon that the rate of the cascade slows and can stop as the theory flows to the infrared

F-theory vacua with $\\mathbb Z_3$ gauge symmetry

CERN Document Server

Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan; Poretschkin, Maximilian

2015-01-01

Discrete gauge groups naturally arise in F-theory compactifications on genus-one fibered Calabi-Yau manifolds. Such geometries appear in families that are parameterized by the Tate-Shafarevich group of the genus-one fibration. While the F-theory compactification on any element of this family gives rise to the same physics, the corresponding M-theory compactifications on these geometries differ and are obtained by a fluxed circle reduction of the former. In this note, we focus on an element of order three in the Tate-Shafarevich group of the general cubic. We discuss how the different M-theory vacua and the associated discrete gauge groups can be obtained by Higgsing of a pair of five-dimensional U(1) symmetries. The Higgs fields arise from vanishing cycles in $I_2$-fibers that appear at certain codimension two loci in the base. We explicitly identify all three curves that give rise to the corresponding Higgs fields. In this analysis the investigation of different resolved phases of the underlying geometry pla...

Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces

CERN Document Server

Hosono, S.; Theisen, S.; Yau, Shing-Tung

1995-01-01

We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton corrected Yukawa couplings and the topological one loop partition function to the case of complete intersections with higher dimensional moduli spaces. We will develop a new method of obtaining the instanton corrected Yukawa couplings through a study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the K\\"ahler moduli fields induced from the ambient space for all complete intersections in nonsingular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three generation models which are found in this class. We also apply our method to solve the simplest model in which topology change was observed and discuss examples of complete intersections in singular ambient spaces.

Modeling Diesel engine combustion using pressure dependent Flamelet Generated Manifolds

NARCIS (Netherlands)

Bekdemir, C.; Somers, L.M.T.; Goey, de L.P.H.

2011-01-01

Flamelet Generated Manifolds (FGMs) are constructed and applied to simulations of a conventional compression ignition engine cycle. To study the influence of pressure and temperature variations on the ignition process after the compression stroke, FGMs with several pressure levels are created. These

Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds

Energy Technology Data Exchange (ETDEWEB)

Assel, Benjamin; Martelli, Dario; Murthy, Sameer; Yokoyama, Daisuke [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom)

2017-03-17

We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS{sub 3}. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supersymmetry in manifolds with a conformal boundary, including supersymmetric actions and boundary conditions.

Compactifications of the Heterotic string with unitary bundles

Energy Technology Data Exchange (ETDEWEB)

Weigand, T.

2006-05-23

In this thesis we investigate a large new class of four-dimensional supersymmetric string vacua defined as compactifications of the E{sub 8} x E{sub 8} and the SO(32) heterotic string on smooth Calabi-Yau threefolds with unitary gauge bundles and heterotic five-branes. The first part of the thesis discusses the implementation of this idea into the E{sub 8} x E{sub 8} heterotic string. After specifying a large class of group theoretic embeddings featuring unitary bundles, we analyse the effective four-dimensional N=1 supergravity upon compactification. From the gauge invariant Kaehler potential for the moduli fields we derive a modification of the Fayet-Iliopoulos D-terms arising at one-loop in string perturbation theory. From this we conjecture a one-loop deformation of the Hermitian Yang-Mills equation and introduce the idea of {lambda}-stability as the perturbatively correct stability concept generalising the notion of Mumford stability valid at tree-level. We then proceed to a definition of SO(32) heterotic vacua with unitary gauge bundles in the presence of heterotic five-branes and find agreement of the resulting spectrum with the S-dual framework of Type I/Type IIB orientifolds. A similar analysis of the effective four-dimensional supergravity is performed. Further evidence for the proposed one-loop correction to the stability condition is found by identifying the heterotic corrections as the S-dual of the perturbative part of {pi}-stability as the correct stability concept in Type IIB theory. After reviewing the construction of holomorphic stable vector bundles on elliptically fibered Calabi-Yau manifolds via spectral covers, we provide semi-realistic examples for SO(32) heterotic vacua with Pati-Salam and MSSM-like gauge sectors. We finally discuss the construction of realistic vacua with flipped SU(5) GUT and MSSM gauge group within the E{sub 8} x E{sub 8} framework, based on the embedding of line bundles into both E{sub 8} factors. Some of the appealing

Can the superstring inspire the standard model?

International Nuclear Information System (INIS)

Ellis, J.; Enqvist, K.; Nanopoulos, D.V.; Olive, K.A.

1988-01-01

We discuss general features of models in which the E 8 xE' 8 heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m I to the standard model group SU(3) C x SU(2) L x U(1) Y , as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m I > or approx. 10 16 GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other ΔL ≠ 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions. (orig.)

General U(1)xU(1) F-theory Compactifications and Beyond: Geometry of unHiggsings and novel Matter Structure

CERN Document Server

Cvetic, Mirjam; Piragua, Hernan; Taylor, Washington

2015-01-01

We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)xU(1) gauge symmetry. Generic U(1)xU(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)xSU(2)xSU(3), SU(2)^3xSU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first expl...

Elliptic CY3folds and non-perturbative modular transformation

International Nuclear Information System (INIS)

Iqbal, Amer; Shabbir, Khurram

2016-01-01

We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections. (orig.)

Geometric transitions and integrable systems

International Nuclear Information System (INIS)

Diaconescu, D.-E.; Dijkgraaf, R.; Donagi, R.; Hofman, C.; Pantev, T.

2006-01-01

We consider B-model large N duality for a new class of noncompact Calabi-Yau spaces modeled on the neighborhood of a ruled surface in a Calabi-Yau threefold. The closed string side of the transition is governed at genus zero by an A 1 Hitchin integrable system on a genus g Riemann surface Σ. The open string side is described by a holomorphic Chern-Simons theory which reduces to a generalized matrix model in which the eigenvalues lie on the compact Riemann surface Σ. We show that the large N planar limit of the generalized matrix model is governed by the same A 1 Hitchin system therefore proving genus zero large N duality for this class of transitions

Elliptic CY3folds and non-perturbative modular transformation

Energy Technology Data Exchange (ETDEWEB)

Iqbal, Amer [Government College University, Abdus Salam School of Mathematical Sciences, Lahore (Pakistan); Shabbir, Khurram [Government College University, Department of Mathematics, Lahore (Pakistan)

2016-03-15

We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections. (orig.)

Geometric regularizations and dual conifold transitions

International Nuclear Information System (INIS)

Landsteiner, Karl; Lazaroiu, Calin I.

2003-01-01

We consider a geometric regularization for the class of conifold transitions relating D-brane systems on noncompact Calabi-Yau spaces to certain flux backgrounds. This regularization respects the SL(2,Z) invariance of the flux superpotential, and allows for computation of the relevant periods through the method of Picard-Fuchs equations. The regularized geometry is a noncompact Calabi-Yau which can be viewed as a monodromic fibration, with the nontrivial monodromy being induced by the regulator. It reduces to the original, non-monodromic background when the regulator is removed. Using this regularization, we discuss the simple case of the local conifold, and show how the relevant field-theoretic information can be extracted in this approach. (author)

Book Review:

Science.gov (United States)

Walcher, J.

2006-10-01

-sphere inside of T*S3, while the B-branes supporting the matrix models are wrapped on holomorphic curves in a certain class of toric Calabi Yau 3-folds. The gravity sides are reached via appropriate 'geometric transitions'. It is worth remarking that while the embedding in string theory gives a credible justification of the duality as well as a heuristic derivation, it also touches on at least as many questions as it answers: Are we restricted to non-compact Calabi Yau manifolds? Does the Chern Simons theory have to live on the 3-sphere (or a Lens space) or could it be a more general three-manifold? Why are we restricted to B-branes wrapping 2-cycles? Can we derive the duality from worldsheet considerations? Can we see open strings on the gravity side? What is the relevance of four-dimensional topological gauge theory? Certainly fully answering these questions requires mastering the 'phenomenology' of topological gauge/gravity duality, and this is precisely what this book helps to achieve. There are several important applications of these topological dualities. The A-model version is useful for the all-genus solution of the topological string on certain local Calabi Yau manifolds via the topological vertex. It also gives a new point of view on the theory of invariants of knots and three-manifolds via the incorporation of Wilson loops, which are dual to certain D-branes on the string theory side. On the other hand, the main application of the B-model topological gauge / gravity duality is to superpotential computations in four-dimensional N=1 gauge theories via the classical BCOV interpretation of topological amplitudes as computing F-terms in an effective space-time theory. The presentation is extremely well-balanced with an emphasis on computational techniques. This aspect in particular, and despite the large amount of required background material will facilitate access to the rich and fascinating subjects that are explained in the book. While written from the perspective of a

Multiple dark matter scenarios from ubiquitous stringy throats

DEFF Research Database (Denmark)

Chialva, D.; Dev, P.S.B.; Mazumdar, A.

2013-01-01

We discuss the possibility of having multiple Kaluza-Klein dark matter candidates which arise naturally in generic type-IIB string theory compactification scenarios. These dark matter candidates reside in various throats of the Calabi-Yau manifold. In principle, they can come with a varied range......, we find that the mass scales allowed for the Kaluza-Klein dark matter particles in various throats can vary between 0.1 eV and 10 TeV, depending upon the throat geometry. Thus, there could be simultaneously more than one kind of cold (and possibly warm and hot) dark matter components residing...... in the Universe. This multiple dark matter scenario could weaken the bound on a conventional supersymmetric dark matter candidate and could also account for extra relativistic degrees of freedom in our Universe....

Point interactions in two- and three-dimensional Riemannian manifolds

International Nuclear Information System (INIS)

Erman, Fatih; Turgut, O Teoman

2010-01-01

We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac-delta interactions on two- and three-dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator Φ(E). In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for a general class of manifolds, e.g. for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by the Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the β function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by Rajeev.

Gauged supergravities from M-theory reductions

Science.gov (United States)

Katmadas, Stefanos; Tomasiello, Alessandro

2018-04-01

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.

Swiss-Cheese Gravitino Dark Matter

Science.gov (United States)

Misra, Aalok

2014-06-01

We present a phenomenological model which we show can be obtained as a local realization of large volume D 3 / D 7 μ-Split SUSY on a nearly special Lagrangian three-cycle embedded in the big divisor of a Swiss-Cheese Calabi-Yau [Mansi Dhuria, Aalok Misra, arxiv:arXiv:1207.2774 [hep-ph], Nucl. Phys. B867 (2013) 636-748]. After identification of the first generation of SM leptons and quarks with fermionic super-partners of four Wilson line moduli, we discuss the identification of gravitino as a potential dark matter candidate. We also show that it is possible to obtain a 125 GeV light Higgs in our setup.

Swiss-Cheese Gravitino Dark Matter

International Nuclear Information System (INIS)

Misra, Aalok

2014-01-01

We present a phenomenological model which we show can be obtained as a local realization of large volume D3/D7μ-Split SUSY on a nearly special Lagrangian three-cycle embedded in the big divisor of a Swiss-Cheese Calabi-Yau [Mansi Dhuria, Aalok Misra, (arXiv:1207.2774 [hep-ph]), Nucl. Phys. B867 (2013) 636–748]. After identification of the first generation of SM leptons and quarks with fermionic super-partners of four Wilson line moduli, we discuss the identification of gravitino as a potential dark matter candidate. We also show that it is possible to obtain a 125 GeV light Higgs in our setup

Swiss-Cheese Gravitino Dark Matter

Energy Technology Data Exchange (ETDEWEB)

Misra, Aalok

2014-06-15

We present a phenomenological model which we show can be obtained as a local realization of large volume D3/D7μ-Split SUSY on a nearly special Lagrangian three-cycle embedded in the big divisor of a Swiss-Cheese Calabi-Yau [Mansi Dhuria, Aalok Misra, (arXiv:1207.2774 [hep-ph]), Nucl. Phys. B867 (2013) 636–748]. After identification of the first generation of SM leptons and quarks with fermionic super-partners of four Wilson line moduli, we discuss the identification of gravitino as a potential dark matter candidate. We also show that it is possible to obtain a 125 GeV light Higgs in our setup.

Modeling of complex premixed burner systems by using flamelet-generated manifolds

NARCIS (Netherlands)

Oijen, van J.A.; Lammers, F.A.; Goey, de L.P.H.

2001-01-01

The numerical modeling of realistic burner systems puts a very high demand on computational recources.The computational cost of combustion simulations can be reduced by reduction techniques which simplify the chemical kinetics. In this paper the recently introduced Flamelet-Generated Manifold method

D-brane physics. From weak to strong coupling

Energy Technology Data Exchange (ETDEWEB)

Vieira Lopes, Daniel Ordine

2013-01-10

In this thesis we discuss two aspects of branes relevant to high-energy phenomenology. First, we consider a single D6-brane wrapping a special Lagrangian cycle and the background space compactified in a Calabi-Yau orientifold the conditions needed to obtain a four-dimensional N=1 supersymmetric theory. We calculate the bosonic part of the effective action by performing a Kaluza-Klein reduction of the brane seven-dimensional action, and obtain the N=1 characteristic data. To discuss the moduli, we first fix the moduli from deformations of the background Calabi-Yau and study the D-brane deformation moduli space. We next allow for Calabi-Yau deformations, and show that the moduli space for complex structure deformations is corrected by the fields living on the D6-brane. We also calculate the scalar potential from D- and F-terms generated from brane and background configurations that would break the supersymmetry condition. We then, via Mirror Symmetry, relate the spectrum obtained in our work to the spectrum in Type IIB effective theory with D3- D5- and D7-branes, and we propose a Kaehler potential for the moduli space of brane deformations in Type IIB theories. In the second part of the thesis we discuss effects of brane intersections when the string coupling can become strong, and we work in the framework of F-theory. After reviewing the basics of F-theory constructions and a particular SU(5) model already discussed in the literature, we construct a model which contains a point of E{sub 8} singularity, and curves of E{sub 6} singularity. By explicitly resolving the space, we show that the resolution requires the introduction of higher dimensional fibers, and argue how we can circumvent this problem for the E{sub 6} curve, leading to the expected resolution that generate an E{sub 6} group, while at the E{sub 8} point we cannot make the resolution lead to an expected E{sub 8} structure.

N=1 Mirror Symmetry and Open/Closed String Duality

CERN Document Server

Mayr, Peter

2002-01-01

We show that the exact N=1 superpotential of a class of 4d string compactifications is computed by the closed topological string compactified to two dimensions. A relation to the open topological string is used to define a special geometry for N=1 mirror symmetry. Flat coordinates, an N=1 mirror map for chiral multiplets and the exact instanton corrected superpotential are obtained from the periods of a system of differential equations. The result points to a new class of open/closed string dualities which map individual string world-sheets with boundary to ones without. It predicts an mathematically unexpected coincidence of the closed string Gromov-Witten invariants of one Calabi-Yau geometry with the open string invariants of the dual Calabi-Yau.

Premixed and non-premixed generated manifolds in large-eddy simulation of Sandia flame D and F

NARCIS (Netherlands)

Vreman, A.W.; Albrecht, B.A.; Oijen, van J.A.; Goey, de L.P.H.; Bastiaans, R.J.M.

2008-01-01

Premixed and nonpremixed flamelet-generated manifolds have been constructed and applied to large-eddy simulation of the piloted partially premixed turbulent flames Sandia Flame D and F. In both manifolds the chemistry is parameterized as a function of the mixture fraction and a progress variable.

Flamelet Generated Manifold Strategies in Modeling of an Igniting Diesel Spray

NARCIS (Netherlands)

Bekdemir, C.; Somers, L.M.T.; Goey, de L.P.H.

2009-01-01

A study is presented on the modeling of fuel spray combustion in diesel engines. The objective is to model igniting diesel sprays with the detailed chemistry tabulation method FGM (Flamelet GeneratedManifold). The emphasis is on the accurate prediction of auto-ignition as well as the steady

Hyperspin manifolds

International Nuclear Information System (INIS)

Finkelstein, D.; Finkelstein, S.R.; Holm, C.

1986-01-01

Riemannian manifolds are but one of three ways to extrapolate from fourdimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors by N-ary hyperspinors with new ''internal'' components besides the usual two ''external'' ones, this leads to a second line, the hyperspin manifolds /sub n/ and their tangent spaces d/sub n/, different in structure and symmetry group from the Riemannian line, except that the binary spaces d 2 (Minkowski time space) and 2 (Minkowskian manifold) lie on both. d/sub n/ and /sub n/ have dimension n = N 2 . In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and the N-ary chronometric form is not quadratic, but N-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist

Some problems of dynamical systems on three dimensional manifolds

International Nuclear Information System (INIS)

Dong Zhenxie.

1985-08-01

It is important to study the dynamical systems on 3-dimensional manifolds, its importance is showing up in its close relation with our life. Because of the complication of topological structure of Dynamical systems on 3-dimensional manifolds, generally speaking, the search for 3-dynamical systems is not easier than 2-dynamical systems. This paper is a summary of the partial result of dynamical systems on 3-dimensional manifolds. (author)

Pop / Tõnu Kaalep

Index Scriptorium Estoniae

Kaalep, Tõnu, 1966-

2003-01-01

Heliplaatidest: Mihkel Kleis "Quest For Fire/Visit To Minotaur", Andrew W. K. "The Wolf",Client "Client", Bubba Sparxxx "Deliverance", Yes "The Ultimate Yes - 35th Anniversary Collection", Joseph Suchy "calabi.yau", Luomo "Present Lover"

Flux compactifications and generalized geometries

International Nuclear Information System (INIS)

Grana, Mariana

2006-01-01

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry

Flux compactifications and generalized geometries

Energy Technology Data Exchange (ETDEWEB)

Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)

2006-11-07

Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

Orientifolds and D-branes in N=2 gauged linear sigma models

CERN Document Server

Brunner, Ilka

We study parity symmetries and boundary conditions in the framework of gauged linear sigma models. This allows us to investigate the Kaehler moduli dependence of the physics of D-branes as well as orientifolds in a Calabi-Yau compactification. We first determine the parity action on D-branes and define the set of orientifold-invariant D-branes in the linear sigma model. Using probe branes on top of orientifold planes, we derive a general formula for the type (SO vs Sp) of orientifold planes. As applications, we show how compactifications with and without vector structure arise naturally at different real slices of the Kaehler moduli space of a Calabi-Yau compactification. We observe that orientifold planes located at certain components of the fixed point locus can change type when navigating through the stringy regime.

Problems for superstring models with vacuum expectation values for conjugate sneutrinos

International Nuclear Information System (INIS)

Campbell, B.; Ellis, J.; Gaillard, M.K.; Nanopoulos, D.V.; Olive, K.A.

1986-01-01

Superstring models compactified on Calabi-Yau manifolds contain two new neutral scalars in each 27 generation of chiral supermultiplets. We consider implications of a vacuum expectation value for one of the neutral scalars, the conjugates neutrino ν tilde L c : L c vertical stroke0>=y. Apart from a coupling which generates a Dirac neutrino mass and which must be small [ -9 )], its only superpotential interaction is with D L d L , so there wold be D-d mixing if y≠0. The fact that m d is not much less than m e or m u then tells us that y ν , arises if y≠0, and the D-d mixing would then induce the decay K→π+a ν at an unacceptable rate. Regardless of the gauge group rank, we show that the combined constraints on D-d mixing, and on the flavour-changing neutral currents it would induce, are sufficient to rule out D L d L c ν L c superpotential coupling large enough to produce L c vertical stroke0>≠0. These problems are avoided in models with a rank-5 gauge group and L c vertical stroke0>< or approx.40 KeV. (orig.)

Can the superstring inspire the standard model

Energy Technology Data Exchange (ETDEWEB)

Ellis, J.; Enqvist, K.; Nanopoulos, D.V.; Olive, K.A.

1988-02-01

We discuss general features of models in which the E/sub 8/xE'/sub 8/ heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m/sub I/ to the standard model group SU(3)/sub C/ x SU(2)/sub L/ x U(1)/sub Y/, as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m/sub I/ > or approx. 10/sup 16/ GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other ..delta..L not = 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions.

Y-formalism and curved {beta}-{gamma} systems

Energy Technology Data Exchange (ETDEWEB)

Grassi, Pietro Antonio [DISTA, Universita del Piemonte Orientale, via Bellini 25/g, 15100 Alessandria (Italy); INFN - Sezione di Torino (Italy)], E-mail: antonio.pietro.grassi@cern.ch; Oda, Ichiro [Department of Physics, Faculty of Science, University of the Ryukyus, Nishihara, Okinawa 903-0213 (Japan); Tonin, Mario [Dipartimento di Fisica, Universita degli Studi di Padova, INFN, Sezionedi Padova, Via F. Marzolo 8, 35131 Padova (Italy)

2009-01-01

We adopt the Y-formalism to study {beta}-{gamma} systems on hypersurfaces. We compute the operator product expansions of gauge-invariant currents and we discuss some applications of the Y-formalism to model on Calabi-Yau spaces.

Y-formalism and curved β-γ systems

International Nuclear Information System (INIS)

Grassi, Pietro Antonio; Oda, Ichiro; Tonin, Mario

2009-01-01

We adopt the Y-formalism to study β-γ systems on hypersurfaces. We compute the operator product expansions of gauge-invariant currents and we discuss some applications of the Y-formalism to model on Calabi-Yau spaces

Wilson loops on three-manifolds and their M2-brane duals

International Nuclear Information System (INIS)

Farquet, Daniel; Sparks, James

2014-01-01

We compute the large N limit of Wilson loop expectation values for a broad class of N=2 supersymmetric gauge theories defined on a general class of background three-manifolds M_3, diffeomorphic to S"3. We find a simple closed formula which depends on the background geometry only through a certain supersymmetric Killing vector field. The supergravity dual of such a Wilson loop is an M2-brane wrapping the M-theory circle, together with a complex curve Σ_2 in a self-dual Einstein manifold M_4, whose conformal boundary is M_3. We show that the regularized action of this M2-brane also depends only on the supersymmetric Killing vector, precisely reproducing the large N field theory computation.

Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds

Science.gov (United States)

Roth, Julien

2010-06-01

We give spinorial characterizations of isometrically immersed surfaces into three-dimensional homogeneous manifolds with four-dimensional isometry group in terms of the existence of a particular spinor field. This generalizes works by Friedrich for R3 and Morel for S3 and H3. The main argument is the interpretation of the energy-momentum tensor of such a spinor field as the second fundamental form up to a tensor depending on the structure of the ambient space.

String loop moduli stabilisation and cosmology in IIB flux compactifications

International Nuclear Information System (INIS)

Cicoli, M.

2010-01-01

We present a detailed review of the moduli stabilisation mechanism and possible cosmological implications of the LARGE Volume Scenario (LVS) that emerges naturally in the context of type IIB Calabi-Yau flux compactifications. After a quick overview of physics beyond the Standard Model, we present string theory as the most promising candidate for a consistent theory of quantum gravity. We then give a pedagogical introduction to type IIB compactifications on Calabi-Yau orientifolds where most of the moduli are stabilised by turning on background fluxes. However in order to fix the Kaehler moduli one needs to consider several corrections beyond the leading order approximations. After presenting a survey of all the existing solutions to this problem, we derive the topological conditions on an arbitrary Calabi-Yau to obtain the LVS since it requires no fine-tuning of the fluxes and provides a natural solution of the hierarchy problem. After performing a systematic study of the behaviour of string loop corrections for general type IIB compactifications, we show how they play a crucial role to achieve full Kaehler moduli stabilisation in the LVS. Before examining the possible cosmological implication of these scenarios, we present a broad overview of string cosmology. We then notice how, in the case of K3-fibrations, string loop corrections give rise naturally to an inflationary model which yields observable gravity waves. We finally study the finite-temperature behaviour of the LVS and discuss prospects for future work. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem

Science.gov (United States)

Guzzo, Massimiliano; Lega, Elena

2018-06-01

The circular restricted three-body problem has five relative equilibria L1 ,L2, . . . ,L5. The invariant stable-unstable manifolds of the center manifolds originating at the partially hyperbolic equilibria L1 ,L2 have been identified as the separatrices for the motions which transit between the regions of the phase-space which are internal or external with respect to the two massive bodies. While the stable and unstable manifolds of the planar problem have been extensively studied both theoretically and numerically, the spatial case has not been as deeply investigated. This paper is devoted to the global computation of these manifolds in the spatial case with a suitable finite time chaos indicator. The definition of the chaos indicator is not trivial, since the mandatory use of the regularizing Kustaanheimo-Stiefel variables may introduce discontinuities in the finite time chaos indicators. From the study of such discontinuities, we define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifolds of L1 ,L2. We illustrate the method for the Sun-Jupiter mass ratio, and represent the topology of the asymptotic manifolds using sections and three-dimensional representations.

Refined BPS invariants of 6d SCFTs from anomalies and modularity

Energy Technology Data Exchange (ETDEWEB)

Gu, Jie [Laboratoire de Physique Théorique de l’École Normale Supérieure, CNRS,PSL Research University, Sorbonne Universités, UPMC,75005 Paris (France); Huang, Min-xin [Interdisciplinary Center for Theoretical Study, University of Science and Technology of China,Hefei, Anhui 230026 (China); Kashani-Poor, Amir-Kian [Laboratoire de Physique Théorique de l’École Normale Supérieure, CNRS,PSL Research University, Sorbonne Universités, UPMC,75005 Paris (France); Klemm, Albrecht [Bethe Center for Theoretical Physics (BCTP), Physikalisches Institut, Universität Bonn,53115 Bonn (Germany)

2017-05-23

F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function Z{sub top} of the refined topological string on these geometries captures the particle BPS spectrum of this class of theories compactified on a circle. Organizing Z{sub top} in terms of contributions Z{sub β} at base degree β of the elliptic fibration, we find that these, up to a multiplier system, are meromorphic Jacobi forms of weight zero with modular parameter the Kähler class of the elliptic fiber and elliptic parameters the couplings and mass parameters. The indices with regard to the multiple elliptic parameters are fixed by the refined holomorphic anomaly equations, which we show to be completely determined from knowledge of the chiral anomaly of the corresponding SCFT. We express Z{sub β} as a quotient of weak Jacobi forms, with a universal denominator inspired by its pole structure as suggested by the form of Z{sub top} in terms of 5d BPS numbers. The numerator is determined by modularity up to a finite number of coefficients, which we prove to be fixed uniquely by imposing vanishing conditions on 5d BPS numbers as boundary conditions. We demonstrate the feasibility of our approach with many examples, in particular solving the E-string and M-string theories including mass deformations, as well as theories constructed as chains of these. We make contact with previous work by showing that spurious singularities are cancelled when the partition function is written in the form advocated here. Finally, we use the BPS invariants of the E-string thus obtained to test a generalization of the Göttsche-Nakajima-Yoshioka K-theoretic blowup equation, as inspired by the Grassi-Hatsuda-Mariño conjecture, to generic local Calabi-Yau threefolds.

Static BPS black holes in AdS{sub 4} with general dyonic charges

Energy Technology Data Exchange (ETDEWEB)

Halmagyi, Nick [Sorbonne Universités, UPMC Paris 06, UMR 7589, LPTHE,75005, Paris (France); CNRS, UMR 7589, LPTHE,75005, Paris (France)

2015-03-06

We complete the study of static BPS, asymptotically AdS{sub 4} black holes within N=2 FI-gauged supergravity and where the scalar manifold is a symmetric very special Kähler manifold. We find the analytic form for the general solution to the BPS equations, the horizon appears as a double root of a particular quartic polynomial whereas in previous work this quartic polynomial further factored into a pair of double roots. A new and distinguishing feature of our solutions is that the phase of the supersymmetry parameter varies throughout the black hole. The general solution has 2n{sub v} independent parameters; there are two algebraic constraints on 2n{sub v}+2 charges, matching our previous analysis on BPS solutions of the form AdS{sub 2}×Σ{sub g}. As a consequence we have proved that every BPS geometry of this form can arise as the horizon geometry of a BPS AdS{sub 4} black hole. When specialized to the STU-model our solutions uplift to M-theory and describe a stack of M2-branes wrapped on a Riemman surface in a Calabi-Yau fivefold with internal angular momentum.

Geometric singularities and spectra of Landau-Ginzburg models

International Nuclear Information System (INIS)

Greene, B.R.; Roan, S.S.; Yau, S.T.

1991-01-01

Some mathematical and physical aspects of superconformal string compactification in weighted projective space are discussed. In particular, we recast the path integral argument establishing the connection between Landau-Ginsburg conformal theories and Calabi-Yau string compactification in a geometric framework. We then prove that the naive expression for the vanishing of the first Chern class for a complete intersection (adopted from the smooth case) is sufficient to ensure that the resulting variety, which is generically singular, can be resolved to a smooth Calabi-Yau space. This justifies much analysis which has recently been expended on the study of Landau-Ginzburg models. Furthermore, we derive some simple formulae for the determination of the Witten index in these theories which are complementary to those derived using semiclassical reasoning by Vafa. Finally, we also comment on the possible geometrical significance of unorbifolded Landau-Ginzburg theories. (orig.)

Birationality and Landau-Ginzburg Models

Science.gov (United States)

Clarke, Patrick

2017-08-01

We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev-Nill (Integer points in polyhedra—geometry, number theory, representation theory, algebra, optimization, statistics, volume 452 of Contemporary mathematics. American Mathematical Society, Providence, pp 35-66, 2008) about the birationality of Calabi-Yau families associated to multiple mirror nef-partitions. This completes the progress in this direction made by Li's breakthrough (Li in Adv Math 299:71-107, 2016). In the process, we obtain results in the theory of Borisov's nef-partitions (Borisov in Towards the mirror symmetry for Calabi-Yau complete intersections in Gorenstein toric Fano varieties, 1993. arXiv:alg-geom/9310001 ) and provide new insight into the geometric content of the multiple mirror phenomenon.

A TQFT associated to the LMO invariant of three-dimensional manifolds

DEFF Research Database (Denmark)

Cheptea, Dorin; Le, Thang

2007-01-01

We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is ......We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category...

Generalized graph manifolds and their effective recognition

International Nuclear Information System (INIS)

Matveev, S V

1998-01-01

A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented

New N=1 superconformal field theories in four dimensions from D-brane probes

International Nuclear Information System (INIS)

Aharony, O.; Kachru, S.; Silverstein, E.

1997-01-01

We present several new examples of non-trivial 4D N=1 superconformal field theories. Some of these theories exhibit exotic global symmetries, including non-simply laced groups (such as F 4 ). They are obtained by studying three-brane probes in F-theory compactifications on elliptic Calabi-Yau threefolds. The geometry of the compactification encodes in a simple way the behavior of the gauge coupling and the Kaehler potential on the Coulomb branch of these theories. (orig.)

Evaluating Small Sphere Limit of the Wang-Yau Quasi-Local Energy

Science.gov (United States)

Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

2018-01-01

In this article, we study the small sphere limit of the Wang-Yau quasi-local energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009, Commun Math Phys 288(3):919-942, 2009). Given a point p in a spacetime N, we consider a canonical family of surfaces approaching p along its future null cone and evaluate the limit of the Wang-Yau quasi-local energy. The evaluation relies on solving an "optimal embedding equation" whose solutions represent critical points of the quasi-local energy. For a spacetime with matter fields, the scenario is similar to that of the large sphere limit found in Chen et al. (Commun Math Phys 308(3):845-863, 2011). Namely, there is a natural solution which is a local minimum, and the limit of its quasi-local energy recovers the stress-energy tensor at p. For a vacuum spacetime, the quasi-local energy vanishes to higher order and the solution of the optimal embedding equation is more complicated. Nevertheless, we are able to show that there exists a solution that is a local minimum and that the limit of its quasi-local energy is related to the Bel-Robinson tensor. Together with earlier work (Chen et al. 2011), this completes the consistency verification of the Wang-Yau quasi-local energy with all classical limits.

1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry

International Nuclear Information System (INIS)

Kim, Hyojoong; Kim, Kyung Kiu; Kim, Nakwoo

2007-01-01

In this paper we generalize the work of Lin, Lunin and Maldacena on the classification of 1/2-BPS M-theory solutions to a specific class of 1/4-BPS configurations. We are interested in the solutions of 11 dimensional supergravity with SO(3) x SO(4) symmetry, and it is shown that such solutions are constructed over a one-parameter familiy of 4 dimensional almost Calabi-Yau spaces. Through analytic continuations we can obtain M-theory solutions having AdS 2 x S 3 or AdS 3 x S 2 factors. It is shown that our result is equivalent to the AdS solutions which have been recently reported as the near-horizon geometry of M2 or M5-branes wrapped on 2 or 4-cycles in Calabi-Yau threefolds. We also discuss the hierarchy of M-theory bubbles with different number of supersymmetries

N = 1 dual string pairs and their modular superpotentials

International Nuclear Information System (INIS)

Luest, D.

1998-01-01

We review the duality between heterotic and F-theory string vacua with N=1 space-time supersymmetry in eight, six and four dimensions. In particular, we discuss two chains of four-dimensional F-theory/heterotic dual string pairs, where F-theory is compactified on certain elliptic Calabi-Yau fourfolds, and the dual heterotic vacua are given by compactifications on elliptic Calabi-Yau threefolds plus the specification of the E 8 x E 8 gauge bundles. We show that the massless spectra of the dual pairs agree by using, for one chain of models, an index formula to count the heterotic bundle moduli and determine the dual F-theory spectra from the Hodge numbers of the fourfolds and of the type IIB base spaces. Moreover as a further check, we demonstrate that for one particular heterotic/F-theory dual pair the N=1 superpotentials are the same. (orig.)

Quiver gauge theory and extended electric-magnetic duality

International Nuclear Information System (INIS)

Maruyoshi, Kazunobu

2009-01-01

We construct N = 1 A-D-E quiver gauge theory with the gauge kinetic term which depends on the adjoint chiral superfields, as a low energy effective theory on D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The field-dependent gauge kinetic term can be engineered by introducing B-field which holomorphically varies on the base space (complex plane) of Calabi-Yau. We consider Weyl reflection on A-D-E node, which acts non-trivially on the gauge kinetic term. It is known that Weyl reflection is related to N = 1 electric-magnetic duality. Therefore, the non-trivial action implies an extension of the electric-magnetic duality to the case with the field-dependent gauge kinetic term. We show that this extended duality is consistent from the field theoretical point of view. We also consider the duality map of the operators.

Calabi–Yau metrics and string compactification

Directory of Open Access Journals (Sweden)

Michael R. Douglas

2015-09-01

Full Text Available Yau proved an existence theorem for Ricci-flat Kähler metrics in the 1970s, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory.

Estimating Turaev-Viro three-manifold invariants is universal for quantum computation

International Nuclear Information System (INIS)

Alagic, Gorjan; Reichardt, Ben W.; Jordan, Stephen P.; Koenig, Robert

2010-01-01

The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-dimensional topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a relation between the task of distinguishing nonhomeomorphic 3-manifolds and the power of a general quantum computer.

Remodeling the B-model

CERN Document Server

Bouchard, Vincent; Marino, Marcos; Pasquetti, Sara

2009-01-01

We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi-Yau geometries, including the mirrors of toric manifolds. The formalism is based on the recursive solution of matrix models recently proposed by Eynard and Orantin. The resulting amplitudes are non-perturbative in both the closed and the open moduli. The formalism can then be used to study stringy phase transitions in the open/closed moduli space. At large radius, this formalism may be seen as a mirror formalism to the topological vertex, but it is also valid in other phases in the moduli space. We develop the formalism in general and provide an extensive number of checks, including a test at the orbifold point of A_p fibrations, where the amplitudes compute the 't Hooft expansion of Wilson loops in lens spaces. We also use our formalism to predict the disk amplitude for the orbifold C^3/Z_3.

Enhanced gauge symmetry in type II string theory

International Nuclear Information System (INIS)

Katz, S.; Ronen Plesser, M.

1996-01-01

We show how enhanced gauge symmetry in type II string theory compactified on a Calabi-Yau threefold arises from singularities in the geometry of the target space. When the target space of the type IIA string acquires a genus g curve C of A N-1 singularities, we find that an SU(N) gauge theory with g adjoint hypermultiplets appears at the singularity. The new massless states correspond to solitons wrapped about the collapsing cycles, and their dynamics is described by a twisted supersymmetric gauge theory on C x R 4 . We reproduce this result from an analysis of the S-dual D-manifold. We check that the predictions made by this model about the nature of the Higgs branch, the monodromy of period integrals, and the asymptotics of the one-loop topological amplitude are in agreement with geometrical computations. In one of our examples we find that the singularity occurs at strong coupling in the heterotic dual proposed by Kachru and Vafa. (orig.)

Vertex operator algebras and conformal field theory

International Nuclear Information System (INIS)

Huang, Y.Z.

1992-01-01

This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics

Residues and world-sheet instantons

International Nuclear Information System (INIS)

Beasley, Chris; Witten, Edward

2003-01-01

We reconsider the question of which Calabi-Yau compactifications of the heterotic string are stable under world-sheet instanton corrections to the effective space-time superpotential. For instance, compactifications described by (0; 2) linear sigma models are believed to be stable, suggesting a remarkable cancellation among the instanton effects in these theories. Here, we show that this cancellation follows directly from a residue theorem, whose proof relies only upon the right-moving world-sheet supersymmetries and suitable compactness properties of the (0; 2) linear sigma model. Our residue theorem also extends to a new class of 'half-linear' sigma models. Using these half-linear models, we show that heterotic compactifications on the quintic hypersurface in CP 4 for which the gauge bundle pulls back from a bundle on CP 4 are stable. Finally, we apply similar ideas to compute the superpotential contributions from families of membrane instantons in M-theory compactifications on manifolds of G 2 holonomy. (author)

Fluxbrane Inflation

CERN Document Server

Hebecker, Arthur; Lust, Dieter; Steinfurt, Stephan; Weigand, Timo

2012-01-01

As a first step towards inflation in genuinely F-theoretic setups, we propose a scenario where the inflaton is the relative position of two 7-branes on holomorphic 4-cycles. Non-supersymmetric gauge flux induces an attractive inter-brane potential. The latter is sufficiently flat in the supergravity regime of large volume moduli. Thus, in contrast to brane-antibrane inflation, fluxbrane inflation does not require warping. We calculate the inflaton potential both in the supergravity approximation and via an open-string one-loop computation on toroidal backgrounds. This leads us to propose a generalisation to genuine Calabi-Yau manifolds. We also comment on competing F-term effects. The end of inflation is marked by the condensation of tachyonic recombination fields between the 7-branes, triggering the formation of a bound state described as a stable extension along the 7-brane divisor. Hence our model fits in the framework of hybrid D-term inflation. We work out the main phenomenological properties of our D-te...

Non-Perturbative Quantum Geometry III

CERN Document Server

Krefl, Daniel

2016-08-02

The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.

The D5-brane effective action and superpotential in N=1 compactifications

International Nuclear Information System (INIS)

Grimm, Thomas W.; Ha, Tae-Won; Klemm, Albrecht; Klevers, Denis

2009-01-01

The four-dimensional effective action for D5-branes in generic compact Calabi-Yau orientifolds is computed by performing a Kaluza-Klein reduction. The N=1 Kaehler potential, the superpotential, the gauge-kinetic coupling function and the D-terms are derived in terms of the geometric data of the internal space and of the two-cycle wrapped by the D5-brane. In particular, we obtain the D5-brane and flux superpotential by integrating out four-dimensional three-forms which couple via the Chern-Simons action. Also the infinitesimal complex structure deformations of the two-cycle induced by the deformations of the ambient space contribute to the F-terms. The superpotential can be expressed in terms of relative periods depending on both the open and closed moduli. To analyze this dependence we blow up along the two-cycle and obtain a rigid divisor in an auxiliary compact threefold with negative first Chern class. The variation of the mixed Hodge structure on this blown-up geometry is equivalent to the original deformation problem and can be analyzed by Picard-Fuchs equations. We exemplify the blow-up procedure for a non-compact Calabi-Yau threefold given by the canonical bundle over del Pezzo surfaces.

Physics of F-theory compactifications without section

International Nuclear Information System (INIS)

Anderson, Lara B.; García-Etxebarria, Iñaki; Grimm, Thomas W.; Keitel, Jan

2014-01-01

We study the physics of F-theory compactifications on genus-one fibrations without section by using an M-theory dual description. The five-dimensional action obtained by considering M-theory on a Calabi-Yau threefold is compared with a six-dimensional F-theory effective action reduced on an additional circle. We propose that the six-dimensional effective action of these setups admits geometrically massive U(1) vectors with a charged hypermultiplet spectrum. The absence of a section induces NS-NS and R-R three-form fluxes in F-theory that are non-trivially supported along the circle and induce a shift-gauging of certain axions with respect to the Kaluza-Klein vector. In the five-dimensional effective theory the Kaluza-Klein vector and the massive U(1)s combine into a linear combination that is massless. This U(1) is identified with the massless U(1) corresponding to the multi-section of the Calabi-Yau threefold in M-theory. We confirm this interpretation by computing the one-loop Chern-Simons terms for the massless vectors of the five-dimensional setup by integrating out all massive states. A closed formula is found that accounts for the hypermultiplets charged under the massive U(1)s.

Double scaling limits and twisted non-critical superstrings

International Nuclear Information System (INIS)

Bertoldi, Gaetano

2006-01-01

We consider double-scaling limits of multicut solutions of certain one matrix models that are related to Calabi-Yau singularities of type A and the respective topological B model via the Dijkgraaf-Vafa correspondence. These double-scaling limits naturally lead to a bosonic string with c ≤ 1. We argue that this non-critical string is given by the topologically twisted non-critical superstring background which provides the dual description of the double-scaled little string theory at the Calabi-Yau singularity. The algorithms developed recently to solve a generic multicut matrix model by means of the loop equations allow to show that the scaling of the higher genus terms in the matrix model free energy matches the expected behaviour in the topological B-model. This result applies to a generic matrix model singularity and the relative double-scaling limit. We use these techniques to explicitly evaluate the free energy at genus one and genus two

The topological B model as a twisted spinning particle

International Nuclear Information System (INIS)

Marcus, Neil; Yankielowicz, Shimon

1994-01-01

The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string, and the Kodaira-Spencer theory for the closed string. We show that the B model can be represented as a particle theory, obtained by reducing the sigma model to one dimension, and replacing the coupling to topological gravity by a coupling to a twisted one-dimensional supergravity. The particle can be defined on any Kaehler manifold - it does not require the Calabi-Yau condition - so it may provide a more generalized setting for the B model than the topological sigma model.The one-loop partition function of the particle can be written in terms of the Ray-Singer torsion of the manifold, and agrees with that of the original B model. After showing how to deform the Kaehler and complex structures in the particle, we prove the independence of this partition function on the Kaehler structure, and investigate the origin of the holomorphic anomaly. To define other amplitudes, one needs to introduce interactions into the particle. The particle will then define a field theory, which may or may not be the Chern-Simons or Kodaira-Spencer theories. ((orig.))

Towards numerical simulation of turbulent hydrogen combustion
 based on flamelet generated manifolds in OpenFOAM

NARCIS (Netherlands)

Fancello, A.; Bastiaans, R.J.M.; Goey, de L.P.H.

2013-01-01

This work proposes an application of the Flamelet-Generated Manifolds (FGM) technique in the OpenFOAM environment. FGM is a chemical reduced method for combustion modeling. This technique treats the combustion process as the solution of a small amount of controlling variables. Regarding laminar

Generation of single domain antibody fragments derived from camelids and generation of manifold constructs.

Science.gov (United States)

Vincke, Cécile; Gutiérrez, Carlos; Wernery, Ulrich; Devoogdt, Nick; Hassanzadeh-Ghassabeh, Gholamreza; Muyldermans, Serge

2012-01-01

Immunizing a camelid (camels and llamas) with soluble, properly folded proteins raises an affinity-matured immune response in the unique camelid heavy-chain only antibodies (HCAbs). The peripheral blood lymphocytes of the immunized animal are used to clone the antigen-binding antibody fragment from the HCAbs in a phage display vector. A representative aliquot of the library of these antigen-binding fragments is used to retrieve single domain antigen-specific binders by successive rounds of panning. These single domain antibody fragments are cloned in tandem to generate manifold constructs (bivalent, biparatopic or bispecific constructs) to increase their functional affinity, to increase specificity, or to connect two independent antigen molecules.

Combustion modeling including heat loss using flamelet generated manifolds: a validation study in OpenFOAM

NARCIS (Netherlands)

Ottino, G.M.; Fancello, A.; Falcone, M.; Bastiaans, R.J.M.; Goey, de L.P.H.

In numerical combustion applications the Flamelet Generated Manifolds technique (FGM) is being used at an increasingly number of occasions. This technique is an approach to reduce the chemistry efficiently and accurately. In the present work FGM is coupled to an OpenFOAM-based CFD solver. The

Rank Two Affine Manifolds in Genus 3

OpenAIRE

Aulicino, David; Nguyen, Duc-Manh

2016-01-01

We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.

A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds

OpenAIRE

Baker, Mark; Cooper, Daryl

2005-01-01

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...

Hemisphere partition function and monodromy

Energy Technology Data Exchange (ETDEWEB)

Erkinger, David; Knapp, Johanna [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10, 1040 Vienna (Austria)

2017-05-29

We discuss D-brane monodromies from the point of view of the gauged linear sigma model. We give a prescription on how to extract monodromy matrices directly from the hemisphere partition function. We illustrate this procedure by recomputing the monodromy matrices associated to one-parameter Calabi-Yau hypersurfaces in weighted projected space.

Wilson loops, instantons and quantum mechanics

International Nuclear Information System (INIS)

Schiereck, Marc

2014-05-01

In this thesis we examine two different problems. The first is the computation of vacuum expectation values of Wilson loop operators in ABJM theory, the other problem is finding the instanton series of the refined topological string on certain local Calabi-Yau geometries in the Nekrasov-Shatashvili limit. Based on the description of ABJM theory as a matrix model, it is possible to find a description of it in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. The vacuum-expectation-values of Wilson loop operators in ABJM theory correspond to averages of operators in the statistical-mechanical problem. Using the WKB expansion, it is possible to extract the full 1/N expansion of the vevs, up to exponentially small contributions, for arbitrary Chern-Simons coupling. We compute these vevs for the 1/6 and 1/2 BPS Wilson loops at any winding number. These can be written in terms of the Airy function. The expressions we found reproduce the low genus results previously obtained in the 't Hooft expansion. In another problem we use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies, given in terms of an instanton sum, in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum geometry here is to be understood as a quantum deformed version of rigid special geometry, which has its origin in the quantum mechanical behavior of branes in the topological string B-model. We argue that in the Seiberg-Witten picture only the Coulomb parameters lead to quantum corrections, while the mass parameters remain uncorrected. In certain cases we also compute the expansion of the free energies at the orbifold point and the conifold locus. We compute the quantum corrections order by order on ℎ by deriving second order differential operators, which act on the classical periods.

Schoen manifold with line bundles as resolved magnetized orbifolds

Energy Technology Data Exchange (ETDEWEB)

Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-12-15

We give an alternative description of the Schoen manifold as the blow-up of a Z{sub 2} x Z{sub 2} orbifold in which one Z{sub 2} factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non-perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.

Principal Curves on Riemannian Manifolds.

Science.gov (United States)

Hauberg, Soren

2016-09-01

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

The Green-Schwarz mechanism and geometric anomaly relations in 2d (0,2) F-theory vacua

Science.gov (United States)

Weigand, Timo; Xu, Fengjun

2018-04-01

We study the structure of gauge and gravitational anomalies in 2d N = (0 , 2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory. We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms. These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon. Cancellation of anomalies in the effective theory predicts intricate topological identities which must hold on every elliptically fibered Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but their proof from a purely mathematical perspective remains as an interesting open problem. Some of the identities we find on elliptic 5-folds are related in an intriguing way to previously studied topological identities governing the structure of anomalies in 6d N = (1 , 0) and 4d N = 1 theories obtained from F-theory.

The monodromy property for K3 surfaces allowing a triple-point-free model

DEFF Research Database (Denmark)

Jaspers, Annelies Kristien J

2017-01-01

The aim of this thesis is to study under which conditions K3 surfaces allowing a triple-point-free model satisfy the monodromy property. This property is a quantitative relation between the geometry of the degeneration of a Calabi-Yau variety X and the monodromy action on the cohomology of...... X: a Calabi- Yau variety X satisfies the monodromy property if poles of the motivic zeta function ZX,ω(T) induce monodromy eigenvalues on the cohomology of X. Let k be an algebraically closed field of characteristic 0, and set K = k((t)). In this thesis, we focus on K3 surfaces over K allowing a triple-point...... is very precise, which allows to use a combination of geometrical and combinatorial techniques to check the monodromy property in practice. The first main result is an explicit computation of the poles of ZX,ω(T) for a K3 surface X allowing a triple-point-free model and a volume form ! on X. We show that...

Hirzebruch genera of manifolds with torus action

International Nuclear Information System (INIS)

Panov, T E

2001-01-01

A quasitoric manifold is a smooth 2n-manifold M 2n with an action of the compact torus T n such that the action is locally isomorphic to the standard action of T n on C n and the orbit space is diffeomorphic, as a manifold with corners, to a simple polytope P n . The name refers to the fact that topological and combinatorial properties of quasitoric manifolds are similar to those of non-singular algebraic toric varieties (or toric manifolds). Unlike toric varieties, quasitoric manifolds may fail to be complex. However, they always admit a stably (or weakly almost) complex structure, and their cobordism classes generate the complex cobordism ring. Buchstaber and Ray have recently shown that the stably complex structure on a quasitoric manifold is determined in purely combinatorial terms, namely, by an orientation of the polytope and a function from the set of codimension-one faces of the polytope to primitive vectors of the integer lattice. We calculate the χ y -genus of a quasitoric manifold with a fixed stably complex structure in terms of the corresponding combinatorial data. In particular, this gives explicit formulae for the classical Todd genus and the signature. We also compare our results with well-known facts in the theory of toric varieties

Global monodromy modulo 5 of quintic-mirror family

OpenAIRE

Shirakawa, Kennichiro

2011-01-01

The quintic-mirror family is a well-known one-parameter family of Calabi-Yau threefolds. A complete description of the global monodromy group of this family is not yet known. In this paper, we give a presentation of the global monodromy group in the general linear group of degree 4 over the ring of integers modulo 5.

New Li-Yau-Hamilton Inequalities for the Ricci Flow via the Space-Time Approach

OpenAIRE

Chow, Bennett; Knopf, Dan

2002-01-01

We generalize Hamilton's matrix Li-Yau-type Harnack estimate for the Ricci flow by considering the space of all LYH (Li-Yau-Hamilton) quadratics that arise as curvature tensors of space-time connections satisfying the Ricci flow with respect to the natural space-time degenerate metric. As a special case, we employ scaling arguments to derive a linear-type matrix LYH estimate. The new LYH quadratics obtained in this way are associated to the system of the Ricci flow coupled to a 1-form and a 2...

Kaluza-Klein Multidimensional Models with Ricci-Flat Internal Spaces: The Absence of the KK Particles

Directory of Open Access Journals (Sweden)

Alexey Chopovsky

2013-01-01

Full Text Available We consider a multidimensional Kaluza-Klein (KK model with a Ricci-flat internal space, for example, a Calabi-Yau manifold. We perturb this background metrics by a system of gravitating masses, for example, astrophysical objects such as our Sun. We suppose that these masses are pressureless in the external space but they have relativistic pressure in the internal space. We show that metric perturbations do not depend on coordinates of the internal space and gravitating masses should be uniformly smeared over the internal space. This means, first, that KK modes corresponding to the metric fluctuations are absent and, second, particles should be only in the ground quantum state with respect to the internal space. In our opinion, these results look very unnatural. According to statistical physics, any nonzero temperature should result in fluctuations, that is, in KK modes. We also get formulae for the metric correction terms which enable us to calculate the gravitational tests: the deflection of light, the time-delay of the radar echoes, and the perihelion advance.

Yukawa couplings in SO(10) heterotic M-theory vacua

International Nuclear Information System (INIS)

Faraggi, Alon E.; Garavuso, Richard S.

2003-01-01

We demonstrate the existence of a class of N=1 supersymmetric nonperturbative vacua of Horava-Witten M-theory compactified on a torus fibered Calabi-Yau 3-fold Z with first homotopy group π 1 (Z)=Z 2 , having the following properties: (1) SO(10) grand unification group, (2) net number of three generations of chiral fermions in the observable sector, and (3) potentially viable matter Yukawa couplings. These vacua correspond to semistable holomorphic vector bundles V Z over Z having structure group SU(4) C , and generically contain M5-branes in the bulk space. The nontrivial first homotopy group allows Wilson line breaking of the SO(10) symmetry. Additionally, we propose how the 11-dimensional Horava-Witten M-theory framework may be used to extend the perturbative calculation of the top quark Yukawa coupling in the realistic free-fermionic models to the nonperturbative regime. The basic argument being that the relevant coupling couples twisted-twisted-untwisted states and can be calculated at the level of the Z 2 xZ 2 orbifold without resorting to the full three generation models

Characteristic manifolds in relativistic hypoelasticity

Energy Technology Data Exchange (ETDEWEB)

Giambo, S [Messina Univ. (Italy). Istituto di Matematica

1978-10-02

The relativistic hypoelasticity is considered and the characteristic manifolds are determined by using the Cauchy-Kovalevski theorem for the Cauchy problem with analytic initial conditions. Taking into account that the characteristic manifold represents the image of the front-wave in the space-time, it is possible to determine the velocities of propagation. Three wave-species are obtained: material waves, longitudinal waves and transverse waves.

BIRS Workshop on Calabi-Yau Varieties and Mirror Symmetry

CERN Document Server

Yau, Shing-Tung; Lewis, James D; Mirror Symmetry V

2006-01-01

Since its discovery in the early 1990s, mirror symmetry, or more generally, string theory, has exploded onto the mathematical landscape. This topic touches upon many branches of mathematics and mathematical physics, and has revealed deep connections between subjects previously considered unrelated. The papers in this volume treat mirror symmetry from the perspectives of both mathematics and physics. The articles can be roughly grouped into four sub-categories within the topic of mirror symmetry: arithmetic aspects, geometric aspects, differential geometric and mathematical physics aspects, and geometric analytic aspects. In these works, the reader will find mathematics addressing, and in some cases solving, problems inspired and influenced by string theory. - See more at: http://bookstore.ams.org/amsip-38#sthash.imkmWYgJ.dpuf

Toric Vaisman manifolds

Science.gov (United States)

Pilca, Mihaela

2016-09-01

Vaisman manifolds are strongly related to Kähler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if a complete Vaisman manifold is toric, then the associated Sasaki manifold is also toric. Conversely, a toric complete Sasaki manifold, whose Kähler cone is equipped with an appropriate compatible action, gives rise to a toric Vaisman manifold. In the special case of a strongly regular compact Vaisman manifold, we show that it is toric if and only if the corresponding Kähler quotient is toric.

Flipped SU(6) from ten dimensions

Energy Technology Data Exchange (ETDEWEB)

Panagiotakopoulos, C. (Bartol Research Inst., Univ. of Delaware, Newark, DE (US))

1990-06-20

The authors study the compactification of the heterotic supersting on the only known three generation Calabi-Yau space with flux breakings leading to SU(6) {times} U(1) as the gauge group in four dimensions. We compute the massless spectrum and identify the discrete symmetries of the internal space that survive flux breaking. The possible four-dimensional models are classified according to their honest discrete symmetries. The allowed breaking chains of SU(6) {times} U(1) are listed. Model building with SU(6) {times} U(1) is discussed in general and a concrete realistic model is constructed which does not suffer from the gauge hierarchy problem, fast proton decay or any other obvious phenomenological disaster. A distinct experimental signature of this class of models is the presence in the low energy spectrum of vector-like quarks and antiquarks, outside the three known families, with masses of the order of the supersymmetry breaking scale.

Robinson manifolds and Cauchy-Riemann spaces

CERN Document Server

Trautman, A

2002-01-01

A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...

Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds

OpenAIRE

Barreto, Yadira; Verjovsky, Alberto

2013-01-01

We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.

Warped Kähler potentials and fluxes

International Nuclear Information System (INIS)

Martucci, Luca

2017-01-01

The four-dimensional effective theory for type IIB warped flux compactifications proposed in https://www.doi.org/10.1007/JHEP03(2015)067 is completed by taking into account the backreaction of the Kähler moduli on the three-form fluxes. The only required modification consists in a flux-dependent contribution to the chiral fields parametrising the Kähler moduli. The resulting supersymmetric effective theory satisfies the no-scale condition and consistently combines previous partial results present in the literature. Similar results hold for M-theory warped compactifications on Calabi-Yau fourfolds, whose effective field theory and Kähler potential are also discussed.

Warped Kähler potentials and fluxes

Energy Technology Data Exchange (ETDEWEB)

Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei' ,Università di Padova & I.N.F.N. Sezione di Padova,Via Marzolo 8, 35131 Padova (Italy)

2017-01-13

The four-dimensional effective theory for type IIB warped flux compactifications proposed in https://www.doi.org/10.1007/JHEP03(2015)067 is completed by taking into account the backreaction of the Kähler moduli on the three-form fluxes. The only required modification consists in a flux-dependent contribution to the chiral fields parametrising the Kähler moduli. The resulting supersymmetric effective theory satisfies the no-scale condition and consistently combines previous partial results present in the literature. Similar results hold for M-theory warped compactifications on Calabi-Yau fourfolds, whose effective field theory and Kähler potential are also discussed.

Four-manifolds, geometries and knots

CERN Document Server

Hillman, Jonathan A

2007-01-01

The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...

Polynomial chaos representation of databases on manifolds

Energy Technology Data Exchange (ETDEWEB)

Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.

The study is believed to be used to treat illnesses Yau ceremony of Phutai. Natal village , Tambon Tao Ngoi, Tao Ngoi District, Sakon Nakhon Province

Directory of Open Access Journals (Sweden)

Boonchom Srisa-ard

2016-12-01

Full Text Available This research aimed to 1 study the beliefs and the cause of the ailments of the ceremony to Yau. Which is from Thailand, Village Natal district, Tao Ngoi District, Sakon Nakhon 2 to study the composition of the ceremony Yao and 3 to study the Yau ceremony. The method resources from data collection divided into two parts, there were 1 documentation research articles, theses, books, textbooks and information from the Internet, and 2 the interview with the people who knew the four ceremonies of You. The study found the phenomenon as follows: 1 Belief in the Yau ceremony, that Yau is believed to cure illness, disease caused by an act of the devil. The treatment with modern medicine can not be cured. Parents or family elders had prior therapy with Yau. The disease which is believed to occur in this manner must be gone because of Yao. Some of which can actually be cured, mean while some extended for several more years. The treatment facilities for patients is that Yao can be come home. And pitched immediate treatment faster than the health center or hospital where the procedure was hospitalized several timeconsuming steps. 2 The components of Yau ceremony, are Yau illnesses, Yau is patient, the Yao spit, and music instruments. 3 The ceremony of Yau has five phases: preparation before starting the ceremony. Next, the invitation to the major deities or spirits. then Yao toss the cause of the illness. the reassure patients to leave the various deities and spirits. leave the body return to and live in their residence.

Smooth manifolds

CERN Document Server

Sinha, Rajnikant

2014-01-01

This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book ...

Riemannian multi-manifold modeling and clustering in brain networks

Science.gov (United States)

Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.

2017-08-01

This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.

Four-flux and warped heterotic M-theory compactifications

International Nuclear Information System (INIS)

Curio, Gottfried; Krause, Axel

2001-01-01

In the framework of heterotic M-theory compactified on a Calabi-Yau threefold 'times' an interval, the relation between geometry and four-flux is derived beyond first order. Besides the case with general flux which cannot be described by a warped geometry one is naturally led to consider two special types of four-flux in detail. One choice shows how the M-theory relation between warped geometry and flux reproduces the analogous one of the weakly coupled heterotic string with torsion. The other one leads to a quadratic dependence of the Calabi-Yau volume with respect to the orbifold direction which avoids the problem with negative volume of the first order approximation. As in the first order analysis we still find that Newton's constant is bounded from below at just the phenomenologically relevant value. However, the bound does not require an ad hoc truncation of the orbifold-size any longer. Finally we demonstrate explicitly that to leading order in κ 2/3 no Cosmological constant is induced in the four-dimensional low-energy action. This is in accord with what one can expect from supersymmetry

Ensemble manifold regularization.

Science.gov (United States)

Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng

2012-06-01

We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.

Comments on exact quantization conditions and non-perturbative topological strings

International Nuclear Information System (INIS)

Hatsuda, Yasuyuki

2015-12-01

We give some remarks on exact quantization conditions associated with quantized mirror curves of local Calabi-Yau threefolds, conjectured in arXiv:1410.3382. It is shown that they characterize a non-perturbative completion of the refined topological strings in the Nekrasov-Shatashvili limit. We find that the quantization conditions enjoy an exact S-dual invariance. We also discuss Borel summability of the semi-classical spectrum.

Natural differential operations on manifolds: an algebraic approach

International Nuclear Information System (INIS)

Katsylo, P I; Timashev, D A

2008-01-01

Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles V,W→M all the natural differential operations D:Γ(V)→Γ(W) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds. Bibliography: 21 titles.

Introduction to string theory and string compactifications

International Nuclear Information System (INIS)

GarcIa-Compean, Hugo

2005-01-01

Basics of some topics on perturbative and non-perturbative string theory are reviewed. After a mathematical survey of the Standard Model of particle physics and GUTs, the bosonic string kinematics for the free case and with interaction is described. The effective action of the bosonic string and the spectrum is also discussed. T-duality in closed and open strings and the definition of D-brane are surveyed. Five perturbative superstring theories and their spectra is briefly outlined. Calabi-Yau three-fold compactifications of heterotic strings and their relation to some four-dimensional physics are given. Finally, non-perturbative issues like S-duality, M-theory and F-theory are also reviewed

Tuned and non-Higgsable U(1)s in F-theory

Energy Technology Data Exchange (ETDEWEB)

Wang, Yi-Nan [Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA 02139 (United States)

2017-03-27

We study the tuning of U(1) gauge fields in F-theory models on a base of general dimension. We construct a formula that computes the change in Weierstrass moduli when such a U(1) is tuned, based on the Morrison-Park form of a Weierstrass model with an additional rational section. Using this formula, we propose the form of “minimal tuning” on any base, which corresponds to the case where the decrease in the number of Weierstrass moduli is minimal. Applying this result, we discover some universal features of bases with non-Higgsable U(1)s. Mathematically, a generic elliptic fibration over such a base has additional rational sections. Physically, this condition implies the existence of U(1) gauge group in the low-energy supergravity theory after compactification that cannot be Higgsed away. In particular, we show that the elliptic Calabi-Yau manifold over such a base has a small number of complex structure moduli. We also suggest that non-Higgsable U(1)s can never appear on any toric bases. Finally, we construct the first example of a threefold base with non-Higgsable U(1)s.

“Finite” non-Gaussianities and tensor-scalar ratio in large volume Swiss-cheese compactifications

Science.gov (United States)

Misra, Aalok; Shukla, Pramod

2009-03-01

Developing on the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi-Yau's, Nucl. Phys. B 799 (2008) 165-198, arXiv: 0707.0105] and [A. Misra, P. Shukla, Large volume axionic Swiss-cheese inflation, Nucl. Phys. B 800 (2008) 384-400, arXiv: 0712.1260 [hep-th

Singularity theory and N = 2 superconformal field theories

International Nuclear Information System (INIS)

Warner, N.P.

1989-01-01

The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs

Flat connections in three-manifolds and classical Chern–Simons invariant

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Enore Guadagnini

2017-12-01

Full Text Available A general method for the construction of smooth flat connections on 3-manifolds is introduced. The procedure is strictly connected with the deduction of the fundamental group of a manifold M by means of a Heegaard splitting presentation of M. For any given matrix representation of the fundamental group of M, a corresponding flat connection A on M is specified. It is shown that the associated classical Chern–Simons invariant assumes then a canonical form which is given by the sum of two contributions: the first term is determined by the intersections of the curves in the Heegaard diagram, and the second term is the volume of a region in the representation group which is determined by the representation of π1(M and by the Heegaard gluing homeomorphism. Examples of flat connections in topologically nontrivial manifolds are presented and the computations of the associated classical Chern–Simons invariants are illustrated.

Duality constructions from quantum state manifolds

Science.gov (United States)

Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.

2015-11-01

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.

Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications

Energy Technology Data Exchange (ETDEWEB)

Blaszczyk, Michael [Johannes-Gutenberg-Universität,Staudingerweg 7, 55099 Mainz (Germany); Oehlmann, Paul-Konstantin [Bethe Center for Theoretical Physics, Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany)

2016-04-12

We are considering the class of heterotic N=(2,2) Landau-Ginzburg orbifolds with 9 fields corresponding to A{sub 1}{sup 9} Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror symmetry with N=1,2 and 4 supersymmetry in 4D. We compute the full massless matter spectrum at the Fermat locus and find a universal relation satisfied by all models. In addition we give prescriptions of how to compute all quantum numbers of the 4D states including their discrete R-symmetries. Using mirror symmetry of rigid geometries we describe orbifold and smooth Calabi-Yau phases as deformations away from the Landau-Ginzburg Fermat locus in two explicit examples. We match the non-Fermat deformations to the 4D Higgs mechanism and study the conservation of R-symmetries. The first example is a ℤ{sub 3} orbifold on an E{sub 6} lattice where the R-symmetry is preserved. Due to a permutation symmetry of blow-up and torus Kähler parameters the R-symmetry stays conserved also in the smooth Calabi-Yau phase. In the second example the R-symmetry gets broken once we deform to the geometric ℤ{sub 3}×ℤ{sub 3,free} orbifold regime.

Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications

International Nuclear Information System (INIS)

Blaszczyk, Michael; Oehlmann, Paul-Konstantin

2016-01-01

We are considering the class of heterotic N=(2,2) Landau-Ginzburg orbifolds with 9 fields corresponding to A 1 9 Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror symmetry with N=1,2 and 4 supersymmetry in 4D. We compute the full massless matter spectrum at the Fermat locus and find a universal relation satisfied by all models. In addition we give prescriptions of how to compute all quantum numbers of the 4D states including their discrete R-symmetries. Using mirror symmetry of rigid geometries we describe orbifold and smooth Calabi-Yau phases as deformations away from the Landau-Ginzburg Fermat locus in two explicit examples. We match the non-Fermat deformations to the 4D Higgs mechanism and study the conservation of R-symmetries. The first example is a ℤ 3 orbifold on an E 6 lattice where the R-symmetry is preserved. Due to a permutation symmetry of blow-up and torus Kähler parameters the R-symmetry stays conserved also in the smooth Calabi-Yau phase. In the second example the R-symmetry gets broken once we deform to the geometric ℤ 3 ×ℤ 3,free orbifold regime.

Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications

Science.gov (United States)

Blaszczyk, Michael; Oehlmann, Paul-Konstantin

2016-04-01

We are considering the class of heterotic N=(2,2) Landau-Ginzburg orbifolds with 9 fields corresponding to A 1 9 Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror symmetry with N=1 , 2 and 4 supersymmetry in 4D. We compute the full massless matter spectrum at the Fermat locus and find a universal relation satisfied by all models. In addition we give prescriptions of how to compute all quantum numbers of the 4D states including their discrete R-symmetries. Using mirror symmetry of rigid geometries we describe orbifold and smooth Calabi-Yau phases as deformations away from the Landau-Ginzburg Fermat locus in two explicit examples. We match the non-Fermat deformations to the 4D Higgs mechanism and study the conservation of R-symmetries. The first example is a Z_3 orbifold on an E6 lattice where the R-symmetry is preserved. Due to a permutation symmetry of blow-up and torus Kähler parameters the R-symmetry stays conserved also in the smooth Calabi-Yau phase. In the second example the R-symmetry gets broken once we deform to the geometric Z_3× Z_{3,free} orbifold regime.

Dual manifold heat pipe evaporator

Science.gov (United States)

Adkins, D.R.; Rawlinson, K.S.

1994-01-04

An improved evaporator section is described for a dual manifold heat pipe. Both the upper and lower manifolds can have surfaces exposed to the heat source which evaporate the working fluid. The tubes in the tube bank between the manifolds have openings in their lower extensions into the lower manifold to provide for the transport of evaporated working fluid from the lower manifold into the tubes and from there on into the upper manifold and on to the condenser portion of the heat pipe. A wick structure lining the inner walls of the evaporator tubes extends into both the upper and lower manifolds. At least some of the tubes also have overflow tubes contained within them to carry condensed working fluid from the upper manifold to pass to the lower without spilling down the inside walls of the tubes. 1 figure.

3-manifolds

CERN Document Server

Hempel, John

2004-01-01

A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. -Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The t

Manifolds, Tensors, and Forms

Science.gov (United States)

Renteln, Paul

2013-11-01

Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.

LCD OF AIR INTAKE MANIFOLDS PHASE 2: FORD F250 AIR INTAKE MANIFOLD

Science.gov (United States)

The life cycle design methodology was applied to the design analysis of three alternatives for the lower plehum of the air intake manifold for us with a 5.4L F-250 truck engine: a sand cast aluminum, a lost core molded nylon composite, and a vibration welded nylon composite. The ...

On the possibility of large axion moduli spaces

Energy Technology Data Exchange (ETDEWEB)

Rudelius, Tom [Jefferson Physical Laboratory, Harvard University,Cambridge, MA 02138 (United States)

2015-04-28

We study the diameters of axion moduli spaces, focusing primarily on type IIB compactifications on Calabi-Yau three-folds. In this case, we derive a stringent bound on the diameter in the large volume region of parameter space for Calabi-Yaus with simplicial Kähler cone. This bound can be violated by Calabi-Yaus with non-simplicial Kähler cones, but additional contributions are introduced to the effective action which can restrict the field range accessible to the axions. We perform a statistical analysis of simulated moduli spaces, finding in all cases that these additional contributions restrict the diameter so that these moduli spaces are no more likely to yield successful inflation than those with simplicial Kähler cone or with far fewer axions. Further heuristic arguments for axions in other corners of the duality web suggest that the difficulty observed in http://dx.doi.org/10.1088/1475-7516/2003/06/001 of finding an axion decay constant parametrically larger than M{sub p} applies not only to individual axions, but to the diagonals of axion moduli space as well. This observation is shown to follow from the weak gravity conjecture of http://dx.doi.org/10.1088/1126-6708/2007/06/060, so it likely applies not only to axions in string theory, but also to axions in any consistent theory of quantum gravity.

Entropy of N=2 black holes and their M-brane description

International Nuclear Information System (INIS)

Behrndt, K.; Mohaupt, T.

1997-01-01

In this paper we discuss the M-brane description for an N=2 black hole. This solution is a result of the compactification of M-5-brane configurations over a Calabi-Yau threefold with arbitrary intersection numbers C ABC . In analogy with the D-brane description where one counts open string states we count here open M-2-branes which end on the M-5-brane. copyright 1997 The American Physical Society

Diffeomorphisms of elliptic 3-manifolds

CERN Document Server

Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam

2012-01-01

This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...

Electromiographic and kinematic characteristics of Kung Fu Yau-Man palm strike.

Science.gov (United States)

Neto, O P; Magini, Marcio

2008-12-01

A kinematic and electromyographic analysis of Kung Fu (KF) Yau-Man palm strikes without impact is presented. An empirical model applied to data obtained by a high-speed camera describes the kinematic characteristics of the movement. The electromyographic patterns of the biceps brachii, brachioradialis and triceps brachii muscles were studied during the strike in the time (root mean square) and frequency (wavelet transform) domains. Eight KF practitioners participated in the investigation. A wooden board was placed in front of the subjects, and they were asked to perform the strike imagining a target above the board. The results show that the Yau-Man KF palm strike has very similar kinematic characteristics to a simple moderate speed elbow extension movement. All practitioners positioned themselves in relation to the wooden board in a way to achieve their highest hand speeds in the instant their hands crossed the board. The analyses of the electromyography data shows a well developed muscle coordination of the practitioners in agreement with kinematic results. The results of this paper are important not only for improving the performance of practitioners but also to demonstrate the applicability of KF in the process of motor control development.

Introduction to differentiable manifolds

CERN Document Server

Auslander, Louis

2009-01-01

The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary diff

Renormalization, unstable manifolds, and the fractal structure of mode locking

International Nuclear Information System (INIS)

Cvitanovic, P.; Jensen, M.H.; Kadanoff, L.P.; Procaccia, I.

1985-01-01

The apparent universality of the fractal dimension of the set of quasiperiodic windings at the onset of chaos in a wide class of circle maps is described by construction of a universal one-parameter family of maps which lies along the unstable manifold of the renormalization group. The manifold generates a universal ''devil's staircase'' whose dimension agrees with direct numerical calculations. Applications to experiments are discussed

Markov's theorem and algorithmically non-recognizable combinatorial manifolds

International Nuclear Information System (INIS)

Shtan'ko, M A

2004-01-01

We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem

Dual giant gravitons in Sasaki-Einstein backgrounds

International Nuclear Information System (INIS)

Martelli, Dario; Sparks, James

2006-01-01

We study the dynamics of a BPS D3-brane wrapped on a three-sphere in AdS 5 xL, a so-called dual giant graviton, where L is a Sasakian five-manifold. The phase space of these configurations is the symplectic cone X over L, and geometric quantisation naturally produces a Hilbert space of L 2 -normalisable holomorphic functions on X, whose states are dual to scalar chiral BPS operators in the dual superconformal field theory. We define classical and quantum partition functions and relate them to earlier mathematical constructions by the authors and S.-T. Yau, [D. Martelli, J. Sparks, S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation, hep-th/0603021]. In particular, a Sasaki-Einstein metric then minimises an entropy function associated with the D3-brane. Finally, we introduce a grand canonical partition function that counts multiple dual giant gravitons. This is related simply to the index-character of the above reference, and provides a method for counting multi-trace scalar BPS operators in the dual superconformal field theory

Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

Directory of Open Access Journals (Sweden)

Zeki Kasap

2015-01-01

Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories

Energy Technology Data Exchange (ETDEWEB)

Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)

2016-11-15

We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)

The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold

Directory of Open Access Journals (Sweden)

J. A. Helayël-Neto

2017-01-01

Full Text Available It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.

The spinorial geometry of supersymmetric backgrounds

International Nuclear Information System (INIS)

Gillard, J; Gran, U; Papadopoulos, G

2005-01-01

We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N = 1 and some N = 2, N = 3 and N = 4 backgrounds. In the N = 2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N = 2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N = 2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure. The spacelike Killing vector field leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds preserving more than two supersymmetries, N > 2. We investigate a class of N = 3 and N = 4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi-Yau compactifications with fluxes to one dimension

The spinorial geometry of supersymmetric backgrounds

Energy Technology Data Exchange (ETDEWEB)

Gillard, J; Gran, U; Papadopoulos, G [Department of Mathematics, King' s College London, Strand, London WC2R 2LS (United Kingdom)

2005-03-21

We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N = 1 and some N = 2, N = 3 and N = 4 backgrounds. In the N = 2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N = 2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N = 2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure. The spacelike Killing vector field leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds preserving more than two supersymmetries, N > 2. We investigate a class of N = 3 and N = 4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi-Yau compactifications with fluxes to one dimension.

ELECTROMYOGRAPHIC STUDY OF A SEQUENCE OF YAU-MAN KUNG FU PALM STRIKES WITH AND WITHOUT IMPACT

Directory of Open Access Journals (Sweden)

Osmar Pinto Neto

2007-10-01

Full Text Available In martial arts and contact sports, strikes are often trained in two different ways: with and without impacts. This study aims to compare the electromyographical activity (EMG of the triceps brachii (TB, biceps brachii (BB and brachioradialis (BR muscles during strikes with and without impacts. Eight Yau-Man Kung Fu practitioners participated in the experiment. Each participant performed 5 sequences of 5 consecutive KF Yau-Man palm strikes with no impact intercalated with 5 sequences of 5 repetitions targeting a KF training shield. Surface EMG signals were obtained from the TB, BB, and RB for 3.0 seconds using an eight-channel module with a total amplifier gain of 2000 and sampled at 3500 Hz. The EMG analyses were done in the time (rms and frequency (wavelet domains. For the frequency domain, Morlet wavelet power spectra were obtained and an original method was used to quantify statistically significant regions on the power spectra. The results both in the time and frequency domains indicate a higher TB and BR muscle activity for the strikes with impacts. No significant difference was found for the BB in the two different scenarios. In addition, the results show that the wavelet power spectra pattern for the three analysed muscles obtained from the strikes with and without impacts were similar

A study of Para-Sasakian manifold

International Nuclear Information System (INIS)

Rahman, M.S.

1995-08-01

A Para-Sasakian manifold M is viewed in the light of an almost paracontact manifold. The fundamental concepts of M in spirit to Recurrent, Ricci-recurrent, 2-Recurrent and 2-Ricci-recurrent manifolds are presented. An η-Einstein manifold modelled on P-Sasakian manifold is then treated with simplified proofs of some results. (author). 7 refs

Gauge/gravity duality and meta-stable dynamical supersymmetry breaking

International Nuclear Information System (INIS)

Argurio, Riccardo; Bertolini, Matteo; Franco, Sebastian; Kachru, Shamit

2007-01-01

We engineer a class of quiver gauge theories with several interesting features by studying D-branes at a simple Calabi-Yau singularity. At weak 't Hooft coupling we argue using field theory techniques that these theories admit both supersymmetric vacua and meta-stable non-supersymmetric vacua, though the arguments indicating the existence of the supersymmetry breaking states are not decisive. At strong 't Hooft coupling we find simple candidate gravity dual descriptions for both sets of vacua

Splitting Parabolic Manifolds

OpenAIRE

Kalka, Morris; Patrizio, Giorgio

2014-01-01

We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\\C^{N}$ viewed as a product of lower dimensional complex euclidean spaces.

De Sitter vacua and inflation in no-scale string models

Energy Technology Data Exchange (ETDEWEB)

Gross, Christian

2009-09-15

This thesis studies the question of how de Sitter vacua and slow-roll inflation may be realized in string-motivated models. More specifically, we consider 4d N = 1 supergravity theories (without vector multiplets) with Kaehler potentials which are 'no-scale' at leading order. Such theories frequently arise in the moduli sector of string compactifications. We discuss a condition on the scalar geometry (defined by the Kaehler potential) and on the direction of supersymmetry breaking in the scalar manifold, which has to be met in order for the average of the masses of the sGoldstinos to be positive, and hence for metastable vacua to be possible. This condition also turns out to be necessary for the existence of trajectories admitting slow-roll inflation. Its implications for certain scalar manifolds which arise from Calabi-Yau string compactifications are discussed. In particular, for two-moduli models arising from compactifications of heterotic- and type IIB string theory, a simple criterion on the intersection numbers needs to be satisfied for possible de Sitter phases to exist. In addition, we show that subleading corrections breaking the no-scale property may allow the condition on the scalar geometry to be fulfilled, even when it is violated at leading order. Finally, we develop a procedure to construct superpotentials for a given viable Kaehler potential, such that the scalar potential has a realistic local minimum. We propose two-moduli models, with superpotentials which could arise from flux backgrounds and non-perturbative effects, which have a viable vacuum without employing subleading corrections or an uplifting sector. (orig.)

Holonomy of Einstein Lorentzian manifolds

International Nuclear Information System (INIS)

Galaev, Anton S

2010-01-01

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp. vacuum Einstein) Lorentzian manifold; the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.

Eigenvalue pinching on spinc manifolds

Science.gov (United States)

Roos, Saskia

2017-02-01

We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.

Harmonic maps of V-manifolds

International Nuclear Information System (INIS)

Chiang, Yuan-Jen.

1989-01-01

Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S

LIFE CYCLE DESIGN OF AIR INTAKE MANIFOLDS; PHASE I: 2.0 L FORD CONTOUR AIR INTAKE MANIFOLD

Science.gov (United States)

The project team applied the life cycle design methodology to the design analysis of three alternative air intake manifolds: a sand cast aluminum, brazed aluminum tubular, and nylon composite. The design analysis included a life cycle inventory analysis, environmental regulatory...

F-theory and 2d (0,2) theories

Energy Technology Data Exchange (ETDEWEB)

Schäfer-Nameki, Sakura [Department of Mathematics, King’s College London, The Strand, London WC2R 2LS (United Kingdom); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, 69120 Heidelberg (Germany)

2016-05-11

F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.

The topology of toric origami manifolds

OpenAIRE

Holm, Tara; Pires, Ana Rita

2012-01-01

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and co-orientable folding hypersurface. We prove that the cohomology i...

Smooth Maps of a Foliated Manifold in a Symplectic Manifold

Indian Academy of Sciences (India)

Let be a smooth manifold with a regular foliation F and a 2-form which induces closed forms on the leaves of F in the leaf topology. A smooth map f : ( M , F ) ⟶ ( N , ) in a symplectic manifold ( N , ) is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the ...

Classical mirror symmetry

CERN Document Server

Jinzenji, Masao

2018-01-01

This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold. First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold. On the B-model side, the process of construct...

The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map

OpenAIRE

Mavlyutov, Anvar R.

2000-01-01

We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the space of infinitesimal deformations for a mirror pair of Calabi-Yau hypersurfaces. This map is compatible with certain vanishing limiting products of the subrings of the chiral rings, on which the ring structure is related to a product of the roots of $A$-typ...

Generalized regular genus for manifolds with boundary

Directory of Open Access Journals (Sweden)

Paola Cristofori

2003-05-01

Full Text Available We introduce a generalization of the regular genus, a combinatorial invariant of PL manifolds ([10], which is proved to be strictly related, in dimension three, to generalized Heegaard splittings defined in [12].

Smooth maps of a foliated manifold in a symplectic manifold

Indian Academy of Sciences (India)

Abstract. Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f : (M, F) −→ (N,σ) in a symplectic manifold (N,σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the.

RG cascades in hyperbolic quiver gauge theories

International Nuclear Information System (INIS)

Ahl Laamara, R.; Ait Ben Haddou, M.; Belhaj, A.; Drissi, L.B.; Saidi, E.H.

2004-01-01

In this paper, we provide a general classification of supersymmatric QFT4s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super-QFT4s. This includes, amongst others, its embedding in type II string on local Calabi-Yau threefolds. We give realizations of these supersymmetric QFT4s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non-zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made

Compactifications of IIA supergravity on SU(2)-structure manifolds

Energy Technology Data Exchange (ETDEWEB)

Spanjaard, B.

2008-07-15

In this thesis, we study compactifications of type IIA supergravity on six-dimensional manifolds with an SU(2)-structure. A general study of six-dimensional manifolds with SU(2)-structure shows that IIA supergravity compactified on such a manifold should yield a four-dimensional gauged N=4 supergravity. We explicitly derive the bosonic spectrum, gauge transformations and action for IIA supergravity compactified on two different manifolds with SU(2)-structure, one of which also has an H{sup (3)}{sub 10}-flux, and confirm that the resulting four-dimensional theories are indeed N=4 gauged supergravities. In the second chapter, we study an explicit construction of a set of SU(2)-structure manifolds. This construction involves a Scherk-Schwarz duality twist reduction of the half-maximal six-dimensional supergravity obtained by compactifying IIA supergravity on a K3. This reduction results in a gauged N=4 four-dimensional supergravity, where the gaugings can be divided into three classes of parameters. We relate two of the classes to parameters we found before, and argue that the third class of parameters could be interpreted as a mirror flux. (orig.)

Graded manifolds and supermanifolds

International Nuclear Information System (INIS)

Batchelor, M.

1984-01-01

In this paper, a review is presented on graded manifolds and supermanifolds. Many theorems, propositions, corrollaries, etc. are given with proofs or sketch proofs. Graded manifolds, supereuclidian space, Lie supergroups, etc. are dealt with

Hazy spaces, tangent spaces, manifolds and groups

International Nuclear Information System (INIS)

Dodson, C.T.J.

1977-03-01

The results on hazy spaces and the developments leading to hazy manifolds and groups are summarized. Proofs have appeared elsewhere so here examples are considered and some motivation for definitions and constructions in the theorems is analyzed. It is shown that quite simple ideas, intuitively acceptable, lead to remarkable similarity with the theory of differentiable manifolds. Hazy n manifolds have tangent bundles that are hazy 2n manifolds and there are hazy manifold structures for groups. Products and submanifolds are easily constructed and in particular the hazy n-sphere manifolds as submanifolds of the standard hazy manifold Zsup(n+1)

Flexible fuel cell gas manifold system

Science.gov (United States)

Cramer, Michael; Shah, Jagdish; Hayes, Richard P.; Kelley, Dana A.

2005-05-03

A fuel cell stack manifold system in which a flexible manifold body includes a pan having a central area, sidewall extending outward from the periphery of the central area, and at least one compound fold comprising a central area fold connecting adjacent portions of the central area and extending between opposite sides of the central area, and a sidewall fold connecting adjacent portions of the sidewall. The manifold system further includes a rail assembly for attachment to the manifold body and adapted to receive pins by which dielectric insulators are joined to the manifold assembly.

Differential manifolds

CERN Document Server

Kosinski, Antoni A

2007-01-01

The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho

Right-angled polyhedra and hyperbolic 3-manifolds

Science.gov (United States)

Vesnin, A. Yu.

2017-04-01

Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. Bibliography: 89 titles.

Topology of high-dimensional manifolds

Energy Technology Data Exchange (ETDEWEB)

Farrell, F T [State University of New York, Binghamton (United States); Goettshe, L [Abdus Salam ICTP, Trieste (Italy); Lueck, W [Westfaelische Wilhelms-Universitaet Muenster, Muenster (Germany)

2002-08-15

The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001. The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. The school consisted of 2 weeks of lecture courses and one week of conference. Thwo-part lecture notes volume contains the notes of most of the lecture courses.

Large Eddy Simulations of a Premixed Jet Combustor Using Flamelet-Generated Manifolds: Effects of Heat Loss and Subgrid-Scale Models

KAUST Repository

Hernandez Perez, Francisco E.; Lee, Bok Jik; Im, Hong G.; Fancello, Alessio; Donini, Andrea; van Oijen, Jeroen A.; de Goey, Philip H.

2017-01-01

Large eddy simulations of a turbulent premixed jet flame in a confined chamber were conducted using the flamelet-generated manifold technique for chemistry tabulation. The configuration is characterized by an off-center nozzle having an inner diameter of 10 mm, supplying a lean methane-air mixture with an equivalence ratio of 0.71 and a mean velocity of 90 m/s, at 573 K and atmospheric pressure. Conductive heat loss is accounted for in the manifold via burner-stabilized flamelets and the subgrid-scale (SGS) turbulencechemistry interaction is modeled via presumed probability density functions. Comparisons between numerical results and measured data show that a considerable improvement in the prediction of temperature is achieved when heat losses are included in the manifold, as compared to the adiabatic one. Additional improvement in the temperature predictions is obtained by incorporating radiative heat losses. Moreover, further enhancements in the LES predictions are achieved by employing SGS models based on transport equations, such as the SGS turbulence kinetic energy equation with dynamic coefficients. While the numerical results display good agreement up to a distance of 4 nozzle diameters downstream of the nozzle exit, the results become less satisfactory along the downstream, suggesting that further improvements in the modeling are required, among which a more accurate model for the SGS variance of progress variable can be relevant.

Large Eddy Simulations of a Premixed Jet Combustor Using Flamelet-Generated Manifolds: Effects of Heat Loss and Subgrid-Scale Models

KAUST Repository

Hernandez Perez, Francisco E.

2017-01-05

Large eddy simulations of a turbulent premixed jet flame in a confined chamber were conducted using the flamelet-generated manifold technique for chemistry tabulation. The configuration is characterized by an off-center nozzle having an inner diameter of 10 mm, supplying a lean methane-air mixture with an equivalence ratio of 0.71 and a mean velocity of 90 m/s, at 573 K and atmospheric pressure. Conductive heat loss is accounted for in the manifold via burner-stabilized flamelets and the subgrid-scale (SGS) turbulencechemistry interaction is modeled via presumed probability density functions. Comparisons between numerical results and measured data show that a considerable improvement in the prediction of temperature is achieved when heat losses are included in the manifold, as compared to the adiabatic one. Additional improvement in the temperature predictions is obtained by incorporating radiative heat losses. Moreover, further enhancements in the LES predictions are achieved by employing SGS models based on transport equations, such as the SGS turbulence kinetic energy equation with dynamic coefficients. While the numerical results display good agreement up to a distance of 4 nozzle diameters downstream of the nozzle exit, the results become less satisfactory along the downstream, suggesting that further improvements in the modeling are required, among which a more accurate model for the SGS variance of progress variable can be relevant.

Dynamical generation of maximally entangled states in two identical cavities

International Nuclear Information System (INIS)

Alexanian, Moorad

2011-01-01

The generation of entanglement between two identical coupled cavities, each containing a single three-level atom, is studied when the cavities exchange two coherent photons and are in the N=2,4 manifolds, where N represents the maximum number of photons possible in either cavity. The atom-photon state of each cavity is described by a qutrit for N=2 and a five-dimensional qudit for N=4. However, the conservation of the total value of N for the interacting two-cavity system limits the total number of states to only 4 states for N=2 and 8 states for N=4, rather than the usual 9 for two qutrits and 25 for two five-dimensional qudits. In the N=2 manifold, two-qutrit states dynamically generate four maximally entangled Bell states from initially unentangled states. In the N=4 manifold, two-qudit states dynamically generate maximally entangled states involving three or four states. The generation of these maximally entangled states occurs rather rapidly for large hopping strengths. The cavities function as a storage of periodically generated maximally entangled states.

The Hantzsche-Wendt manifold in cosmic topology

Science.gov (United States)

Aurich, R.; Lustig, S.

2014-08-01

The Hantzsche-Wendt space is one of the 17 multiply connected spaces of the three-dimensional Euclidean space {{{E}}^{3}}. It is a compact and orientable manifold which can serve as a model for a spatial finite universe. Since it possesses much fewer matched back-to-back circle pairs on the cosmic microwave background (CMB) sky than the other compact flat spaces, it can escape the detection by a search for matched circle pairs. The suppression of temperature correlations C(\\vartheta ) on large angular scales on the CMB sky is studied. It is shown that the large-scale correlations are of the same order as for the three-torus topology but express a much larger variability. The Hantzsche-Wendt manifold provides a topological possibility with reduced large-angle correlations that can hide from searches for matched back-to-back circle pairs.

Connections and curvatures on complex Riemannian manifolds

International Nuclear Information System (INIS)

Ganchev, G.; Ivanov, S.

1991-05-01

Characteristic connection and characteristic holomorphic sectional curvatures are introduced on a complex Riemannian manifold (not necessarily with holomorphic metric). For the class of complex Riemannian manifolds with holomorphic characteristic connection a classification of the manifolds with (pointwise) constant holomorphic characteristic curvature is given. It is shown that the conformal geometry of complex analytic Riemannian manifolds can be naturally developed on the class of locally conformal holomorphic Riemannian manifolds. Complex Riemannian manifolds locally conformal to the complex Euclidean space are characterized with zero conformal fundamental tensor and zero conformal characteristic tensor. (author). 12 refs

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin

2013-01-01

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.

2013-09-26

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Strongly not relatives Kähler manifolds

Directory of Open Access Journals (Sweden)

Zedda Michela

2017-02-01

Full Text Available In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.

Differential geometry of quasi-Sasakian manifolds

International Nuclear Information System (INIS)

Kirichenko, V F; Rustanov, A R

2002-01-01

The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of CR 1 quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the B-transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind

Manifold seal structure for fuel cell stack

Science.gov (United States)

Collins, William P.

1988-01-01

The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.

BPS state counting using wall-crossing, holomorphic anomalies and modularity

Energy Technology Data Exchange (ETDEWEB)

Wotschke, Thomas

2013-05-15

In this thesis we examine the counting of BPS states using wall-crossing, holomorphic anomalies and modularity. We count BPS states that arise in two setups: multiple M5-branes wrapping P x T{sup 2}, where P denotes a divisor inside a Calabi-Yau threefold and topological string theory on elliptic Calabi-Yau threefolds. The first setup has a dual description as type IIA string theory via a D4-D2-D0 brane system. Furthermore it leads to two descriptions depending on the size of P and T{sup 2} relative to each other. For the case of a small divisor P this setup is described by the (0,4) Maldacena-Strominger-Witten conformal field theory of a black hole in M-theory and for the case of small T{sup 2} the setup can by described by N=4 topological Yang-Mills theory on P. The BPS states are counted by the modified elliptic genus, which can be decomposed into a vector-valued modular form that provides the generating function for the BPS invariants and a Siegel-Narain theta function. In the first part we discuss the holomorphic anomaly of the modified elliptic genus for the case of two M5-branes and divisors with b{sup +}{sub 2}(P)=1. Due to the wall-crossing effect the change in the generating function is captured by an indefinite theta function, which is a mock modular form. We use the Kontsevich-Soibelman wall-crossing formula to determine the jumps in the modified elliptic genus. Using the regularisation procedure for mock modular forms of Zwegers, modularity can be restored at the cost of holomorphicity. We show that the non-holomorphic completion is due to bound states of single M5-branes. At the attractor point in the moduli space we prove the holomorphic anomaly equation, which is compatible with the holomorphic anomaly equations observed in the context of N=4 Yang-Mills theory on P{sup 2} and E-strings on a del Pezzo surface. We calculate the generating functions of BPS invariants for the divisors P{sup 2}, F{sub 0}, F{sub 1} and the del Pezzo surface dP{sub 8} and

BPS state counting using wall-crossing, holomorphic anomalies and modularity

International Nuclear Information System (INIS)

Wotschke, Thomas

2013-05-01

In this thesis we examine the counting of BPS states using wall-crossing, holomorphic anomalies and modularity. We count BPS states that arise in two setups: multiple M5-branes wrapping P x T 2 , where P denotes a divisor inside a Calabi-Yau threefold and topological string theory on elliptic Calabi-Yau threefolds. The first setup has a dual description as type IIA string theory via a D4-D2-D0 brane system. Furthermore it leads to two descriptions depending on the size of P and T 2 relative to each other. For the case of a small divisor P this setup is described by the (0,4) Maldacena-Strominger-Witten conformal field theory of a black hole in M-theory and for the case of small T 2 the setup can by described by N=4 topological Yang-Mills theory on P. The BPS states are counted by the modified elliptic genus, which can be decomposed into a vector-valued modular form that provides the generating function for the BPS invariants and a Siegel-Narain theta function. In the first part we discuss the holomorphic anomaly of the modified elliptic genus for the case of two M5-branes and divisors with b + 2 (P)=1. Due to the wall-crossing effect the change in the generating function is captured by an indefinite theta function, which is a mock modular form. We use the Kontsevich-Soibelman wall-crossing formula to determine the jumps in the modified elliptic genus. Using the regularisation procedure for mock modular forms of Zwegers, modularity can be restored at the cost of holomorphicity. We show that the non-holomorphic completion is due to bound states of single M5-branes. At the attractor point in the moduli space we prove the holomorphic anomaly equation, which is compatible with the holomorphic anomaly equations observed in the context of N=4 Yang-Mills theory on P 2 and E-strings on a del Pezzo surface. We calculate the generating functions of BPS invariants for the divisors P 2 , F 0 , F 1 and the del Pezzo surface dP 8 and dP 9 ((1)/(2) K3). In the second part we study

On some classes of super quasi-Einstein manifolds

International Nuclear Information System (INIS)

Ozguer, Cihan

2009-01-01

Quasi-Einstein and generalized quasi-Einstein manifolds are the generalizations of Einstein manifolds. In this study, we consider a super quasi-Einstein manifold, which is another generalization of an Einstein manifold. We find the curvature characterizations of a Ricci-pseudosymmetric and a quasi-conformally flat super quasi-Einstein manifolds. We also consider the condition C ∼ .S=0 on a super quasi-Einstein manifold, where C ∼ and S denote the quasi-conformal curvature tensor and Ricci tensor of the manifold, respectively.

Natural Connections on Riemannian Product Manifolds

OpenAIRE

Gribacheva, Dobrinka

2011-01-01

A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.

Invariance for Single Curved Manifold

KAUST Repository

Castro, Pedro Machado Manhaes de

2012-01-01

Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.

Invariance for Single Curved Manifold

KAUST Repository

Castro, Pedro Machado Manhaes de

2012-08-01

Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.

Abelian gauge symmetries in F-theory and dual theories

Science.gov (United States)

Song, Peng

In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by

On the geometry of Riemannian manifolds with a Lie structure at infinity

Directory of Open Access Journals (Sweden)

Bernd Ammann

2004-01-01

Full Text Available We study a generalization of the geodesic spray and give conditions for noncomapct manifolds with a Lie structure at infinity to have positive injectivity radius. We also prove that the geometric operators are generated by the given Lie algebra of vector fields. This is the first one in a series of papers devoted to the study of the analysis of geometric differential operators on manifolds with Lie structure at infinity.

The manifold model for space-time

International Nuclear Information System (INIS)

Heller, M.

1981-01-01

Physical processes happen on a space-time arena. It turns out that all contemporary macroscopic physical theories presuppose a common mathematical model for this arena, the so-called manifold model of space-time. The first part of study is an heuristic introduction to the concept of a smooth manifold, starting with the intuitively more clear concepts of a curve and a surface in the Euclidean space. In the second part the definitions of the Csub(infinity) manifold and of certain structures, which arise in a natural way from the manifold concept, are given. The role of the enveloping Euclidean space (i.e. of the Euclidean space appearing in the manifold definition) in these definitions is stressed. The Euclidean character of the enveloping space induces to the manifold local Euclidean (topological and differential) properties. A suggestion is made that replacing the enveloping Euclidean space by a discrete non-Euclidean space would be a correct way towards the quantization of space-time. (author)

Manifold Regularized Correlation Object Tracking

OpenAIRE

Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling

2017-01-01

In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped fr...

Toric geometry of G2-manifolds

DEFF Research Database (Denmark)

Madsen, Thomas Bruun; Swann, Andrew Francis

We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz...

Analysis of mixed mode microwave distribution manifolds

International Nuclear Information System (INIS)

White, T.L.

1982-09-01

The 28-GHz microwave distribution manifold used in the ELMO Bumpy Torus-Scale (EBT-S) experiments consists of a toroidal metallic cavity, whose dimensions are much greater than a wavelength, fed by a source of microwave power. Equalization of the mixed mode power distribution ot the 24 cavities of EBT-S is accomplished by empirically adjusting the coupling irises which are equally spaced around the manifold. The performance of the manifold to date has been very good, yet no analytical models exist for optimizing manifold transmission efficiency or for scaling this technology to the EBT-P manifold design. The present report develops a general model for mixed mode microwave distribution manifolds based on isotropic plane wave sources of varying amplitudes that are distributed toroidally around the manifold. The calculated manifold transmission efficiency for the most recent EBT-S coupling iris modification is 90%. This agrees with the average measured transmission efficiency. Also, the model predicts the coupling iris areas required to balance the distribution of microwave power while maximizing transmission efficiency, and losses in waveguide feeds connecting the irises to the cavities of EBT are calculated using an approach similar to the calculation of mainfold losses. The model will be used to evaluate EBT-P manifold designs

Heterotic M-theory, warped geometry and the cosmological constant problem

International Nuclear Information System (INIS)

Krause, A.

2001-01-01

The first part of this thesis analyzes whether a locally flat background represents a stable vacuum for the proposed heterotic M-theory. A calculation of the leading order supergravity exchange diagrams leads to the conclusion that the locally flat vacuum cannot be stable. Afterwards a comparison with the corresponding weakly coupled heterotic string amplitudes is made. Next, we consider compactifications of heterotic M-theory on a Calabi-Yau threefold, including a non-vanishing G-flux. The ensuing warped-geometry is determined completely and used to show that the variation of the Calabi-Yau volume along the orbifold direction varies quadratically with distance instead linearly as suggested by an earlier first order approximation. In the second part of this thesis we propose a mechanism for obtaining a small cosmological constant. This mechanism consists of the separation of two domain-walls, which together constitute our world, up to a distance 2l ≅1/M GUT . The resulting warped-geometry leads to an exponential suppression of the cosmological constant, which thereby can obtain its observed value without introducing a large hierarchy. An embedding of this set-up into IIB string-theory entails an SU(6) grand unified theory with a natural explanation of the Higgs doublet-triplet splitting. Finally, we examine to what extent the string-theory T-duality can influence curvature. To this aim we derive the full transformation of the curvature-tensor under T-duality. (orig.)

Towards generalized mirror symmetry for twisted connected sum G 2 manifolds

Science.gov (United States)

Braun, Andreas P.; Del Zotto, Michele

2018-03-01

We revisit our construction of mirror symmetries for compactifications of Type II superstrings on twisted connected sum G 2 manifolds. For a given G 2 manifold, we discuss evidence for the existence of mirror symmetries of two kinds: one is an autoequivalence for a given Type II superstring on a mirror pair of G 2 manifolds, the other is a duality between Type II strings with different chiralities for another pair of mirror manifolds. We clarify the role of the B-field in the construction, and check that the corresponding massless spectra are respected by the generalized mirror maps. We discuss hints towards a homological version based on BPS spectroscopy. We provide several novel examples of smooth, as well as singular, mirror G 2 backgrounds via pairs of dual projecting tops. We test our conjectures against a Joyce orbifold example, where we reproduce, using our geometrical methods, the known mirror maps that arise from the SCFT worldsheet perspective. Along the way, we discuss non-Abelian gauge symmetries, and argue for the generation of the Affleck-Harvey-Witten superpotential in the pure SYM case.

Torsions of 3-dimensional manifolds

CERN Document Server

Wurzbacher, T

2002-01-01

From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews

TBA-like integral equations from quantized mirror curves

Energy Technology Data Exchange (ETDEWEB)

Okuyama, Kazumi [Department of Physics, Shinshu University,Matsumoto 390-8621 (Japan); Zakany, Szabolcs [Département de Physique Théorique, Université de Genève,Genève, CH-1211 (Switzerland)

2016-03-15

Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in certain cases, this resolvent function satisfies a system of non-linear integral equations whose structure is very similar to the Thermodynamic Bethe Ansatz (TBA) systems. This can be used to compute spectral traces, both exactly and as a semiclassical expansion. As a main example, we consider the system related to the quantized mirror curve of local ℙ{sup 2}. According to a recent proposal, the traces of this operator are determined by the refined BPS indices of the underlying CY. We use our non-linear integral equations to test that proposal.

TBA-like integral equations from quantized mirror curves

Science.gov (United States)

Okuyama, Kazumi; Zakany, Szabolcs

2016-03-01

Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in certain cases, this resolvent function satisfies a system of non-linear integral equations whose structure is very similar to the Thermodynamic Bethe Ansatz (TBA) systems. This can be used to compute spectral traces, both exactly and as a semiclassical expansion. As a main example, we consider the system related to the quantized mirror curve of local P2. According to a recent proposal, the traces of this operator are determined by the refined BPS indices of the underlying CY. We use our non-linear integral equations to test that proposal.

Flipped SU(5) from manifold compactification of the ten-dimensional heterotic string

Energy Technology Data Exchange (ETDEWEB)

Campbell, B.A.; Ellis, J.; Hagelin, J.S.; Ticciati, R.; Nanopoulos, D.V.

1987-11-19

We show that a recently proposed flipped SU(5) x U(1) GUT cannot be obtained from a conventional SO(10) GUT, nor from the heterotic string by Hosotani gauge symmetry breaking of E/sub 6/ on a manifold with (2,2) world-sheet supersymmetry. It can in principle be obtained by Hosotani gauge symmetry breaking of SO(10) on a manifold with (1,2) world-sheet supersymmetry. We identify the topological conditions under which the required chiral matter generations, Higgs multiplets, and gauge singlet fields can be light. In particular we show that non-perturbative world-sheet instanton effects neither destabilize the manifold nor give masses to the gauge singlets. The required Yukawa couplings are not forbidden by any known selection rules.

Toric Methods in F-Theory Model Building

Directory of Open Access Journals (Sweden)

Johanna Knapp

2011-01-01

Full Text Available We discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework. After introducing the basic properties of global F-theory GUTs, we give a self-contained review of toric geometry and introduce all the tools that are necessary to construct and analyze global F-theory models. We will explain how to systematically obtain a large class of compact Calabi-Yau fourfolds which can support F-theory GUTs by using the software package PALP.

Holographic effective field theories

Energy Technology Data Exchange (ETDEWEB)

Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei' , Università di Padova,and INFN - Sezione di Padova, Via Marzolo 8, I-35131 Padova (Italy); Zaffaroni, Alberto [Dipartimento di Fisica, Università di Milano-Bicocca,and INFN - Sezione di Milano-Bicocca, I-20126 Milano (Italy)

2016-06-28

We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.

Orientifolds and duality cascades: confinement before the wall

Science.gov (United States)

Argurio, Riccardo; Bertolini, Matteo

2018-02-01

We consider D-branes at orientifold singularities and discuss two properties of the corresponding low energy four-dimensional effective theories which are not shared, generically, by other Calabi-Yau singularities. The first property is that duality cascades are finite and, unlike ordinary ones, do not require an infinite number of degrees of freedom to be UV-completed. The second is that orientifolds tend to stabilize runaway directions. These two properties can have interesting implications and widen in an intriguing way the variety of gauge theories one can describe using D-branes.

TeV scale leptoquarks as a signature of standard-like superstring models

International Nuclear Information System (INIS)

Halyo, E.

1993-12-01

We show that there can be TeV scale scalar and fermionic leptoquarks with very weak Yukawa couplings in a generic standard-like superstring model. Leptoquark (down-like) quark mixing though present, is not large enough to violate the unitary bounds on the CKM matrix. The constraints on the leptoquark masses and couplings from flavor changing neutral currents are easily satisfied whereas those from baryon number violation may cause problems. The leptoquarks of the model are compared to the ones in the E 6 Calabi-Yau models. (author) 14 refs

On Kähler–Norden manifolds

Indian Academy of Sciences (India)

Abstract. This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler–Norden manifolds using the theory of Tachibana operators is presented.

Analytic manifolds in uniform algebras

International Nuclear Information System (INIS)

Tonev, T.V.

1988-12-01

Here we extend Bear-Hile's result concerning the version of famous Bishop's theorem for one-dimensional analytic structures in two directions: for n-dimensional complex analytic manifolds, n>1, and for generalized analytic manifolds. 14 refs

On the interplay between string theory and field theory

International Nuclear Information System (INIS)

Brunner, I.

1998-01-01

In this thesis, we have discussed various aspects of branes in string theory and M-theory. In chapter 2 we were able to construct six-dimensional chiral interacting eld theories from Hanany-Witten like brane setups. The field theory requirement that the anomalies cancel was reproduced by RR-charge conservation in the brane setup. The data of the Hanany-Witten setup, which consists of brane positions, was mapped to instanton data. The orbifold construction can be extended to D and E type singularities. In chapter 3 we discussed a matrix conjecture, which claims that M-theory in the light cone gauge is described by the quantum mechanics of D0 branes. Toroidal compactifications of M-theory have a description in terms of super Yang-Mills theory an the dual torus. For more than three compactified dimensions, more degrees of freedom have to be added. In some sense, the philosophy in this chapter is orthogonal to the previous chapter: Here, we want to get M-theory results from eld theory considerations, whereas in the previous chapter we obtained eld theory results by embedding the theories in string theory. Our main focus was on the compactification on T 6 , which leads to complications. Here, the Matrix model is again given by an eleven dimensional theory, not by a lower dimensional field theory. Other problems and possible resolutions of Matrix theory are discussed at the end of chapter 3. In the last chapter we considered M- and F-theory compactifications on Calabi-Yau fourfolds. After explaining some basics of fourfolds, we showed that the web of fourfolds is connected by singular transitions. The two manifolds which are connected by the transition are different resolutions of the same singular manifold. The resolution of the singularities can lead to a certain type of divisors, which lead to non-perturbative superpotentials, when branes wrap them. The vacua connected by the transitions can be physically very different. (orig.)

On the interplay between string theory and field theory

Energy Technology Data Exchange (ETDEWEB)

Brunner, I.

1998-07-08

In this thesis, we have discussed various aspects of branes in string theory and M-theory. In chapter 2 we were able to construct six-dimensional chiral interacting eld theories from Hanany-Witten like brane setups. The field theory requirement that the anomalies cancel was reproduced by RR-charge conservation in the brane setup. The data of the Hanany-Witten setup, which consists of brane positions, was mapped to instanton data. The orbifold construction can be extended to D and E type singularities. In chapter 3 we discussed a matrix conjecture, which claims that M-theory in the light cone gauge is described by the quantum mechanics of D0 branes. Toroidal compactifications of M-theory have a description in terms of super Yang-Mills theory an the dual torus. For more than three compactified dimensions, more degrees of freedom have to be added. In some sense, the philosophy in this chapter is orthogonal to the previous chapter: Here, we want to get M-theory results from eld theory considerations, whereas in the previous chapter we obtained eld theory results by embedding the theories in string theory. Our main focus was on the compactification on T{sup 6}, which leads to complications. Here, the Matrix model is again given by an eleven dimensional theory, not by a lower dimensional field theory. Other problems and possible resolutions of Matrix theory are discussed at the end of chapter 3. In the last chapter we considered M- and F-theory compactifications on Calabi-Yau fourfolds. After explaining some basics of fourfolds, we showed that the web of fourfolds is connected by singular transitions. The two manifolds which are connected by the transition are different resolutions of the same singular manifold. The resolution of the singularities can lead to a certain type of divisors, which lead to non-perturbative superpotentials, when branes wrap them. The vacua connected by the transitions can be physically very different. (orig.)

On topological approach to local theory of surfaces in Calabi-Yau threefolds

DEFF Research Database (Denmark)

Gukov, Sergei; Liu, Chiu-Chu Melissa; Sheshmani, Artan

2017-01-01

We study the web of dualities relating various enumerative invariants, notably Gromov-Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson-Thomas gauge theory and its reductions to D=4 and D=2 which are relevant to the local theory of surfaces...

De Sitter vacua in no-scale supergravities and Calabi-Yau string models

CERN Document Server

Covi, Laura; Gross, Christian; Louis, Jan; Palma, Gonzalo A; Scrucca, Claudio A

2008-01-01

We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N=1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kahler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the `sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kahler potential which b...

de Sitter vacua in no-scale supergravities and Calabi-Yau string models

International Nuclear Information System (INIS)

Covi, L.; Gross, C.; Scrucca, C.A.

2008-04-01

We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N = 1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kaehler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the 'sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kaehler potential which break the no-scale property may allow to lift these masses. (orig.)

Slow manifolds in chemical kinetics

International Nuclear Information System (INIS)

Shahzad, M.; Haq, I. U.; Sultan, F.; Wahab, A.; Faizullah, F.; Rahman, G. U.

2016-01-01

Modelling the chemical system, especially for complex and higher dimensional problems, gives an easy way to handle the ongoing reaction process with respect to time. Here, we will consider some of the newly developed computational methods commonly used for model reductions in a chemical reaction. An effective (simple) method is planned to measure the low dimensional manifold, which reduces the higher dimensional system in such a way that it may not affect the precision of the whole mechanism. The phase flow of the solution trajectories near the equilibrium point is observed while the initial approximation is measured with the spectral quasi equilibrium manifold, which starts from the equilibrium point. To make it an invariant curve, the approximated curve is first refined a certain number of times using the method of invariant grids. The other way of getting the reduced data in the low dimensional manifold is possible through the intrinsic low dimensional manifold. Then, we compare these two invariant curves given by both the methods. Finally, the idea is extended to the higher dimensional manifold, where more number of progress variables will be added. (author)

Manifold Regularized Correlation Object Tracking.

Science.gov (United States)

Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling

2018-05-01

In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions. Thus, the final classifier in our method is trained with positive, negative, and unlabeled base samples, which is a semisupervised learning framework. A block optimization strategy is further introduced to learn a manifold regularization-based correlation filter for efficient online tracking. Experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state-of-the-art tracking approaches.

Automatic detection of end-diastole and end-systole from echocardiography images using manifold learning

International Nuclear Information System (INIS)

Gifani, Parisa; Behnam, Hamid; Shalbaf, Ahmad; Sani, Zahra Alizadeh

2010-01-01

The automatic detection of end-diastole and end-systole frames of echocardiography images is the first step for calculation of the ejection fraction, stroke volume and some other features related to heart motion abnormalities. In this paper, the manifold learning algorithm is applied on 2D echocardiography images to find out the relationship between the frames of one cycle of heart motion. By this approach the nonlinear embedded information in sequential images is represented in a two-dimensional manifold by the LLE algorithm and each image is depicted by a point on reconstructed manifold. There are three dense regions on the manifold which correspond to the three phases of cardiac cycle ('isovolumetric contraction', 'isovolumetric relaxation', 'reduced filling'), wherein there is no prominent change in ventricular volume. By the fact that the end-systolic and end-diastolic frames are in isovolumic phases of the cardiac cycle, the dense regions can be used to find these frames. By calculating the distance between consecutive points in the manifold, the isovolumic frames are mapped on the three minimums of the distance diagrams which were used to select the corresponding images. The minimum correlation between these images leads to detection of end-systole and end-diastole frames. The results on six healthy volunteers have been validated by an experienced echo cardiologist and depict the usefulness of the presented method

Classical and quantum N=2 supersymmetric black holes

International Nuclear Information System (INIS)

Behrndt, K.; De Wit, B.; Kallosh, R.; Luest, D.; Mohaupt, T.

1997-01-01

We use heterotic/type-II prepotentials to study quantum/classical black holes with half the N=2, D=4 supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula is given by the tree-level entropy formula with the tree-level coupling constant replaced by the perturbative coupling constant. In the case of type-II compactifications, we display a new entropy/area formula associated with axion-free black-hole solutions, which depends on the electric and magnetic charges as well as on certain topological data of Calabi-Yau three-folds, namely the intersection numbers, the second Chern class and the Euler number of the three-fold. We show that, for both heterotic and type-II theories, there is the possibility to relax the usual requirement of the non-vanishing of some of the charges and still have a finite entropy. (orig.)

Total Variation Regularization for Functions with Values in a Manifold

KAUST Repository

Lellmann, Jan

2013-12-01

While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.

Total Variation Regularization for Functions with Values in a Manifold

KAUST Repository

Lellmann, Jan; Strekalovskiy, Evgeny; Koetter, Sabrina; Cremers, Daniel

2013-01-01

While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories. © 2013 IEEE.

Electromyographic Study of a Sequence of Yau-Man Kung Fu Palm Strikes with and without Impact.

Science.gov (United States)

Neto, Osmar Pinto; Magini, Marcio; Pacheco, Marcos T T

2007-01-01

IN MARTIAL ARTS AND CONTACT SPORTS, STRIKES ARE OFTEN TRAINED IN TWO DIFFERENT WAYS: with and without impacts. This study aims to compare the electromyographical activity (EMG) of the triceps brachii (TB), biceps brachii (BB) and brachioradialis (BR) muscles during strikes with and without impacts. Eight Yau-Man Kung Fu practitioners participated in the experiment. Each participant performed 5 sequences of 5 consecutive KF Yau-Man palm strikes with no impact intercalated with 5 sequences of 5 repetitions targeting a KF training shield. Surface EMG signals were obtained from the TB, BB, and RB for 3.0 seconds using an eight-channel module with a total amplifier gain of 2000 and sampled at 3500 Hz. The EMG analyses were done in the time (rms) and frequency (wavelet) domains. For the frequency domain, Morlet wavelet power spectra were obtained and an original method was used to quantify statistically significant regions on the power spectra. The results both in the time and frequency domains indicate a higher TB and BR muscle activity for the strikes with impacts. No significant difference was found for the BB in the two different scenarios. In addition, the results show that the wavelet power spectra pattern for the three analysed muscles obtained from the strikes with and without impacts were similar. Key pointsEMG analysis of a sequence of Kung Fu strikes demonstrates higher Triceps Brachii and Brachioradialis muscle activity for strikes with impact than strikes without impact.An original reliable method for quantifying EMG wavelet transform results is presented.EMG wavelet power spectra describe muscle roles during a Kung Fu sequence of strikes.

One-loop effective potential on hyperbolic manifolds

International Nuclear Information System (INIS)

Cognola, G.; Kirsten, K.; Zerbini, S.

1993-01-01

The one-loop effective potential for a scalar field defined on an ultrastatic space-time whose spatial part is a compact hyperbolic manifold is studied using ζ-function regularization for the one-loop effective action. Other possible regularizations are discussed in detail. The renormalization group equations are derived, and their connection with the conformal anomaly is pointed out. The symmetry breaking and the topological mass generation are also discussed

Hyperspherical Manifold for EEG Signals of Epileptic Seizures

Directory of Open Access Journals (Sweden)

Tahir Ahmad

2012-01-01

Full Text Available The mathematical modelling of EEG signals of epileptic seizures presents a challenge as seizure data is erratic, often with no visible trend. Limitations in existing models indicate a need for a generalized model that can be used to analyze seizures without the need for apriori information, whilst minimizing the loss of signal data due to smoothing. This paper utilizes measure theory to design a discrete probability measure that reformats EEG data without altering its geometric structure. An analysis of EEG data from three patients experiencing epileptic seizures is made using the developed measure, resulting in successful identification of increased potential difference in portions of the brain that correspond to physical symptoms demonstrated by the patients. A mapping then is devised to transport the measure data onto the surface of a high-dimensional manifold, enabling the analysis of seizures using directional statistics and manifold theory. The subset of seizure signals on the manifold is shown to be a topological space, verifying Ahmad's approach to use topological modelling.

The ubiquitous throat

International Nuclear Information System (INIS)

Hebecker, A.; March-Russell, J.

2007-01-01

We attempt to quantify the widely-held belief that large hierarchies induced by strongly-warped geometries are common in the string theory landscape. To this end, we focus on the arguably best-understood subset of vacua-type IIB Calabi-Yau orientifolds with non-perturbative Kaehler stabilization and a SUSY-breaking uplift (the KKLT setup). Within this framework, vacua with a realistically small cosmological constant are expected to come from Calabi-Yaus with a large number of 3-cycles. For appropriate choices of flux numbers, many of these 3-cycles can, in general, shrink to produce near-conifold geometries. Thus, a simple statistical analysis in the spirit of Denef and Douglas allows us to estimate the expected number and length of Klebanov-Strassler throats in the given set of vacua. We find that throats capable of explaining the electroweak hierarchy are expected to be present in a large fraction of the landscape vacua while shorter throats are essentially unavoidable in a statistical sense

Quantum invariants of knots and 3-manifolds. 2. rev. ed.

International Nuclear Information System (INIS)

Turaev, Vladimir G.

2010-01-01

Due to the strong appeal and wide use of this monograph, it is now available in its second revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. From the contents: - Invariants of graphs in Euclidean 3-space and of closed 3-manifolds - Foundations of topological quantum field theory - Three-dimensional topological quantum field theory - Two-dimensional modular functors - 6j-symbols - Simplicial state sums on 3-manifolds - Shadows of manifolds and state sums on shadows - Constructions of modular categories. (orig.)

Laplacian manifold regularization method for fluorescence molecular tomography

Science.gov (United States)

He, Xuelei; Wang, Xiaodong; Yi, Huangjian; Chen, Yanrong; Zhang, Xu; Yu, Jingjing; He, Xiaowei

2017-04-01

Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ℓ1-regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ℓ1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai-Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ℓ1 minimization method in both spatial aggregation and location accuracy.

Role(s) of anti-symmetrical background field in string theory; Role(s) du champ de fond antisymetrique en theorie des cordes

Energy Technology Data Exchange (ETDEWEB)

Fidanza, St

2003-11-15

In the first chapter (titled: non-commutative D-branes), we show that the B anti-symmetrical background fields can be embedded in the non-commutativity of branes and can distort gauge theories that branes convey. We know how to describe this transformation in the Abelian case thanks to the Kontsevic quantification formula. Moreover this formula combined to the Seiberg-Witter transformation allows one to compute more rapidly the explicit terms. For the non-Abelian case the situation is less clear. In the chapter 2 (titled: non-Abelian M5-branes), we have tackled the issue of the fields of a packet of N M5-branes. The direct approach based on a 6 dimensional super-symmetric multiplets has led to a stunning dead end, we have not been able to reproduce the expected anomaly in N{sup 3}. We have presented in a unified manner different gauge theories. We have shown that we can get a number of freedom degrees in the magnitude order of N{sup 3} from computations based on geometrical configurations of M2 membranes. In the chapter 3 (titled: systematizing mirror symmetry) we have shown that if the presence of a non-trivial Neveu-Schwarz flux constrains the compactification manifold geometry to shift from the Calabi-Yau case, we can yet specify a mirror symmetry that mixes geometry and background fields. (A.C.)

Vacua and inflation in string theory and supergravity

International Nuclear Information System (INIS)

Rummel, Markus

2013-07-01

We study the connection between the early and late accelerated expansion of the universe and string theory. In Part I of this thesis, the observational degeneracy between single field models of inflation with canonical kinetic terms and noncanonical kinetic terms, in particular string theory inspired models, is discussed. The 2-point function observables of a given non-canonical theory and its canonical transform that is obtained by matching the inflationary trajectories in phase space are found to match in the case of Dirac-Born-Infeld (DBI) inflation. At the level of the 3-point function observables (non-Gaussianities), we find degeneracy between non-canonical inflation and canonical inflation with a potential that includes a sum of modulated terms. In Part II, we present explicit examples for de Sitter vacua in type IIB string theory. After deriving a sufficient condition for de Sitter vacua in the Kahler uplifting scenario, we show that a globally consistent de Sitter model can be realized on a certain Calabi-Yau manifold. All geometric moduli are stabilized and all known consistency constraints are fulfilled. The complex structure moduli stabilization by fluxes is studied explicitly for a small number of cycles. Extrapolating to a larger number of flux carrying cycles, we verify statistical studies in the literature which show that, in principle, the string landscape can account for a universe with an extremely small cosmological constant.

Role(s) of anti-symmetrical background field in string theory

International Nuclear Information System (INIS)

Fidanza, St.

2003-11-01

In the first chapter (titled: non-commutative D-branes), we show that the B anti-symmetrical background fields can be embedded in the non-commutativity of branes and can distort gauge theories that branes convey. We know how to describe this transformation in the Abelian case thanks to the Kontsevic quantification formula. Moreover this formula combined to the Seiberg-Witter transformation allows one to compute more rapidly the explicit terms. For the non-Abelian case the situation is less clear. In the chapter 2 (titled: non-Abelian M5-branes), we have tackled the issue of the fields of a packet of N M5-branes. The direct approach based on a 6 dimensional super-symmetric multiplets has led to a stunning dead end, we have not been able to reproduce the expected anomaly in N 3 . We have presented in a unified manner different gauge theories. We have shown that we can get a number of freedom degrees in the magnitude order of N 3 from computations based on geometrical configurations of M2 membranes. In the chapter 3 (titled: systematizing mirror symmetry) we have shown that if the presence of a non-trivial Neveu-Schwarz flux constrains the compactification manifold geometry to shift from the Calabi-Yau case, we can yet specify a mirror symmetry that mixes geometry and background fields. (A.C.)

Vacua and inflation in string theory and supergravity

Energy Technology Data Exchange (ETDEWEB)

Rummel, Markus

2013-07-15

We study the connection between the early and late accelerated expansion of the universe and string theory. In Part I of this thesis, the observational degeneracy between single field models of inflation with canonical kinetic terms and noncanonical kinetic terms, in particular string theory inspired models, is discussed. The 2-point function observables of a given non-canonical theory and its canonical transform that is obtained by matching the inflationary trajectories in phase space are found to match in the case of Dirac-Born-Infeld (DBI) inflation. At the level of the 3-point function observables (non-Gaussianities), we find degeneracy between non-canonical inflation and canonical inflation with a potential that includes a sum of modulated terms. In Part II, we present explicit examples for de Sitter vacua in type IIB string theory. After deriving a sufficient condition for de Sitter vacua in the Kahler uplifting scenario, we show that a globally consistent de Sitter model can be realized on a certain Calabi-Yau manifold. All geometric moduli are stabilized and all known consistency constraints are fulfilled. The complex structure moduli stabilization by fluxes is studied explicitly for a small number of cycles. Extrapolating to a larger number of flux carrying cycles, we verify statistical studies in the literature which show that, in principle, the string landscape can account for a universe with an extremely small cosmological constant.

An introduction to differential manifolds

CERN Document Server

Lafontaine, Jacques

2015-01-01

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...

Manifold corrections on spinning compact binaries

International Nuclear Information System (INIS)

Zhong Shuangying; Wu Xin

2010-01-01

This paper deals mainly with a discussion of three new manifold correction methods and three existing ones, which can numerically preserve or correct all integrals in the conservative post-Newtonian Hamiltonian formulation of spinning compact binaries. Two of them are listed here. One is a new momentum-position scaling scheme for complete consistency of both the total energy and the magnitude of the total angular momentum, and the other is the Nacozy's approach with least-squares correction of the four integrals including the total energy and the total angular momentum vector. The post-Newtonian contributions, the spin effects, and the classification of orbits play an important role in the effectiveness of these six manifold corrections. They are all nearly equivalent to correct the integrals at the level of the machine epsilon for the pure Kepler problem. Once the third-order post-Newtonian contributions are added to the pure orbital part, three of these corrections have only minor effects on controlling the errors of these integrals. When the spin effects are also included, the effectiveness of the Nacozy's approach becomes further weakened, and even gets useless for the chaotic case. In all cases tested, the new momentum-position scaling scheme always shows the optimal performance. It requires a little but not much expensive additional computational cost when the spin effects exist and several time-saving techniques are used. As an interesting case, the efficiency of the correction to chaotic eccentric orbits is generally better than one to quasicircular regular orbits. Besides this, the corrected fast Lyapunov indicators and Lyapunov exponents of chaotic eccentric orbits are large as compared with the uncorrected counterparts. The amplification is a true expression of the original dynamical behavior. With the aid of both the manifold correction added to a certain low-order integration algorithm as a fast and high-precision device and the fast Lyapunov

Entangled de Sitter from stringy axionic Bell pair I. An analysis using Bunch-Davies vacuum

International Nuclear Information System (INIS)

Choudhury, Sayantan; Panda, Sudhakar

2018-01-01

In this work, we study the quantum entanglement and compute entanglement entropy in de Sitter space for a bipartite quantum field theory driven by an axion originating from Type IIB string compactification on a Calabi-Yau three fold (CY 3 ) and in the presence of an NS5 brane. For this computation, we consider a spherical surface S 2 , which divides the spatial slice of de Sitter (dS 4 ) into exterior and interior sub-regions. We also consider the initial choice of vacuum to be Bunch-Davies state. First we derive the solution of the wave function of the axion in a hyperbolic open chart by constructing a suitable basis for Bunch-Davies vacuum state using Bogoliubov transformation. We then derive the expression for density matrix by tracing over the exterior region. This allows us to compute the entanglement entropy and Renyi entropy in 3 + 1 dimension. Furthermore, we quantify the UV-finite contribution of the entanglement entropy which contain the physics of long range quantum correlations of our expanding universe. Finally, our analysis complements the necessary condition for generating non-vanishing entanglement entropy in primordial cosmology due to the axion. (orig.)

Entangled de Sitter from stringy axionic Bell pair I. An analysis using Bunch-Davies vacuum

Energy Technology Data Exchange (ETDEWEB)

Choudhury, Sayantan [Inter-University Centre for Astronomy and Astrophysics, Pune (India); Tata Institute of Fundamental Research, Department of Theoretical Physics, Mumbai (India); Panda, Sudhakar [Institute of Physics, Bhubaneswar, Odisha (India); National Institute of Science Education and Research, Bhubaneswar, Odisha (India); Homi Bhabha National Institute, Mumbai (India)

2018-01-15

In this work, we study the quantum entanglement and compute entanglement entropy in de Sitter space for a bipartite quantum field theory driven by an axion originating from Type IIB string compactification on a Calabi-Yau three fold (CY{sup 3}) and in the presence of an NS5 brane. For this computation, we consider a spherical surface S{sup 2}, which divides the spatial slice of de Sitter (dS{sub 4}) into exterior and interior sub-regions. We also consider the initial choice of vacuum to be Bunch-Davies state. First we derive the solution of the wave function of the axion in a hyperbolic open chart by constructing a suitable basis for Bunch-Davies vacuum state using Bogoliubov transformation. We then derive the expression for density matrix by tracing over the exterior region. This allows us to compute the entanglement entropy and Renyi entropy in 3 + 1 dimension. Furthermore, we quantify the UV-finite contribution of the entanglement entropy which contain the physics of long range quantum correlations of our expanding universe. Finally, our analysis complements the necessary condition for generating non-vanishing entanglement entropy in primordial cosmology due to the axion. (orig.)

Pluripotential theory on quaternionic manifolds

Science.gov (United States)

Alesker, Semyon

2012-05-01

On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Ampère operator is defined. It is shown that it satisfies a version of the theorems of A. D. Alexandrov and Chern-Levine-Nirenberg. For more special classes of manifolds analogous results were previously obtained in Alesker (2003) [1] for the flat quaternionic space Hn and in Alesker and Verbitsky (2006) [5] for hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we also prove a new multiplicativity property.

Manifolds of positive scalar curvature

Energy Technology Data Exchange (ETDEWEB)

Stolz, S [Department of Mathematics, University of Notre Dame, Notre Dame (United States)

2002-08-15

This lecture gives an survey on the problem of finding a positive scalar curvature metric on a closed manifold. The Gromov-Lawson-Rosenberg conjecture and its relation to the Baum-Connes conjecture are discussed and the problem of finding a positive Ricci curvature metric on a closed manifold is explained.

Some theorems on a class of harmonic manifolds

International Nuclear Information System (INIS)

Rahman, M.S.; Chen Weihuan.

1993-08-01

A class of harmonic n-manifold, denoted by HM n , is, in fact, focussed on a Riemannian manifold with harmonic curvature. A variety of results, with properties, on HM n is presented in a fair order. Harmonic manifolds are then touched upon manifolds with recurrent Ricci curvature, biRicci-recurrent curvature and recurrent conformal curvature, and, in consequence, a sequence of theorems are deduced. (author). 21 refs

On Riemannian manifolds (Mn, g) of quasi-constant curvature

International Nuclear Information System (INIS)

Rahman, M.S.

1995-07-01

A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs

Minimal genera of open 4-manifolds

OpenAIRE

Gompf, Robert E.

2013-01-01

We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with much more control of these genus functions than the compact setting seems to allow. As an application, we expand the range of 4-manifolds known to have exotic smoothings (up to ...

Higher-order Jordan Osserman pseudo-Riemannian manifolds

International Nuclear Information System (INIS)

Gilkey, Peter B; Ivanova, Raina; Zhang Tan

2002-01-01

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds

Higher-order Jordan Osserman pseudo-Riemannian manifolds

Energy Technology Data Exchange (ETDEWEB)

Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)

2002-09-07

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.

A viewpoint on nearly conformally symmetric manifold

International Nuclear Information System (INIS)

Rahman, M.S.

1990-06-01

Some observations, with definition, on Nearly Conformally Symmetric (NCS) manifold are made. A number of theorems concerning conformal change of metric and parallel tensors on NCS manifolds are presented. It is illustrated that a manifold M = R n-1 x R + 1 , endowed with a special metric, is NCS but not of harmonic curvature. (author). 8 refs

The Hodge theory of projective manifolds

CERN Document Server

de Cataldo, Mark Andrea

2007-01-01

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.

M theory and singularities of exceptional holonomy manifolds

International Nuclear Information System (INIS)

Acharya, Bobby S.; Gukov, Sergei

2004-12-01

M theory compactifications on G 2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory. (author)

Statistical Shape Model for Manifold Regularization: Gleason grading of prostate histology.

Science.gov (United States)

Sparks, Rachel; Madabhushi, Anant

2013-09-01

Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because Gleason grading is done manually by a pathologist visually examining glass (or digital) slides subtle morphologic and architectural differences of histological attributes, in addition to other factors, may result in grading errors and hence cause high inter-observer variability. Recently some researchers have proposed computerized decision support systems to automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving nonlinear relationships between object instances. Classification can then be performed in the low dimensional space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain the low dimensional manifold to a specific range of possible manifold shapes, the range being determined via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1) identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM, and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a

Robust head pose estimation via supervised manifold learning.

Science.gov (United States)

Wang, Chao; Song, Xubo

2014-05-01

Head poses can be automatically estimated using manifold learning algorithms, with the assumption that with the pose being the only variable, the face images should lie in a smooth and low-dimensional manifold. However, this estimation approach is challenging due to other appearance variations related to identity, head location in image, background clutter, facial expression, and illumination. To address the problem, we propose to incorporate supervised information (pose angles of training samples) into the process of manifold learning. The process has three stages: neighborhood construction, graph weight computation and projection learning. For the first two stages, we redefine inter-point distance for neighborhood construction as well as graph weight by constraining them with the pose angle information. For Stage 3, we present a supervised neighborhood-based linear feature transformation algorithm to keep the data points with similar pose angles close together but the data points with dissimilar pose angles far apart. The experimental results show that our method has higher estimation accuracy than the other state-of-art algorithms and is robust to identity and illumination variations. Copyright © 2014 Elsevier Ltd. All rights reserved.

New complete noncompact Spin(7) manifolds

International Nuclear Information System (INIS)

Cvetic, M.; Gibbons, G.W.; Lue, H.; Pope, C.N.

2002-01-01

We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by (A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S 4 . Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S 4 , our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L 2 -normalisable harmonic 4-form for the (A)) 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L 2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 - similar to B 8

Spectral gaps, inertial manifolds and kinematic dynamos

Energy Technology Data Exchange (ETDEWEB)

Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es

2005-10-17

Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.

Space time manifolds and contact structures

Directory of Open Access Journals (Sweden)

K. L. Duggal

1990-01-01

Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.

Confining the state of light to a quantum manifold by engineered two-photon loss

Science.gov (United States)

Leghtas, Z.; Touzard, S.; Pop, I. M.; Kou, A.; Vlastakis, B.; Petrenko, A.; Sliwa, K. M.; Narla, A.; Shankar, S.; Hatridge, M. J.; Reagor, M.; Frunzio, L.; Schoelkopf, R. J.; Mirrahimi, M.; Devoret, M. H.

2015-02-01

Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a specially engineered interaction with the environment can become a resource for the generation and protection of quantum states. This notion can be generalized to the confinement of a system into a manifold of quantum states, consisting of all coherent superpositions of multiple stable steady states. We have confined the state of a superconducting resonator to the quantum manifold spanned by two coherent states of opposite phases and have observed a Schrödinger cat state spontaneously squeeze out of vacuum before decaying into a classical mixture. This experiment points toward robustly encoding quantum information in multidimensional steady-state manifolds.

From maximal to minimal supersymmetry in string loop amplitudes

Energy Technology Data Exchange (ETDEWEB)

Berg, Marcus; Buchberger, Igor [Department of Physics, Karlstad University,651 88 Karlstad (Sweden); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,14476 Potsdam (Germany)

2017-04-28

We calculate one-loop string amplitudes of open and closed strings with N=1,2,4 supersymmetry in four and six dimensions, by compactification on Calabi-Yau and K3 orbifolds. In particular, we develop a method to combine contributions from all spin structures for arbitrary number of legs at minimal supersymmetry. Each amplitude is cast into a compact form by reorganizing the kinematic building blocks and casting the worldsheet integrals in a basis. Infrared regularization plays an important role to exhibit the expected factorization limits. We comment on implications for the one-loop string effective action.

More on Gopakumar-Vafa formula: coefficients F0 and F1

International Nuclear Information System (INIS)

Dedushenko, M.

2015-01-01

In Type IIA compactified on a Calabi-Yau threefold, the genus zero and one terms of the Gopakumar-Vafa (GV) formula describe F-terms that are related to genus zero and one topological amplitudes. While for higher-genus terms F g ,g≥2, the contribution of a light hypermultiplet can be computed via a sum over Kaluza-Klein harmonics, as has been shown in a recent paper, for g≤1, the sum diverges and it is better to compute F 0 and F 1 directly in five-dimensional field theory. Such a computation is presented here.

Toric Lego: A method for modular model building

CERN Document Server

Balasubramanian, Vijay; García-Etxebarria, Iñaki

2010-01-01

Within the context of local type IIB models arising from branes at toric Calabi-Yau singularities, we present a systematic way of joining any number of desired sectors into a consistent theory. The different sectors interact via massive messengers with masses controlled by tunable parameters. We apply this method to a toy model of the minimal supersymmetric standard model (MSSM) interacting via gauge mediation with a metastable supersymmetry breaking sector and an interacting dark matter sector. We discuss how a mirror procedure can be applied in the type IIA case, allowing us to join certain intersecting brane configurations through massive mediators.

Chebyshev-Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

Science.gov (United States)

Mireles James, J. D.; Murray, Maxime

2017-12-01

This paper develops a Chebyshev-Taylor spectral method for studying stable/unstable manifolds attached to periodic solutions of differential equations. The work exploits the parameterization method — a general functional analytic framework for studying invariant manifolds. Useful features of the parameterization method include the fact that it can follow folds in the embedding, recovers the dynamics on the manifold through a simple conjugacy, and admits a natural notion of a posteriori error analysis. Our approach begins by deriving a recursive system of linear differential equations describing the Taylor coefficients of the invariant manifold. We represent periodic solutions of these equations as solutions of coupled systems of boundary value problems. We discuss the implementation and performance of the method for the Lorenz system, and for the planar circular restricted three- and four-body problems. We also illustrate the use of the method as a tool for computing cycle-to-cycle connecting orbits.

On complete manifolds supporting a weighted Sobolev type inequality

International Nuclear Information System (INIS)

Adriano, Levi; Xia Changyu

2011-01-01

Highlights: → We study manifolds supporting a weighted Sobolev or log-Sobolev inequality. → We investigate manifolds of asymptotically non-negative Ricci curvature. → The constant in the weighted Sobolev inequality on complete manifolds is studied. - Abstract: This paper studies the geometric and topological properties of complete open Riemannian manifolds which support a weighted Sobolev or log-Sobolev inequality. We show that the constant in the weighted Sobolev inequality on a complete open Riemannian manifold should be bigger than or equal to the optimal one on the Euclidean space of the same dimension and that a complete open manifold of asymptotically non-negative Ricci curvature supporting a weighted Sobolev inequality must have large volume growth. We also show that a complete manifold of non-negative Ricci curvature on which the log-Sobolev inequality holds is not very far from the Euclidean space.

Sasakian manifolds and M-theory

International Nuclear Information System (INIS)

Figueroa-O’Farrill, José; Santi, Andrea

2016-01-01

We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of η-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterizing them in terms of generalized Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a new class of such backgrounds, extending previous work of Haupt, Lukas and Stelle. (paper)

Moving Manifolds in Electromagnetic Fields

Directory of Open Access Journals (Sweden)

David V. Svintradze

2017-08-01

Full Text Available We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.

Total Generalized Variation for Manifold-valued Data

OpenAIRE

Bredies, K.; Holler, M.; Storath, M.; Weinmann, A.

2017-01-01

In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data. We provide an axiomatic approach to formalize reasonable generalizations of TGV to the manifold setting and present two possible concrete instances that fulfill the proposed axioms. We provide well-posedness results and present algorithms for a numerical realization of these generalizations to the manifold setup. Further, we provide experimental results for syntheti...

Nonassociative geometry of manifold with trajectories

International Nuclear Information System (INIS)

Bouetou, T.B.; Matveev, O.A.

2004-12-01

We give some properties of solution of second order differential or system of differential equations on the manifold. It turns out that such manifolds can be seen as quasigroups or loop under certain circumstances. Output of the operations are given and the connection defined. (author)

Vector Fields on Product Manifolds

OpenAIRE

Kurz, Stefan

2011-01-01

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.

The structure of some classes of K-contact manifolds

Indian Academy of Sciences (India)

Abstract. We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi ...

Towards large volume big divisor D3/D7 “μ-split supersymmetry” and Ricci-flat Swiss-cheese metrics, and dimension-six neutrino mass operators

International Nuclear Information System (INIS)

Dhuria, Mansi; Misra, Aalok

2012-01-01

We show that it is possible to realize a “μ-split SUSY” scenario (Cheng and Cheng, 2005) in the context of large volume limit of type IIB compactifications on Swiss-cheese Calabi-Yau orientifolds in the presence of a mobile space-time filling D3-brane and a (stack of) D7-brane(s) wrapping the “big” divisor. For this, we investigate the possibility of getting one Higgs to be light while other to be heavy in addition to a heavy higgsino mass parameter. Further, we examine the existence of long lived gluino that manifests one of the major consequences of μ-split SUSY scenario, by computing its decay width as well as lifetime corresponding to the three-body decays of the gluino into either a quark, a squark and a neutralino or a quark, squark and goldstino, as well as two-body decays of the gluino into either a neutralino and a gluon or a goldstino and a gluon. Guided by the geometric Kähler potential for Σ B obtained in Misra and Shukla (2010) based on GLSM techniques, and the Donaldson's algorithm (Barun et al., 2008) for obtaining numerically a Ricci-flat metric, we give details of our calculation in Misra and Shukla (2011) pertaining to our proposed metric for the full Swiss-cheese Calabi-Yau (the geometric Kähler potential being needed to be included in the full moduli space Kähler potential in the presence of the mobile space-time filling D3-brane), but for simplicity of calculation, close to the big divisor, which is Ricci-flat in the large volume limit. Also, as an application of the one-loop RG flow solution for the higgsino mass parameter, we show that the contribution to the neutrino masses at the EW scale from dimension-six operators arising from the Kähler potential, is suppressed relative to the Weinberg-type dimension-five operators.

Towards large volume big divisor D3/D7 " μ-split supersymmetry" and Ricci-flat Swiss-cheese metrics, and dimension-six neutrino mass operators

Science.gov (United States)

Dhuria, Mansi; Misra, Aalok

2012-02-01

We show that it is possible to realize a " μ-split SUSY" scenario (Cheng and Cheng, 2005) [1] in the context of large volume limit of type IIB compactifications on Swiss-cheese Calabi-Yau orientifolds in the presence of a mobile space-time filling D3-brane and a (stack of) D7-brane(s) wrapping the "big" divisor. For this, we investigate the possibility of getting one Higgs to be light while other to be heavy in addition to a heavy higgsino mass parameter. Further, we examine the existence of long lived gluino that manifests one of the major consequences of μ-split SUSY scenario, by computing its decay width as well as lifetime corresponding to the three-body decays of the gluino into either a quark, a squark and a neutralino or a quark, squark and goldstino, as well as two-body decays of the gluino into either a neutralino and a gluon or a goldstino and a gluon. Guided by the geometric Kähler potential for Σ obtained in Misra and Shukla (2010) [2] based on GLSM techniques, and the Donaldson's algorithm (Barun et al., 2008) [3] for obtaining numerically a Ricci-flat metric, we give details of our calculation in Misra and Shukla (2011) [4] pertaining to our proposed metric for the full Swiss-cheese Calabi-Yau (the geometric Kähler potential being needed to be included in the full moduli space Kähler potential in the presence of the mobile space-time filling D3-brane), but for simplicity of calculation, close to the big divisor, which is Ricci-flat in the large volume limit. Also, as an application of the one-loop RG flow solution for the higgsino mass parameter, we show that the contribution to the neutrino masses at the EW scale from dimension-six operators arising from the Kähler potential, is suppressed relative to the Weinberg-type dimension-five operators.

Introduction to global analysis minimal surfaces in Riemannian manifolds

CERN Document Server

Moore, John Douglas

2017-01-01

During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...

Submanifolds of a Finsler manifold - I

International Nuclear Information System (INIS)

Rastogi, S.C.

1986-06-01

In 1981, Hojo defined a scalar function φ (p) (x,y), where p is a real number (not= 1). He used this function to define a tensor φ ij (p) (x,y) and a c P Γ-connection which reduce to g ij (x,y) and cΓ-connection for p=2. The aim of this paper is to study submanifolds of a Finsler manifold admitting a c P Γ-connection. In this paper I have obtained four kinds of Gauss-Codazzi equations based on various derivatives in a Finsler manifold admitting a c P Γ-connection. The method used in this paper is similar to the one used by the author in obtaining generalized Gauss-Codazzi equations based on congruences of curves in a Finsler manifold. Besides considering some special cases we have also studied the relationship between the Riemannian curvatures and Ricci tensors of the submanifold and the enveloping manifold. (author)

Lectures on the Topological Vertex

CERN Document Server

Mariño, M

2008-01-01

In this lectures, I will summarize the approach to Gromov–Witten invariants on toric Calabi–Yau threefolds based on large N dualities. Since the large N duality/topological vertex approach computes Gromov–Witten invariants in terms of Chern–Simons knot and link invariants, Sect. 2 is devoted to a review of these. Section 3 reviews topological strings and Gromov–Witten invariants, and gives some information about the open string case. Section 4 introduces the class of geometries we will deal with, namely toric (noncompact) Calabi–Yau manifolds, and we present a useful graphical way to represent these manifolds which constitutes the geometric core of the theory of the topological vertex. Finally, in Sect. 5, we define the vertex and present some explicit formulae for it and some simple applications. A brief Appendix contains useful information about symmetric polynomials. It has not been possible to present all the relevant background and physical derivations in this set of lectures. However, these...

Matrix models and stochastic growth in Donaldson-Thomas theory

Energy Technology Data Exchange (ETDEWEB)

Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, United Kingdom and Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); Tierz, Miguel [Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa (Portugal); Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain)

2012-10-15

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Matrix models and stochastic growth in Donaldson-Thomas theory

International Nuclear Information System (INIS)

Szabo, Richard J.; Tierz, Miguel

2012-01-01

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Multiple D3-Instantons and Mock Modular Forms II

Science.gov (United States)

Alexandrov, Sergei; Banerjee, Sibasish; Manschot, Jan; Pioline, Boris

2018-03-01

We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action of S-duality on this moduli space: the generating function of DT invariants in the large volume attractor chamber must be a vector-valued mock modular form with specified modular properties. In this work, we prove that this condition is also sufficient at two-instanton order. This is achieved by producing a holomorphic action of {SL(2,Z)} on the twistor space which preserves the holomorphic contact structure. The key step is to cancel the anomalous modular variation of the Darboux coordinates by a local holomorphic contact transformation, which is generated by a suitable indefinite theta series. For this purpose we introduce a new family of theta series of signature (2, n - 2), find their modular completion, and conjecture sufficient conditions for their convergence, which may be of independent mathematical interest.

Multiple D3-instantons and mock modular forms I

CERN Document Server

Alexandrov, Sergei; Manschot, Jan; Pioline, Boris

2017-01-01

We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kahler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson-Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular fo...

Hyperbolic manifolds as vacuum solutions in Kaluza-Klein theories

International Nuclear Information System (INIS)

Aref'eva, I.Ya.; Volovich, I.V.

1985-08-01

The relevance of compact hyperbolic manifolds in the context of Kaluza-Klein theories is discussed. Examples of spontaneous compactification on hyperbolic manifolds including d dimensional (d>=8) Einstein-Yang-Mills gravity and 11-dimensional supergravity are considered. Some mathematical facts about hyperbolic manifolds essential for the physical content of the theory are briefly summarized. Non-linear σ-models based on hyperbolic manifolds are discussed. (author)

Higher-order blackhole solutions in N=2 supergravity and Calabi-Yau string backgrounds

NARCIS (Netherlands)

Behrndt, K.; Cardoso, G.L.; de Wit, B.Q.P.J.; Lüst, D.; Mohaupt, T.; Sabra, W.A.

1998-01-01

Based on special geometry, we consider corrections to N=2 extremal black-hole solutions and their entropies originating from higher-order derivative terms in N=2 supergravity. These corrections are described by a holomorphic function, and the higher-order black-hole solutions can be expressed in

Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds

Indian Academy of Sciences (India)

We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...

Unsupervised image matching based on manifold alignment.

Science.gov (United States)

Pei, Yuru; Huang, Fengchun; Shi, Fuhao; Zha, Hongbin

2012-08-01

This paper challenges the issue of automatic matching between two image sets with similar intrinsic structures and different appearances, especially when there is no prior correspondence. An unsupervised manifold alignment framework is proposed to establish correspondence between data sets by a mapping function in the mutual embedding space. We introduce a local similarity metric based on parameterized distance curves to represent the connection of one point with the rest of the manifold. A small set of valid feature pairs can be found without manual interactions by matching the distance curve of one manifold with the curve cluster of the other manifold. To avoid potential confusions in image matching, we propose an extended affine transformation to solve the nonrigid alignment in the embedding space. The comparatively tight alignments and the structure preservation can be obtained simultaneously. The point pairs with the minimum distance after alignment are viewed as the matchings. We apply manifold alignment to image set matching problems. The correspondence between image sets of different poses, illuminations, and identities can be established effectively by our approach.

Quasi-Newton Exploration of Implicitly Constrained Manifolds

KAUST Repository

Tang, Chengcheng

2011-08-01

A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.

Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

Science.gov (United States)

Martínez-Torres, David; Miranda, Eva

2018-01-01

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

Model Transport: Towards Scalable Transfer Learning on Manifolds

DEFF Research Database (Denmark)

Freifeld, Oren; Hauberg, Søren; Black, Michael J.

2014-01-01

We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use...... ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer...... “commutes” with learning. Consequently, our compact framework, applicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image...

Stochastic development regression on non-linear manifolds

DEFF Research Database (Denmark)

Kühnel, Line; Sommer, Stefan Horst

2017-01-01

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....

Moduli space of torsional manifolds

International Nuclear Information System (INIS)

Becker, Melanie; Tseng, L.-S.; Yau, S.-T.

2007-01-01

We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be Hermitian Yang-Mills, and also the anomaly cancellation be satisfied. We perform the linearized variation of these constraints to derive the defining equations for the local moduli. We explicitly determine the metric deformations of the smooth flux solution corresponding to a torus bundle over K3

Discriminative clustering on manifold for adaptive transductive classification.

Science.gov (United States)

Zhang, Zhao; Jia, Lei; Zhang, Min; Li, Bing; Zhang, Li; Li, Fanzhang

2017-10-01

In this paper, we mainly propose a novel adaptive transductive label propagation approach by joint discriminative clustering on manifolds for representing and classifying high-dimensional data. Our framework seamlessly combines the unsupervised manifold learning, discriminative clustering and adaptive classification into a unified model. Also, our method incorporates the adaptive graph weight construction with label propagation. Specifically, our method is capable of propagating label information using adaptive weights over low-dimensional manifold features, which is different from most existing studies that usually predict the labels and construct the weights in the original Euclidean space. For transductive classification by our formulation, we first perform the joint discriminative K-means clustering and manifold learning to capture the low-dimensional nonlinear manifolds. Then, we construct the adaptive weights over the learnt manifold features, where the adaptive weights are calculated through performing the joint minimization of the reconstruction errors over features and soft labels so that the graph weights can be joint-optimal for data representation and classification. Using the adaptive weights, we can easily estimate the unknown labels of samples. After that, our method returns the updated weights for further updating the manifold features. Extensive simulations on image classification and segmentation show that our proposed algorithm can deliver the state-of-the-art performance on several public datasets. Copyright © 2017 Elsevier Ltd. All rights reserved.

Wave equations on anti self dual (ASD) manifolds

Science.gov (United States)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

A framework for optimal kernel-based manifold embedding of medical image data.

Science.gov (United States)

Zimmer, Veronika A; Lekadir, Karim; Hoogendoorn, Corné; Frangi, Alejandro F; Piella, Gemma

2015-04-01

Kernel-based dimensionality reduction is a widely used technique in medical image analysis. To fully unravel the underlying nonlinear manifold the selection of an adequate kernel function and of its free parameters is critical. In practice, however, the kernel function is generally chosen as Gaussian or polynomial and such standard kernels might not always be optimal for a given image dataset or application. In this paper, we present a study on the effect of the kernel functions in nonlinear manifold embedding of medical image data. To this end, we first carry out a literature review on existing advanced kernels developed in the statistics, machine learning, and signal processing communities. In addition, we implement kernel-based formulations of well-known nonlinear dimensional reduction techniques such as Isomap and Locally Linear Embedding, thus obtaining a unified framework for manifold embedding using kernels. Subsequently, we present a method to automatically choose a kernel function and its associated parameters from a pool of kernel candidates, with the aim to generate the most optimal manifold embeddings. Furthermore, we show how the calculated selection measures can be extended to take into account the spatial relationships in images, or used to combine several kernels to further improve the embedding results. Experiments are then carried out on various synthetic and phantom datasets for numerical assessment of the methods. Furthermore, the workflow is applied to real data that include brain manifolds and multispectral images to demonstrate the importance of the kernel selection in the analysis of high-dimensional medical images. Copyright © 2014 Elsevier Ltd. All rights reserved.

Three-dimensional parallelization of microfluidic droplet generators for a litre per hour volume production of single emulsions

KAUST Repository

Conchouso Gonzalez, David

2014-01-01

This paper looks at the design, fabrication and characterization of stackable microfluidic emulsion generators, with coefficients of variation as low as ~6% and with production rates as high as ~1 L h-1. This work reports the highest throughput reported in the literature for a microfluidic device with simultaneous operation of liquid-liquid droplet generators. The device was achieved by stacking several layers of 128 flow-focusing droplet generators, organized in a circular array. These layers are interconnected via through-holes and fed with designated fractal distribution networks. The proposed layers were milled on poly(methylmethacrylate) (PMMA) sheets and the stack was thermo-compression bonded to create a three-dimensional device with a high density of generators and an integrated hydraulic manifold. The effect of stacking multiple layers was studied and the results show that fabrication accuracy has a greater impact on the dispersity of the emulsion than the addition of more layers to the stack. Particle crystallization of drugs was also demonstrated as a possible application of this technology in industry. © 2014 the Partner Organisations.

Stochastic development regression on non-linear manifolds

DEFF Research Database (Denmark)

Kühnel, Line; Sommer, Stefan Horst

2017-01-01

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...

Higher-order meshing of implicit geometries, Part II: Approximations on manifolds

Science.gov (United States)

Fries, T. P.; Schöllhammer, D.

2017-11-01

A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes.

Fluid manifold design for a solar energy storage tank

Science.gov (United States)

Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.

1975-01-01

A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.

Convex functions and optimization methods on Riemannian manifolds

CERN Document Server

Udrişte, Constantin

1994-01-01

This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...

Schwarzian conditions for linear differential operators with selected differential Galois groups

Science.gov (United States)

Abdelaziz, Y.; Maillard, J.-M.

2017-11-01

We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions can be generalized to arbitrary order linear differential operators with polynomial coefficients having selected differential Galois groups. For order three and order four linear differential operators we show that this pullback invariance up to conjugation eventually reduces to symmetric powers of an underlying order-two operator. We give, precisely, the conditions to have modular correspondences solutions for such Schwarzian differential equations, which was an open question in a previous paper. We analyze in detail a pullbacked hypergeometric example generalizing modular forms, that ushers a pullback invariance up to operator homomorphisms. We finally consider the more general problem of the equivalence of two different order-four linear differential Calabi-Yau operators up to pullbacks and conjugation, and clarify the cases where they have the same Yukawa couplings.

STU Black Holes and String Triality

Energy Technology Data Exchange (ETDEWEB)

Shmakova, Marina

2003-05-23

We found double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F = STU. The area formula is STU-moduli independent and has [SL(2, Z)]{sup 3} symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8,Z) transformation. The area formula of one theory equals the area formula of the dual theory when expressed in terms of dual charges. We analyze the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In democratic STU-symmetric version we find that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.

Variable area manifolds for ring mirror heat exchangers

Science.gov (United States)

Eng, Albert; Senterfitt, Donald R.

1988-05-01

A laser ring mirror assembly is disclosed which supports and cools an annular ring mirror of a high powered laser with a cooling manifold which has a coolant flow design which is intended to reduce thermal distortions of the ring mirror by minimizing azimuthal variations in temperature around its circumference. The cooling manifold has complementary pairs of cooling passages each of which conduct coolant in opposite flow directions. The manifold also houses adjusters which vary the depth between the annular ring mirror and each cooling, and which vary the flow area of the cooling passage to produce a control over the cooling characteristics of the cooling manifold.

Cohomological rigidity of manifolds defined by 3-dimensional polytopes

Science.gov (United States)

Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.

2017-04-01

A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.

Example-driven manifold priors for image deconvolution.

Science.gov (United States)

Ni, Jie; Turaga, Pavan; Patel, Vishal M; Chellappa, Rama

2011-11-01

Image restoration methods that exploit prior information about images to be estimated have been extensively studied, typically using the Bayesian framework. In this paper, we consider the role of prior knowledge of the object class in the form of a patch manifold to address the deconvolution problem. Specifically, we incorporate unlabeled image data of the object class, say natural images, in the form of a patch-manifold prior for the object class. The manifold prior is implicitly estimated from the given unlabeled data. We show how the patch-manifold prior effectively exploits the available sample class data for regularizing the deblurring problem. Furthermore, we derive a generalized cross-validation (GCV) function to automatically determine the regularization parameter at each iteration without explicitly knowing the noise variance. Extensive experiments show that this method performs better than many competitive image deconvolution methods.

Trisections in Three and Four Dimensions

Science.gov (United States)

Koenig, Dale R.

Every closed orientable three dimensional manifold has a Heegaard splitting, a decomposition into two handlebodies. Any two Heegaard splittings of the same manifold can be made isotopic after a finite number of stabilization operations. The notion of trisections, developed by Gay and Kirby, provided an analogue in four dimensions. They showed that any closed smooth orientable four dimensional manifold can be broken into three four dimensional handlebodies, with "niceness" conditions on their intersections, and showed that any two trisections are isotopic after stabilizations. In this thesis we investigate the notion of trisections in both three and four dimensions. In dimension three we define trisections of 3-manifolds and stabilization on these trisections. We use this to define the trisection genus of a 3-manifold. We then present several examples, showing among other things that the trisection genus is not additive under connect sum. We prove a stable equivalence theorem for trisections of 3-manifolds, showing that any two trisections of the same three-manifold can be made isotopic after stabilizations. We also show that trisections of S3 can be very complicated, so there is no analogue of Waldhausen's theorem for trisections of three manifolds. We then move on to trisections in four dimensions. We first show that if there exist four manifolds with unbalanced trisection genus lower than their balanced trisection genus, then trisection genus as defined by Gay and Kirby is not additive under connect sum. We produce several new classes of trisections, including several likely such examples. We include a class of examples that are provably minimal genus. We provide trisection diagrams for many of these trisections, and summarize some methods for quickly checking that these diagrams produce valid trisections.

Planckian axions in string theory

International Nuclear Information System (INIS)

Bachlechner, Thomas C.; Long, Cody; McAllister, Liam

2015-01-01

We argue that super-Planckian diameters of axion fundamental domains can arise in Calabi-Yau compactifications of string theory. In a theory with N axions θ i , the fundamental domain is a polytope defined by the periodicities of the axions, via constraints of the form −π√N. This result is robust in the presence of P>N constraints, while for P=N the diameter is further enhanced by eigenvector delocalization to N 3/2 f N . We directly verify our results in explicit Calabi-Yau compactifications of type IIB string theory. In the classic example with h 1,1 =51 where parametrically controlled moduli stabilization was demonstrated by Denef et al. in http://dx.doi.org/10.4310/ATMP.2005.v9.n6.a1, the largest metric eigenvalue obeys f N ≈0.013M pl . The random matrix analysis then predicts, and we exhibit, axion diameters ≈M pl for the precise vacuum parameters found in http://dx.doi.org/10.4310/ATMP.2005.v9.n6.a1. Our results provide a framework for pursuing large-field axion inflation in well-understood flux vacua.