Scalar-induced compactifications in higher dimensional supergravities
Kehagias, Alex [Department of Physics, National Technical University of Athens, GR-15773 Zografou, Athens (Greece); Mattheopoulou, Constantina [Department of Physics, National Technical University of Athens, GR-15773 Zografou, Athens (Greece)
2005-08-01
We discuss compactifications of higher dimensional supergravities which are induced by scalars. In particular, we consider vector multiplets coupled to the supergravity multiplet in the case of D = 9,8 and D = 7 minimal supergravities. These vector multiplets contain scalars, which parametrize coset spaces of the general form SO(10-D,n)/SO(10-D) x SO(n), where n is the number of vector multiplets. We discuss the compactification of the supergravity theory to D-2 dimensons, which is induced by non-trivial vacuum scalar field configurations. There are singular and non-singular solutions, which preserve half of the supersymmetries.
Compactifications of the eleven-dimensional supermembrane
Bergshoeff, E.; Duff, M.J.; Pope, C.N.; Sezgin, E.
1989-01-01
We construct new vacua for the eleven-dimensional supermembrane in which spacetime is the product of four-dimensional anti-de Sitter space and a compact seven-dimensional Einstein space, and the membrane is a sphere of non-zero radius in the anti-de Sitter space. In one class of solution the radius
1+1 dimensional compactifications of string theory.
Goheer, Naureen; Kleban, Matthew; Susskind, Leonard
2004-05-14
We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti-de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero, the conflict is resolved.
Prasetyo, I.; Ramadhan, H. S.
2017-07-01
Here we present some solutions with noncanonical global monopole in nonlinear sigma model in 4-dimensional spacetime. We discuss some blackhole solutions and its horizons. We also obtain some compactification solutions. We list some possible compactification channels from 4-space to 2 × 2-spaces of constant curvatures.
General Perturbations for Braneworld Compactifications and the Six Dimensional Case
Parameswaran, S L; Salvio, A
2009-01-01
Our main objective is to study how braneworld models of higher codimension differ from the 5D case and traditional Kaluza-Klein compactifications. We first derive the classical dynamics describing the physical fluctuations in a wide class of models incorporating gravity, non-Abelian gauge fields, the dilaton and two-form potential, as well as 3-brane sources. Next, we use these results to study braneworld compactifications in 6D supergravity, focusing on the bosonic fields in the minimal model; composed of the supergravity-tensor multiplet and the U(1) gauge multiplet whose flux supports the compactification. For unwarped models sourced by positive tension branes, a harmonic analysis allows us to solve the large, coupled, differential system completely and obtain the full 4D spin-2,1 and 0 particle spectra, establishing (marginal) stability and a qualitative behaviour similar to the smooth sphere compactification. We also find interesting results for models with negative tension branes; extra massless Kaluza-...
General perturbations for braneworld compactifications and the six dimensional case
Parameswaran, S.L. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Randjbar-Daemi, S. [International Center for Theoretical Physics, Trieste (Italy); Salvio, A. [EPFL, Lausanne (Switzerland). Inst. de Theorie des Phenomenes Physiques]|[Universitat Autonoma de Barcelona, Bellaterra (Spain). IFAE
2009-02-15
Our main objective is to study how braneworld models of higher codimension differ from the 5D case and traditional Kaluza-Klein compactifications. We first derive the classical dynamics describing the physical fluctuations in a wide class of models incorporating gravity, non-Abelian gauge fields, the dilaton and two-form potential, as well as 3-brane sources. Next, we use these results to study braneworld compactifications in 6D supergravity, focusing on the bosonic fields in the minimal model; composed of the supergravity-tensor multiplet and the U(1) gauge multiplet whose flux supports the compactification. For unwarped models sourced by positive tension branes, a harmonic analysis allows us to solve the large, coupled, differential system completely and obtain the full 4D spin-2,1 and 0 particle spectra, establishing (marginal) stability and a qualitative behaviour similar to the smooth sphere compactification. We also find interesting results for models with negative tension branes; extra massless Kaluza-Klein vector fields can appear in the spectra, beyond those expected from the isometries in the internal space. These fields imply an enhanced gauge symmetry in the low energy 4D effective theory obtained by truncating to the massless sector, which is explicitly broken as higher modes are excited, until the full 6D symmetries are restored far above the Kaluza-Klein scale. Remarkably, the low energy effective theory does not seem to distinguish between a compactification on a smooth sphere and these singular, deformed spheres. (orig.)
Accetta, F.S.; Gleiser, M.; Holman, R.; Kolb, E.W.
1986-03-01
We show that compactifications of theories with extra dimensions are unstable if due to monopole configurations of an antisymmetric tensor field balanced against one-loop Casimir corrections. In the case of ten dimensional supergravity, it is possible, at least for a portion of the phase space, to achieve a stable compactification without fine-tuning by including the contribution of fermionic condensates to the monopole configurations. 23 refs., 2 figs.
Lovelady, Benjamin; Wheeler, James
2017-01-01
The gauging of the conformal group of n-dim Euclidean space by the homogenous Weyl group leads to a principal bundle known as biconformal space. Time arises naturally on a 2n-dimensional symplectic manifold with SO(n) spanning the fibers. These spaces allow a scale-invariant first-order gravity action, making them ideal candidates for quantizable gravity. We investigate the effect of including m compact dimensions beyond the 4 of spacetime. This gives 2m extra dimensions on the symplectic manifold that need to be compactified. Various compactifications lead to different fields, but for m=1,2 the set of compactifications is countable.
Lobotomy of flux compactifications
Dibitetto, Giuseppe; Guarino, Adolfo; Roest, Diederik
2014-01-01
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on (6) with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification
Standard 4d gravity on a brane in six dimensional flux compactifications
Peloso, M; Tasinato, G; Peloso, Marco; Sorbo, Lorenzo; Tasinato, Gianmassimo
2006-01-01
We consider a six dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4d gravity at large distances. Our model provides a consistent setup for the study of gravity in the rugby (or football) compactification, without having to deal with the complications of a delta-like, codimension two brane. To our knowledge, this is the first complete study of gravity in a realistic brane model with two extra dimensions, in which the mechanism of stabilization of the extra space is consistently taken into account.
Accelerating Cosmologies from Compactification
Townsend, P K; Townsend, Paul K.; Wohlfarth, Mattias N.R.
2003-01-01
A solution of the (4+n)-dimensional vacuum Einstein equations is found for which spacetime is compactified on a compact hyperbolic manifold of time-varying volume to a flat four-dimensional FLRW cosmology undergoing accelerated expansion in Einstein conformal frame. This shows that the `no-go' theorem forbidding acceleration in `standard' (time-independent) compactifications of string/M-theory does not apply to `cosmological' (time-dependent) hyperbolic compactifications.
Cosmology with Two Compactification Scales
A. G. Agnese; M. La Camera
2000-01-01
We consider a (4 + d)-dimensional spacetime broken up into a (4- n)-dimensional Minkowski spacetime (where n goes from 1 to 3) and a compact (n+d)-dimensional manifold. At the present time the n compactification radii are of the order of the Universe size, while the other d compactification radii are of the order of the Plancklength.
Cordova, Clay; Yin, Xi
2015-01-01
We systematically analyze the effective action on the moduli space of (2,0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally supersymmetric Yang-Mills theories in five and four dimensions. We present a streamlined approach to non-renormalization theorems that constrain this effective action. The first several orders in its derivative expansion are determined by a one-loop calculation in five-dimensional Yang-Mills theory. This fixes the leading higher-derivative operators that describe the renormalization group flow into theories residing at singular points on the moduli space of the compactified (2,0) theories. This understanding allows us to compute the a-type Weyl anomaly for all (2,0) superconformal theories. We show that it decreases along every renormalization group flow that preserves (2,0) supersymmetry, thereby establishing the a-theorem for this class of theories. Along the way, we encounter various field-theoretic arguments for the ADE classif...
Lobotomy of Flux Compactifications
Giuseppe Dibitetto; Adolfo Guarino(Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern, Switzerland); Diederik Roest
2014-01-01
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on $ \\mathbb{T} $ 6 with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge...
Signature transition and compactification
Mohseni, M
2000-01-01
It is shown that a change in the signature of the space-time metric together with compactification of internal dimensions could occure in a six-dimensional cosmological model. We also show that this is due to interaction with Maxwell fields having support in the internal part of the space-time.
Inflationary Cosmologies from Compactification?
Wohlfarth, M N R
2004-01-01
We consider the compactification of (d+n)-dimensional pure gravity and of superstring/M-theory on an n-dimensional internal space to a d-dimensional FLRW cosmology, with spatial curvature k=-1,0,+1, in Einstein conformal frame. The internal space is taken to be a product of Einstein spaces, each of which is allowed to have arbitrary curvature and a time-dependent volume. By investigating the effective d-dimensional scalar potential, which is a sum of exponentials, it is shown that such compactifications, in the k=0,+1 cases, do not lead to large amounts of accelerating expansion of the scale factor of the resulting FLRW universe, and, in particular, not to inflation. The case k=-1 admits solutions with eternal accelerating expansion for which the acceleration, however, tends to zero at late times.
Compactification on phase space
Lovelady, Benjamin; Wheeler, James
2016-03-01
A major challenge for string theory is to understand the dimensional reduction required for comparison with the standard model. We propose reducing the dimension of the compactification by interpreting some of the extra dimensions as the energy-momentum portion of a phase-space. Such models naturally arise as generalized quotients of the conformal group called biconformal spaces. By combining the standard Kaluza-Klein approach with such a conformal gauge theory, we may start from the conformal group of an n-dimensional Euclidean space to form a 2n-dimensional quotient manifold with symplectic structure. A pair of involutions leads naturally to two n-dimensional Lorentzian manifolds. For n = 5, this leaves only two extra dimensions, with a countable family of possible compactifications and an SO(5) Yang-Mills field on the fibers. Starting with n=6 leads to 4-dimensional compactification of the phase space. In the latter case, if the two dimensions each from spacetime and momentum space are compactified onto spheres, then there is an SU(2)xSU(2) (left-right symmetric electroweak) field between phase and configuration space and an SO(6) field on the fibers. Such a theory, with minor additional symmetry breaking, could contain all parts of the standard model.
Douglas, Michael R.; Kachru, Shamit
2006-10-24
We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a ''landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea. We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.
Holography and Compactification
Verlinde, Herman L
2000-01-01
Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactification manifold. A specific example is provided by the type II orientifold equivalent to type I theory on (orbifolds of) $T^6$, upon taking into account the gravitational backreaction of the D3-branes localized inside the $T^6$. The conformal factor of the four-dimensional metric depends exponentially on one of the compact directions, which, via the holographic correspondence, becomes identified with the renormalization group scale in the uncompactified world. This set-up can be viewed as a generalization of the AdS/CFT correspondence to boundary theories that include gravitational dynamics. A striking consequence is that, in this scenario, the fundamental Planck size string and the large N QCD string appear as (two different wavefunctions of) one and the same object.
Lobotomy of flux compactifications
Dibitetto, Giuseppe; Guarino, Adolfo; Roest, Diederik
2014-05-01
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on 6 with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge algebra. Besides the known four AdS solutions surviving the orientifold projection to = 4 induced by O6-planes, this theory contains a novel AdS solution that requires non-trivial orientifold-odd fluxes, hence being a genuine critical point of the = 8 theory.
Lobotomy of flux compactifications
Dibitetto, Giuseppe [Institutionen för fysik och astronomi, University of Uppsala,Box 803, SE-751 08 Uppsala (Sweden); Guarino, Adolfo [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics,Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Roest, Diederik [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4 9747 AG Groningen (Netherlands)
2014-05-15
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on T{sup 6} with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge algebra. Besides the known four AdS solutions surviving the orientifold projection to N=4 induced by O6-planes, this theory contains a novel AdS solution that requires non-trivial orientifold-odd fluxes, hence being a genuine critical point of the N=8 theory.
Induced cosmology on a regularized brane in six-dimensional flux compactification
Papantonopoulos, Eleftherios; Zamarias, Vassilios
2007-01-01
We consider a six-dimensional Einstein-Maxwell system compactified in an axisymmetric two-dimensional space with one capped regularized conical brane of codimension one. We study the cosmological evolution which is induced on the regularized brane as it moves in between known static bulk and cap solutions. Looking at the resulting Friedmann equation, we see that the brane cosmology at high energies is dominated by a five-dimensional rho^2 energy density term. At low energies, we obtain a Friedmann equation with a term linear to the energy density with, however, negative effective Newton's constant in the small four-brane radius limit (i.e. we obtain antigravity). We discuss ways out of this problem.
de Sitter vacua and supersymmetry breaking in six-dimensional flux compactifications
Buchmuller, Wilfried; Dierigl, Markus; Ruehle, Fabian; Schweizer, Julian
2016-07-01
We consider six-dimensional supergravity with Abelian bulk flux compactified on an orbifold. The effective low-energy action can be expressed in terms of N =1 chiral moduli superfields with a gauged shift symmetry. The D -term potential contains two Fayet-Iliopoulos terms which are induced by the flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The Green-Schwarz term also leads to a correction of the gauge kinetic function which turns out to be crucial for the existence of Minkowski and de Sitter vacua. Moduli stabilization is achieved by the interplay of the D -term and a nonperturbative superpotential. Varying the gauge coupling and the superpotential parameters, the scale of the extra dimensions can range from the GUT scale down to the TeV scale. Supersymmetry is broken by F - and D -terms, and the scale of gravitino, moduli, and modulini masses is determined by the size of the compact dimensions.
Spacetime compactification induced by scalars
Gell-Mann, M.; Zwiebach, B.
1984-07-05
It is shown that scalars of a nonlinear sigma model coupled to gravity can trigger spontaneous compactification of spacetime if the scalar manifold has an Einstein metric and the scalar self-coupling constant takes a specific value. The compactified space becomes isomorphic to the scalar manifold and the four-dimensional space has no cosmological term at the classical level.
de Sitter vacua and supersymmetry breaking in six-dimensional flux compactifications
Buchmuller, Wilfried; Ruehle, Fabian; Schweizer, Julian
2016-01-01
We consider six-dimensional supergravity with Abelian bulk flux compactified on an orbifold. The effective low-energy action can be expressed in terms of N=1 chiral moduli superfields with a gauged shift symmetry. The D-term potential contains two Fayet-Iliopoulos terms which are induced by the flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The Green-Schwarz term also leads to a correction of the gauge kinetic function which turns out to be crucial for the existence of Minkowski and de Sitter vacua. Moduli stabilization is achieved by the interplay of the D-term and a nonperturbative superpotential. Varying the gauge coupling and the superpotential parameters, the scale of the extra dimensions can range from the GUT scale down to the TeV scale. Supersymmetry is broken by F- and D-terms, and the scale of gravitino, moduli, and modulini masses is determined by the size of the compact dimensions.
String theory compactifications
Graña, Mariana
2017-01-01
The lectures in this book provide graduate students and non-specialist researchers with a concise introduction to the concepts and formalism required to reduce the ten-dimensional string theories to the observable four-dimensional space-time - a procedure called string compactification. The text starts with a very brief introduction to string theory, first working out its massless spectrum and showing how the condition on the number of dimensions arises. It then dwells on the different possible internal manifolds, from the simplest to the most relevant phenomenologically, thereby showing that the most elegant description is through an extension of ordinary Riemannian geometry termed generalized geometry, which was first introduced by Hitchin. Last but not least, the authors review open problems in string phenomenology, such as the embedding of the Standard Model and obtaining de Sitter solutions.
Black branes in flux compactifications
Torroba, Gonzalo; Wang, Huajia
2013-10-01
We construct charged black branes in type IIA flux compactifications that are dual to (2 + 1)-dimensional field theories at finite density. The internal space is a general Calabi-Yau manifold with fluxes, with internal dimensions much smaller than the AdS radius. Gauge fields descend from the 3-form RR potential evaluated on harmonic forms of the Calabi-Yau, and Kaluza-Klein modes decouple. Black branes are described by a four-dimensional effective field theory that includes only a few light fields and is valid over a parametrically large range of scales. This effective theory determines the low energy dynamics, stability and thermodynamic properties. Tools from flux compactifications are also used to construct holographic CFTs with no relevant scalar operators, that can lead to symmetric phases of condensed matter systems stable to very low temperatures. The general formalism is illustrated with simple examples such as toroidal compactifications and manifolds with a single size modulus. We initiate the classification of holographic phases of matter described by flux compactifications, which include generalized Reissner-Nordstrom branes, nonsupersymmetric AdS_{2}×R^{2} and hyperscaling violating solutions.
Matrix theory compactifications on twisted tori
Chatzistavrakidis, Athanasios
2012-01-01
We study compactifications of Matrix theory on twisted tori and non-commutative versions of them. As a first step, we review the construction of multidimensional twisted tori realized as nilmanifolds based on certain nilpotent Lie algebras. Subsequently, matrix compactifications on tori are revisited and the previously known results are supplemented with a background of a non-commutative torus with non-constant non-commutativity and an underlying non-associative structure on its phase space. Next we turn our attention to 3- and 6-dimensional twisted tori and we describe consistent backgrounds of Matrix theory on them by stating and solving the conditions which describe the corresponding compactification. Both commutative and non-commutative solutions are found in all cases. Finally, we comment on the correspondence among the obtained solutions and flux compactifications of 11-dimensional supergravity, as well as on relations among themselves, such as Seiberg-Witten maps and T-duality.
Quantum Kaluza-Klein Compactification
Sochichiu, C.
1999-01-01
Kaluza--Klein compactification in quantum field theory is analysed from the perturbation theory viewpoint. Renormalisation group analysis for compactification size dependence of the coupling constant is proposed.
Convergence S-compactifications
Bernd Losert
2014-07-01
Full Text Available Properties of continuous actions on convergence spaces are investigated. The primary focus is the characterization as to when a continuous action on a convergence space can be continuously extended to an action on a compactification of the convergence space. The largest and smallest such compactifications are studied.
The Massless Spectrum of Heterotic Compactifications
de la Ossa, Xenia; Svanes, Eirik Eik
2015-01-01
We discuss the four-dimensional massless spectrum of supersymmetric Minkowski compactifications of ten-dimensional heterotic supergravity, including the anomaly cancelation condition. This can be calculated from restrictions arising from F-term conditions in a four-dimensional effective theory. The results agree with computations of the infinitesimal moduli space recently performed from a ten-dimensional perspective. The paper is based on a talk given by Eirik Eik Svanes in Leuven for the workshop on "The String Theory Universe".
Dynamical compactification from de Sitter space
Randall, Lisa; Johnson, Matthew C.; Carroll, Sean M.
2009-01-01
We show that \\(D\\)-dimensional de Sitter space is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions, leading to a dynamical mechanism of compactification. These and other solutions to Einstein gravity with flux and a cosmological constant are constructed by performing a dimensional reduction under the assumption of \\(q\\)-dimensional spherical symmetry in the full \\(D\\)-dimensional geometry. In addition to the fa...
Separation properties of the Wallman ordered compactification
D. C. Kent
1990-01-01
Full Text Available The Wallman ordered compactification ω0X of a topological ordered space X is T2-ordered (and hence equivalent to the Stone-Čech ordered compactification iff X is a T4-ordered c-space. In particular, these two ordered compactifications are equivalent when X is n dimensional Euclidean space iff n≤2. When X is a c-space, ω0X is T1-ordered; we give conditions on X under which the converse statement is also true. We also find conditions on X which are necessary and sufficient for ω0X to be T2. Several examples provide further insight into the separation properties of ω0X.
Spontaneous compactification and nonassociativity
Loginov, E K
2009-01-01
We consider the Freund-Rubin-Englert mechanism of compactification of N=1 supergravity in 11 dimensions. We systematically investigate both well-known and some new solutions of the classical equations of motion in 11 dimensions. In particular, we show that any threeform potential in 11 dimension is given locally by the structure constants of a geodesic loop in an affinely connected space.
Belhaj, A.; Saidi, E. H.
2001-01-01
Using a geometric realization of the SU(2)R symmetry and a factorization of the gauge and SU(2)R charges, we study the small instanton singularities of the Higgs branch of supersymmetric U(1)r gauge theories with eight supercharges. We derive new solutions for the moduli space of vacua preserving manifestly the eight supercharges. In particular, we obtain an extension of the ordinary ADE singularities for hyper-Kähler manifolds and show that the classical moduli space of vacua is, in general, given by cotangent bundles of compact weighted projective spaces describing new models which flow in the infrared to two-dimensional (2D) N = (4,4) scale-invariant models. We also study the N = 4 conformal Liouville description near an An singularity of the metric of the 2D N = 4 Higgs branch using a field-theoretical approach.
Warped branches of flux compactifications
Lim, Yen-Kheng
2012-01-01
We consider Freund-Rubin-type compactifications which are described by (p+q)-dimensional Einstein gravity with a positive cosmological constant and a q-form flux. Using perturbative expansions of Kinoshita's ansatz for warped dS_pxS^q and AdS_pxS^q spacetimes, we obtain analytical solutions describing the warped branches and their respective phase spaces. These equations are given by inhomogeneous Gegenbauer differential equations which can be solved by the Green's function method. The requirement that the Green's functions are regular provides constraints which determine the structure of the phase space of the warped branches. We apply the perturbation results to calculate the thermodynamic variables for the warped dS_pxS^q branch. In particular, the first law of thermodynamics can be reproduced using this method.
Bubbles of Nothing and Supersymmetric Compactifications
Blanco-Pillado, Jose J; Sousa, Kepa; Urrestilla, Jon
2016-01-01
We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such "topologically unobstructed" cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to $M_3 \\times S_1$ presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this dec...
Algebraic treatment of compactification on noncommutative tori
Casalbuoni, R.
1998-07-01
In this paper we study the compactification conditions of the M theory on D-dimensional noncommutative tori. The main tool used for this analysis is the algebra A(ZD) of the projective representations of the abelian group ZD. We exhibit the explicit solutions in the space of the multiplication algebra of A(ZD), that is the algebra generated by right and left multiplications.
Supermassive cosmic string compactifications
Blanco-Pillado, Jose J.; Reina, Borja; Sousa, Kepa; Urrestilla, Jon, E-mail: josejuan.blanco@ehu.es, E-mail: borja.reina@ehu.es, E-mail: kepa.sousa@ehu.es, E-mail: jon.urrestilla@ehu.es [Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain)
2014-06-01
The space-time dimensions transverse to a static straight cosmic string with a sufficiently large tension (supermassive cosmic strings) are compact and typically have a singularity at a finite distance form the core. In this paper, we discuss how the presence of multiple supermassive cosmic strings in the 4d Abelian-Higgs model can induce the spontaneous compactification of the transverse space and explicitly construct solutions where the gravitational background becomes regular everywhere. We discuss the embedding of this model in N = 1 supergravity and show that some of these solutions are half-BPS, in the sense that they leave unbroken half of the supersymmetries of the model.
Supermassive Cosmic String Compactifications
Blanco-Pillado, Jose J; Sousa, Kepa; Urrestilla, Jon
2014-01-01
The space-time dimensions transverse to a static straight cosmic string with a sufficiently large tension (supermassive cosmic strings) are compact and typically have a singularity at a finite distance form the core. In this paper, we discuss how the presence of multiple supermassive cosmic strings in the 4D Abelian-Higgs model can induce the spontaneous compactification of the transverse space and explicitly construct solutions where the gravitational background becomes regular everywhere. We discuss the embedding of this model in N=1 supergravity and show that some of these solutions are half-BPS, in the sense that they leave unbroken half of the supersymmetries of the model.
Bubbles of nothing and supersymmetric compactifications
Blanco-Pillado, Jose J. [IKERBASQUE, Basque Foundation for Science, 48011, Bilbao (Spain); Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Shlaer, Benjamin [Department of Physics, University of Auckland,Private Bag 92019, Auckland (New Zealand); Institute of Cosmology, Department of Physics and Astronomy,Tufts University, Medford, MA 02155 (United States); Sousa, Kepa [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Urrestilla, Jon [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain)
2016-10-03
We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such “topologically unobstructed” cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to M{sub 3}×S{sub 1} presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification.
Matrix Strings, Compactification Scales and Hagedorn Transition
Meana, M L; Meana, Marco Laucelli; Peñalba, Jesús Puente
1999-01-01
In this work we use the Matrix Model of Strings in order to extract some non-perturbative information on how the Hagedorn critical temperature arises from eleven-dimensional physics. We study the thermal behavior of M and Matrix theories on the compactification backgrounds that correspond to string models. We obtain some information that allows us to state that the Hagedorn temperature is not unique for all Matrix String models and we are also able to sketch how the $S$-duality transformation works in this framework.
Compactification of Superstrings and Chain or Oriented Strings in Interactions
Morales, Robert O.
2000-04-10
Superstring theories command the study of their various possible compactifications, and their consequence physics. Thus, the role of topology is likely to be far more central, in particular in ten-dimensional physics. Topological invariants on a chain of oriented strings in interaction are discussed. Attempts to link superstrings with the reality of the physical world in four dimensions are discussed.
Exact and asymptotic black branes with spherical compactification
Chopovsky, Alexey; Zhuk, Alexander
2012-01-01
In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant $\\Lambda_6$, we obtain the black brane with spherical compactification of the internal space. The matter source for this exact solution consists of two parts. First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension $\\hat p_1=-(1/2)\\hat\\varepsilon$ in the internal space. This solution exists both in the presence and absence of $\\Lambda_6$. In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state $\\hat p_1=\\Omega \\hat\\varepsilon$ in the internal space. In the case $\\Lambda_6>0$ and $\\Omega\
Projective Compactifications and Einstein metrics
Cap, Andreas
2013-01-01
For complete affine manifolds we introduce a definition of compactification based on the projective differential geometry (i.e.\\ geodesic path data) of the given connection. The definition of projective compactness involves a real parameter $\\alpha$ called the order of projective compactness. For volume preserving connections, this order is captured by a notion of volume asymptotics that we define. These ideas apply to complete pseudo-Riemannian spaces, via the Levi-Civita connection, and thus provide a notion of compactification alternative to conformal compactification. For each order $\\alpha$, we provide an asymptotic form of a metric which is sufficient for projective compactness of the given order, thus also providing many local examples. Distinguished classes of projectively compactified geometries of orders one and two are associated with Ricci-flat connections and non--Ricci--flat Einstein metrics, respectively. Conversely, these geometric conditions are shown to force the indicated order of projectiv...
Nonrelativistic gauged quantum mechanics: From Kaluza–Klein compactifications to Bargmann structures
Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co
2015-08-14
Highlights: • Null compactification techniques are used to derive the nonrelativistic gauged Schrödinger equation. • Compactification of both Klein–Gordon and Maxwell theories are revisited. • Connections with Kaluza–Klein-like Bargmann frameworks are established. - Abstract: The Schrödinger equation for a spinless particle in presence of an external electromagnetic field is derived by means of null compactification of five dimensional massless Klein–Gordon theory and five–dimensional Maxwell electrodynamics. Connections with Kaluza–Klein-like Bargmann frameworks are established.
Controlling Chaos through Compactification in Cosmological Models with a Collapsing Phase
Wesley, D H; Turok, N G; Wesley, Daniel H.; Steinhardt, Paul J.; Turok, Neil
2005-01-01
We consider the effect of compactification of extra dimensions on the onset of classical chaotic "Mixmaster" behavior during cosmic contraction. Assuming a universe that is well--approximated as a four--dimensional Friedmann--Robertson--Walker model (with negligible Kaluza--Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N = 1 supersymmetry and M--theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big...
Metastable Quivers in String Compactifications
Diaconescu, Duiliu-Emanuel; /Rutgers U., Piscataway; Donagi, Ron; /Pennsylvania U. /SLAC; Florea, Bogdan; /SLAC
2007-01-08
We propose a scenario for dynamical supersymmetry breaking in string compactifications based on geometric engineering of quiver gauge theories. In particular we show that the runaway behavior of fractional branes at del Pezzo singularities can be stabilized by a flux superpotential in compact models. Our construction relies on homological mirror symmetry for orientifolds.
Effective field theory for magnetic compactifications
Buchmuller, Wilfried; Dudas, Emilian; Schweizer, Julian
2016-01-01
Magnetic flux plays an important role in compactifications of field and string theories in two ways, it generates a multiplicity of chiral fermion zero modes and it can break supersymmetry. We derive the complete four-dimensional effective action for N=1 supersymmetric Abelian and non-Abelian gauge theories in six dimensions compactified on a torus with flux. The effective action contains the tower of charged states and it accounts for the mass spectrum of bosonic and fermionic fields as well as their level-dependent interactions. This allows us to compute quantum corrections to the mass and couplings of Wilson lines. We find that the one-loop corrections vanish, contrary to the case without flux. This can be traced back to the spontaneous breaking of a symmetry of the six-dimensional theory by the background gauge field, with the Wilson line as Goldstone boson.
Compactification over coset spaces with torsion and vanishing cosmological constant
Batakis, N.A.; Farakos, K.; Koutsoumbas, G.; Zoupanos, G.; Kapetanakis, D.
1989-04-13
We consider the compactification of ten-dimensional Einstein-Yang-Mills theories over non-symmetric, six-dimensional homogeneous coset spaces with torsion. We examine the Einstein-Yang-Mills equations of motion requiring vanishing cosmological constant at ten and four dimensions and we present examples of compactifying solutions. It appears that the introduction of more than one radii in the coset space, when possible, may be mandatory for the existence of compactifying solutions.
Discrete structures in F-theory compactifications
Till, Oskar
2016-05-04
In this thesis we study global properties of F-theory compactifications on elliptically and genus-one fibered Calabi-Yau varieties. This is motivated by phenomenological considerations as well as by the need for a deeper understanding of the set of consistent F-theory vacua. The global geometric features arise from discrete and arithmetic structures in the torus fiber and can be studied in detail for fibrations over generic bases. In the case of elliptic fibrations we study the role of the torsion subgroup of the Mordell-Weil group of sections in four dimensional compactifications. We show how the existence of a torsional section restricts the admissible matter representations in the theory. This is shown to be equivalent to inducing a non-trivial fundamental group of the gauge group. Compactifying F-theory on genus-one fibrations with multisections gives rise to discrete selection rules. In field theory the discrete symmetry is a broken U(1) symmetry. In the geometry the higgsing corresponds to a conifold transition. We explain in detail the origin of the discrete symmetry from two different M-theory phases and put the result into the context of torsion homology. Finally we systematically construct consistent gauge fluxes on genus-one fibrations and show that these induce an anomaly free chiral spectrum.
Bouncing Brane Cosmologies from Warped String Compactifications
Kachru, S
2003-01-01
We study the cosmology induced on a brane probing a warped throat region in a Calabi-Yau compactification of type IIB string theory. For the case of a BPS D3-brane probing the Klebanov-Strassler warped deformed conifold, the cosmology described by a suitable brane observer is a bouncing, spatially flat Friedmann-Robertson-Walker universe with time-varying Newton's constant, which passes smoothly from a contracting to an expanding phase. In the Klebanov-Tseytlin approximation to the Klebanov-Strassler solution the cosmology would end with a big crunch singularity. In this sense, the warped deformed conifold provides a string theory resolution of a spacelike singularity in the brane cosmology. The four-dimensional effective action appropriate for a brane observer is a simple scalar-tensor theory of gravity. In this description of the physics, a bounce is possible because the relevant energy-momentum tensor can classically violate the null energy condition.
Noncommutative Compactifications of Type I Strings on Tori with Magnetic Background Flux
Blumenhagen, R; Körs, B; Lüst, Dieter; Blumenhagen, Ralph; Goerlich, Lars; Kors, Boris; Lust, Dieter
2000-01-01
We construct six- and four-dimensional toroidal compactifications of the Type I string with magnetic flux on the D-branes. The open strings in this background probe a noncommutative internal geometry. Phenomenologically appealing features such as chiral fermions and supersymmetry breaking in the gauge sector are naturally realized by these vacua. We investigate the spectra of such noncommutative string compactifications and in a bottom-up approach discuss the possibility to obtain the standard or some GUT like model.
A simple class of non-geometric M-theory compactification backgrounds
Shahbazi, C S
2015-01-01
We study a particular class of supersymmetric M-theory eight-dimensional non-geometric compactification backgrounds to three-dimensional Minkowski space-time, proving that the global space of the non-geometric compactification is still a differentiable manifold, although with very different geometric and topological properties with respect to the corresponding standard M-theory compactification background: it is a compact complex manifold admitting a K\\"ahler covering with deck transformations acting by holomorphic homotheties with respect to the K\\"ahler metric. We show that this class of non-geometric compactifications evade the Maldacena-Nu\\~nez no-go theorem and thus do not require $\\alpha^{\\prime}$-corrections to allow for a non-trivial warp factor or four-form flux. We obtain an explicit compactification background on a complex Hopf four-fold that solves all the equations of motion of the theory. We also show that this class of non-geometric compactification backgrounds is equipped with a holomorphic pr...
Can compactifications solve the cosmological constant problem?
Hertzberg, Mark P. [Institute of Cosmology, Department of Physics and Astronomy, Tufts University,574 Boston Ave, Medford, MA 02155 (United States); Center for Theoretical Physics, Department of Physics,Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, MA 02139 (United States); Masoumi, Ali [Institute of Cosmology, Department of Physics and Astronomy, Tufts University,574 Boston Ave, Medford, MA 02155 (United States)
2016-06-30
Recently, there have been claims in the literature that the cosmological constant problem can be dynamically solved by specific compactifications of gravity from higher-dimensional toy models. These models have the novel feature that in the four-dimensional theory, the cosmological constant Λ is much smaller than the Planck density and in fact accumulates at Λ=0. Here we show that while these are very interesting models, they do not properly address the real cosmological constant problem. As we explain, the real problem is not simply to obtain Λ that is small in Planck units in a toy model, but to explain why Λ is much smaller than other mass scales (and combinations of scales) in the theory. Instead, in these toy models, all other particle mass scales have been either removed or sent to zero, thus ignoring the real problem. To this end, we provide a general argument that the included moduli masses are generically of order Hubble, so sending them to zero trivially sends the cosmological constant to zero. We also show that the fundamental Planck mass is being sent to zero, and so the central problem is trivially avoided by removing high energy physics altogether. On the other hand, by including various large mass scales from particle physics with a high fundamental Planck mass, one is faced with a real problem, whose only known solution involves accidental cancellations in a landscape.
Flavor mixings in flux compactifications
Buchmuller, Wilfried; Schweizer, Julian
2017-04-01
A multiplicity of quark-lepton families can naturally arise as zero modes in flux compactifications. The flavor structure of quark and lepton mass matrices is then determined by the wave function profiles of the zero modes. We consider a supersymmetric S O (10 )×U (1 ) model in six dimensions compactified on the orbifold T2/Z2 with Abelian magnetic flux. A bulk 16 -plet charged under the U (1 ) provides the quark-lepton generations whereas two uncharged 10 -plets yield two Higgs doublets. Bulk anomaly cancellation requires the presence of additional 16 - and 10 -plets. The corresponding zero modes form vectorlike split multiplets that are needed to obtain a successful flavor phenomenology. We analyze the pattern of flavor mixings for the two heaviest families of the Standard Model and discuss possible generalizations to three and more generations.
Bubbles of Nothing in Flux Compactifications
Blanco-Pillado, Jose J
2010-01-01
We construct a simple $5d$ flux compactification stabilized by a complex scalar field winding the extra dimension and demonstrate an instability via nucleation of a bubble of nothing. This occurs when the Kaluza -- Klein dimension degenerates to a point, defining the bubble surface. Because the extra dimension is stabilized by a flux, the bubble surface must be charged, in this case under the axionic part of the complex scalar. This smooth geometry can be seen as a de Sitter topological defect with asymptotic behavior identical to the pure compactification. We discuss how a similar construction can be implemented in more general Freund -- Rubin compactifications.
Holomorphic couplings in non-perturbative string compactifications
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.)
The Fate of Unstable Gauge Flux Compactifications
Burgess, C P; Zavala, I
2009-01-01
Fluxes are widely used to stabilise extra dimensions, but if they arise within a non-abelian gauge sector they are often unstable. We seek the fate of this instability, focussing on the simplest examples: sphere-monopole compactifications in six dimensions. Without gravity most non-abelian monopoles are unstable, decaying into the unique stable monopole in the same topological class. We show that the same is true in Einstein-YM systems, with the geometry adjusting accordingly: a Mink(d)xS2 geometry supported by an unstable monopole relaxes to an AdS(d)xS2. For 6D supergravity, the dilaton obstructs this simple evolution, acquiring a gradient and thus breaking some of the spacetime symmetries. We argue that it is the 4D symmetries that break, and examine several endpoint candidates. Oxidising the supergravity system into a higher-dimensional Einstein-YM monopole, we use the latter to guide us to the corresponding endpoint. The result is a singular Kasner-like geometry conformal to Mink(4)xS2. The solution has ...
Spin(7) compactifications and 1/4-BPS vacua in heterotic supergravity
Angus, Stephen [Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS),Daejeon, 34051 Republic of (Korea, Republic of); Matti, Cyril [Department of Mathematics, City University, Northampton Square, London, EC1V 0HB (United Kingdom); Mandelstam Institute for Theoretical Physics, NITheP, andSchool of Physics, University of the Witwatersrand,Johannesburg, WITS 2050 South Africa (South Africa); Svanes, Eirik E. [Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE,Paris, F-75005 (France); CNRS, UMR 7589, LPTHE,Paris, F-75005 (France); Sorbonne Universités, Institut Lagrange de Paris,98 bis Bd Arago, Paris, 75014 (France)
2016-03-25
We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For preservation of supersymmetry, this implies that the internal space must in general be that of a Spin(7) manifold, which leads to a 1/4-BPS four-dimensional supersymmetric perturbative vacuum breaking all but one supercharge. We find that these solutions allow for internal geometries previously excluded by the domain-wall-type solutions, and hence the resulting four-dimensional superpotential is more generic. In particular, we find an interesting resemblance to the superpotentials that appear in non-geometric flux compactifications of type II string theory. If the vacua are to be used for phenomenological applications, they must be lifted to maximal symmetry by some non-perturbative or higher-order effect.
$Spin(7)$ Compactifications and 1/4-BPS Vacua in Heterotic Supergravity
Angus, Stephen; Svanes, Eirik Eik
2015-01-01
We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For preservation of supersymmetry, this implies that the internal space must in general be that of a $Spin(7)$ manifold, which leads to a $1/4$-BPS four-dimensional non-supersymmetric perturbative vacuum. We find that these solutions allow for internal geometries previously excluded by the domain-wall-type solutions, and hence the resulting four-dimensional superpotential is more generic. In particular, we find an interesting resemblance to the superpotentials that appear in non-geometric flux compactifications of type II string theory. If the vacua are to be used for phenomenological applications, they must be lifted to a maximally symmetric one by some non-perturbative or higher-order effect.
On ADE Quiver Models and F-Theory Compactification
Belhaj, A; Sebbar, A; Sedra, M B
2006-01-01
Based on mirror symmetry, we discuss geometric engineering of N=1 ADE quiver models from F-theory compactifications on elliptic K3 surfaces fibered over certain four-dimensional base spaces. The latter are constructed as intersecting 4-cycles according to $ADE$ Dynkin diagrams, thereby mimicking the construction of Calabi-Yau threefolds used in geometric engineering in type II superstring theory. Matter is incorporated by considering D7-branes wrapping these 4-cycles. Using a geometric procedure referred to as folding, we discuss how the corresponding physics can be converted into a scenario with D5-branes wrapping 2-cycles of ALE spaces.
On ADE quiver models and F-theory compactification
Belhaj, A [Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, ON, K1N 6N5 (Canada); Rasmussen, J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia); Sebbar, A [Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave., Ottawa, ON, K1N 6N5 (Canada); Sedra, M B [Laboratoire de Physique de la Matiere et Rayonnement (LPMR), Morocco Faculte des Sciences, Universite Ibn Tofail, Kenitra, Morocco (Morocco)
2006-07-21
Based on mirror symmetry, we discuss geometric engineering of N = 1 ADE quiver models from F-theory compactifications on elliptic K3 surfaces fibred over certain four-dimensional base spaces. The latter are constructed as intersecting 4-cycles according to ADE Dynkin diagrams, thereby mimicking the construction of Calabi-Yau threefolds used in geometric engineering in type II superstring theory. Matter is incorporated by considering D7-branes wrapping these 4-cycles. Using a geometric procedure referred to as folding, we discuss how the corresponding physics can be converted into a scenario with D5-branes wrapping 2-cycles of ALE spaces.
The fate of unstable gauge flux compactifications
Burgess, C.P. [McMaster Univ., Hamilton, ON (Canada). Dept. of Physics and Astronomy]|[Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Parameswaran, S.L. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Zavala, I. [Bonn Univ. (Germany). Bethe Center for Theoretical Physics and Physikalisches Inst.
2008-12-15
Fluxes are widely used to stabilise extra dimensions, but the supporting monopolelike configurations are often unstable, particularly if they arise as gauge flux within a non-abelian gauge sector. We here seek the endpoint geometries to which this instability leads, focussing on the simplest concrete examples: sphere-monopole compactifications in six dimensions. Without gravity most monopoles in non-abelian gauge groups are unstable, decaying into the unique stable monopole in the same topological class. We show that the same is true in Einstein-YM systems, with the new twist that the decay leads to a shrinkage in the size of the extra dimensions and curves the non-compact directions: in D dimensions a Mink{sub D-2} x S{sub 2} geometry supported by an unstable monopole relaxes to AdS{sub D-2} x S{sub 2}, with the endpoint sphere smaller than the initial one. For supergravity the situation is more complicated because the dilaton obstructs such a simple evolution. The endpoint instead acquires a dilaton gradient, thereby breaking some of the spacetime symmetries. For 6D supergravity we argue that it is the 4D symmetries that break, and examine several candidates for the endpoint geometry. By using the trick of dimensional oxidation it is possible to recast the supergravity system as a higher-dimensional Einstein-YM monopole, allowing understanding of this system to guide us to the corresponding endpoint. The result is a Kasner-like geometry conformal to Mink{sub 4} times S{sub 2}, with nontrivial conformal factor and dilaton breaking the maximal 4D symmetry and generating a singularity. Yet the resulting configuration has a lower potential energy than did the initial one, and is perturbatively stable, making it a sensible candidate endpoint for the evolution. (orig.)
Controlling chaos through compactification in cosmological models with a collapsing phase
Wesley, Daniel H.; Steinhardt, Paul J.; Turok, Neil
2005-09-01
We consider the effect of compactification of extra dimensions on the onset of classical chaotic mixmaster behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson-Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close to the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N=1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.
Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications
Apruzzi, Fabio; Parameswaran, Susha; Zagermann, Marco
2014-01-01
We study to what extent Wilson lines in heterotic Calabi-Yau compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson lines are basic ingredients for Standard Model constructions but their induced H-flux may affect the consistency of the leading order background geometry and of the two-dimensional worldsheet theory. Moreover H-flux in heterotic compactifications would play an important role for moduli stabilization and could strongly constrain the supersymmetry breaking scale. We show how to compute H-flux and the corresponding superpotential, given an explicit complete intersection Calabi-Yau compactification and choice of Wilson lines. We do so by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding how the Wilson lines project onto these submanifolds, and computing their Chern-Simons invariants. We illustrate our procedure with the quintic hypersurface as well as the split-bicubic, which can provide a potentially realistic three generation model.
Scales and hierarchies in warped compactifications and brane worlds
De Wolfe, O; Wolfe, Oliver De; Giddings, Steven B.
2003-01-01
Warped compactifications with branes provide a new approach to the hierarchy problem and generate a diversity of four-dimensional thresholds. We investigate the relationships between these scales, which fall into two classes. Geometrical scales, such as thresholds for Kaluza-Klein, excited string, and black hole production, are generically determined soley by the spacetime geometry. Dynamical scales, notably the scale of supersymmetry breaking and moduli masses, depend on other details of the model. We illustrate these relationships in a class of solutions of type IIB string theory with imaginary self-dual fluxes. After identifying the geometrical scales and the resulting hierarchy, we determine the gravitino and moduli masses through explicit dimensional reduction, and estimate their value to be near the four-dimensional Planck scale. In the process we obtain expressions for the superpotential and Kahler potential, including the effects of warping. We identify matter living on certain branes to be effectivel...
Threshold corrections in heterotic flux compactifications
Angelantonj, Carlo; Sarkis, Matthieu
2016-01-01
We compute the one-loop threshold corrections to the gauge and gravitational couplings for a large class of N=2 non-K\\"ahler heterotic compactifications with three-form flux, consisting in principal two-torus bundles over K3 surfaces. We obtain the results as sums of BPS-states contributions, depending on the topological data of the bundle. We analyse also the worldsheet non-perturbative corrections coming from instantons wrapping the torus fiber, that are mapped under S-duality to D-instanton corrections in type I flux compactifications.
Flux compactifications, gauge algebras and De Sitter
Dibitetto, Giuseppe, E-mail: g.dibitetto@rug.n [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Linares, Roman, E-mail: lirr@xanum.uam.m [Departamento de Fisica, Universidad Autonoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, Mexico D.F. (Mexico); Roest, Diederik, E-mail: d.roest@rug.n [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands)
2010-04-26
The introduction of (non-)geometric fluxes allows for N=1 moduli stabilisation in a De Sitter vacuum. The aim of this Letter is to assess to what extent this is true in N=4 compactifications. First we identify the correct gauge algebra in terms of gauge and (non-)geometric fluxes. We then show that this algebra does not lead to any of the known gaugings with De Sitter solutions. In particular, the gaugings that one obtains from flux compactifications involve non-semi-simple algebras, while the known gaugings with De Sitter solutions consist of direct products of (semi-)simple algebras.
On the 4D effective theory in warped compactifications with fluxes and branes
Koyama, K; Koyama, K; Arroja, Frederico; Koyama, Kayoko; Koyama, Kazuya
2006-01-01
We present a systematic way to derive the four-dimensional effective theories for warped compactifications with fluxes and branes in the ten-dimensional type IIB supergravity. The ten-dimensional equations of motion are solved using the gradient expansion method and the effective four-dimensional equations of motions are derived by imposing the consistency condition that the total derivative terms with respect to the six-dimensional internal coordinates vanish when integrated over the internal manifold. By solving the effective four-dimensional equations, we can find the gravitational backreaction to the warped geometry due to the dynamics of moduli fields, branes and fluxes.
Axion stabilization in type IIB flux compactifications
Hristov, K.
2009-01-01
A scenario for stabilization of axionic moduli fields in the context of type IIB Calabi-Yau flux compactifications is discussed in detail. We consider the case of a Calabi-Yau orientifold with h1,1−≠0 which allows for the presence of B2 and C2-moduli. In an attempt to generalize the KKLT and the Lar
The Geometer's Toolkit to String Compactifications
Reffert, S
2007-01-01
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is wholly on the geometry side, not on the physics. The treated topics include toroidal orbifolds, methods of toric geometry, desinglularization of toroidal orbifolds and their orientifold quotients.
Axion stabilization in type IIB flux compactifications
Hristov, K.
2009-01-01
A scenario for stabilization of axionic moduli fields in the context of type IIB Calabi-Yau flux compactifications is discussed in detail. We consider the case of a Calabi-Yau orientifold with h1,1−≠0 which allows for the presence of B2 and C2-moduli. In an attempt to generalize the KKLT and the Lar
A Three-Family SU(6) Type I Compactification
Kakushadze, Z
1998-01-01
We construct a four dimensional chiral N=1 space-time supersymmetric Type I vacuum corresponding to a compactification on a toroidal Z_2 X Z_2 X Z_3 orbifold. Using recent results in four dimensional orientifolds, we argue that this model has a well defined world-sheet description. An interesting feature of this model is that the gauge group contains an SU(6) subgroup with three chiral generations. Moreover, this model contains D5-branes and therefore corresponds to a non-perturbative heterotic vacuum. This is the first example of a consistent chiral N=1 supersymmetric string vacuum which is non-perturbative from the heterotic viewpoint, has a perturbative description in a dual theory, and possesses phenomenologically interesting characteristics. We also compute superpotential in this theory, and point out a feature of this model which appears phenomenologically unappealing.
On N = 2 compactifications of M-theory to AdS{sub 3} using geometric algebra techniques
Babalic, E. M.; Coman, I. A.; Condeescu, C.; Micu, A. [IFIN-HH, Department of Theoretical Physics, 077125 Magurele (Romania); Lazaroiu, C. I. [IFIN-HH, Department of Theoretical Physics, 077125 Magurele, Romania and IBS, Center for Geometry and Physics, and POSTECH, Department of Mathematics, Pohang, Gyeongbuk 790-784 (Korea, Republic of)
2013-11-13
We investigate the most general warped compactification of eleven-dimensional supergravity on eight-dimensional manifolds to AdS{sub 3} spaces (in the presence of non-vanishing four-form flux) which preserves N = 2 supersymmetry in three dimensions. Without imposing any restrictions on the chirality of the internal part of the supersymmetry generators, we use geometric algebra techniques to study some implications of the supersymmetry constraints. In particular, we discuss the Lie bracket of certain vector fields constructed as pinor bilinears on the compactification manifold.
On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications
Ballesteros, Ángel; Gutiérrez-Sagredo, Iván; Naranjo, Pedro
2017-02-01
In a recent paper (Morris (2015) [1]), an inhomogeneous compactification of the extra dimension of a five-dimensional Kaluza-Klein metric has been shown to generate a position-dependent mass (PDM) in the corresponding four-dimensional system. As an application of this dimensional reduction mechanism, a specific static dilatonic scalar field has been connected with a PDM Lagrangian describing a well-known nonlinear PDM oscillator. Here we present more instances of this construction that lead to PDM systems with radial symmetry, and the properties of their corresponding inhomogeneous extra dimensions are compared with the ones in the nonlinear oscillator model. Moreover, it is also shown how the compactification introduced in this type of models can alternatively be interpreted as a novel mechanism for the dynamical generation of curvature.
Heterotic and type II orientifold compactifications on SU(3) structure manifolds
Benmachiche, I.
2006-07-15
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.)
On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications
Ballesteros, Ángel; Naranjo, Pedro
2016-01-01
In a recent paper [1], an inhomogeneous compactification of the extra dimension of a five dimensional Kaluza-Klein metric has been shown to generate a position-dependent mass in the corresponding four dimensional system. As an application of this dimensional reduction mechanism, a specific static dilatonic scalar field has been connected with a PDM Lagrangian describing a well-known nonlinear PDM oscillator. Here we present two more instances of this construction that lead to two distinguished superintegrable PDM systems: the so-called Darboux III and Taub-NUT Hamiltonians, and the properties of the inhomogeneous extra dimensions connected with them are compared with the ones in the nonlinear oscillator model. It is worth stressing that the Darboux III and Taub-NUT define exactly solvable quantum models, whose spectrum and eigenfuctions are explicitly known. Finally, it is shown that the compactification introduced in [1] can be alternatively interpreted as a mechanism for the dynamical generation of curvatur...
Compactifications of IIA supergravity on SU(2)-structure manifolds
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.)
Calabi-Yau compactification of type II string theories
Banerjee, Sibasish
2016-01-01
Superstring theories are the most promising theories for unified description of all fundamental interactions including gravity. However, these theories are formulated consistently only in 10 spacetime dimensions. Therefore, to connect to the observable world, it is required to compactify 6 out of those 10 dimensions in a suitable fashion. In this thesis, we mainly consider compactifications of type II string theories on Calabi-Yau threefolds. As a consequence, the resulting four dimensional theories preserve $\\mathcal{N}=2$ supersymmetry. In these cases the metrics on the moduli spaces of the matter multiplets, vector and hypermultiplets, completely determine the low energy theories. Whereas the former are very well understood by now, the complete description of hypermultiplets is more complicated. In fact, hypermultiplets receive both perturbative and non-perturbative corrections. The thesis mainly pertains to the understanding of the non-perturbative corrections. Our findings for the hypermultiplets rely on...
On Signature Transition and Compactification in Kaluza-Klein Cosmology
Darabi, F
1999-01-01
We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative cosmological constant and a Robertson-Walker type metric. It is shown that the solutions to Einstein field equations have degenerate metric and exhibit transitioins from a Euclidean to a Lorentzian domain. We then suggest a mechanism, based on signature transition which leads to compactification of the internal space in the Lorentzian region as $a \\sim |\\Lambda|^{1/2}$. With the assumption of a very small value for the cosmological constant we find that the size of the universe $R$ and the internal scale factor $a$ would be related according to $Ra\\sim 1$ in the Lorentzian region. The corresponding Wheeler-DeWitt equation has exact solution in the mini-superspace giving rise to a quantum state which peaks in the vicinity of the classical solutions undergoing signature transition.
Generalized N=1 orientifold compactifications and the Hitchin functionals
Benmachiche, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Grimm, T.W. [Wisconsin Univ., Madison, WI (United States). Dept. of Physics
2006-02-15
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.)
Continuous Global Symmetries and Hyperweak Interactions in String Compactifications
Burgess, C P; Hung, L-Y; Kom, C H; Maharana, A; Quevedo, Fernando
2008-01-01
We revisit general arguments for the absence of exact continuous global symmetries in string compactifications and extend them to D-brane models. We elucidate the various ways approximate continuous global symmetries arise in the 4-dimensional effective action. In addition to two familiar methods - axionic Peccei-Quinn symmetries and remnant global abelian symmetries from Green-Schwarz gauge symmetry breaking - we identify new ways to generate approximate continuous global symmetries. Two methods stand out, both of which occur for local brane constructions within the LARGE volume scenario of moduli stabilisation. The first is the generic existence of continuous non-abelian global symmetries associated with local Calabi-Yau isometries. These symmetries are exact in the non-compact limit and are spontaneously broken by the LARGE volume, with breaking effects having phenomenologically interesting sizes \\sim 0.01 for plausible choices for underlying parameters. Such approximate flavour symmetries are phenomenolog...
On the effective theory of type II string compactifications on nilmanifolds and coset spaces
Caviezel, Claudio
2009-07-30
In this thesis we analyzed a large number of type IIA strict SU(3)-structure compactifications with fluxes and O6/D6-sources, as well as type IIB static SU(2)-structure compactifications with fluxes and O5/O7-sources. Restricting to structures and fluxes that are constant in the basis of left-invariant one-forms, these models are tractable enough to allow for an explicit derivation of the four-dimensional low-energy effective theory. The six-dimensional compact manifolds we studied in this thesis are nilmanifolds based on nilpotent Lie-algebras, and, on the other hand, coset spaces based on semisimple and U(1)-groups, which admit a left-invariant strict SU(3)- or static SU(2)-structure. In particular, from the set of 34 distinct nilmanifolds we identified two nilmanifolds, the torus and the Iwasawa manifold, that allow for an AdS{sub 4}, N = 1 type IIA strict SU(3)-structure solution and one nilmanifold allowing for an AdS{sub 4}, N = 1 type IIB static SU(2)-structure solution. From the set of all the possible six-dimensional coset spaces, we identified seven coset spaces suitable for strict SU(3)-structure compactifications, four of which also allow for a static SU(2)-structure compactification. For all these models, we calculated the four-dimensional low-energy effective theory using N = 1 supergravity techniques. In order to write down the most general four-dimensional effective action, we also studied how to classify the different disconnected ''bubbles'' in moduli space. (orig.)
Nonuniversal gaugino masses in a magnetized toroidal compactification of SYM theories
Sumita, Keigo
2015-01-01
This paper proposes a concrete model of nonuniversal gaugino masses on the basis of higher-dimensional supersymmetric Yang-Mills theories compactified on a magnetized factorizable torus, and we estimate the gauge coupling constants and gaugino masses in the model. In the magnetized toroidal compactifications, the four-dimensional effective action can be obtained analytically identifying its dependence on moduli fields, where the magnetic fluxes are able to yield the flavor structure of the minimal supersymmetric standard model (MSSM). The obtained gauge kinetic functions contains multi moduli fields and their dependence is nonuniversal for the three gauge fields. The nonuniversal gauge kinetic functions can lead to nonuniversal gaugino masses at a certain high energy scale (e.g. compactification scale). Our numerical analysis of them shows that, particular ratios of gaugino masses, which were found to enhance the Higgs boson mass and lead to "natural supersymmetry" in the MSSM, can be realized in our model, w...
Spontaneous Compactification of Bimetric Theory
Kan, Nahomi; Shiraishi, Kiyoshi
2014-01-01
We study a model of bimetric gravity in six dimensions. The mixing of two metrics is provided by the term including two gauge field strengths in the model. We assume that each metric in the solution for the background geometry describes the four-dimensional Minkowski spacetime with an $S^2$ extra space, though the two radii of $S^2$ for two metrics take different values in general. The solution is derived by the effective potential method in the presence of the magnetic fluxes on the extra spheres. We find that the a massive graviton is governed by the Fierz-Pauli Lagrangian in the weak field limit and one massless graviton left in four dimensions.
Aspects of string theory compactifications. D-brane statistics and generalised geometry
Gmeiner, F.
2006-05-26
In this thesis we investigate two different aspects of string theory compactifications. The first part deals with the issue of the huge amount of possible string vacua, known as the landscape. Concretely we investigate a specific well defined subset of type II orientifold compactifications. We develop the necessary tools to construct a very large set of consistent models and investigate their gauge sector on a statistical basis. In particular we analyse the frequency distributions of gauge groups and the possible amount of chiral matter for compactifications to six and four dimensions. In the phenomenologically relevant case of four-dimensional compactifications, special attention is paid to solutions with gauge groups that include those of the standard model, as well as Pati-Salam, SU(5) and flipped SU(5) models. Additionally we investigate the frequency distribution of coupling constants and correlations between the observables in the gauge sector. These results are compared with a recent study of Gepner models. Moreover, we elaborate on questions concerning the finiteness of the number of solutions and the computational complexity of the algorithm. In the second part of this thesis we consider a new mathematical framework, called generalised geometry, to describe the six-manifolds used in string theory compactifications. In particular, the formulation of T-duality and mirror symmetry for nonlinear topological sigma models is investigated. Therefore we provide a reformulation and extension of the known topological A- and B-models to the generalised framework. The action of mirror symmetry on topological D-branes in this setup is presented and the transformation of the boundary conditions is analysed. To extend the considerations to D-branes in type II string theory, we introduce the notion of generalised calibrations. We show that the known calibration conditions of supersymmetric branes in type IIA and IIB can be obtained as special cases. Finally we investigate
Stability and Spectrum of Compactifications on Product Manifolds
Brown, Adam R
2013-01-01
We study the spectrum and perturbative stability of Freund-Rubin compactifications on $M_p \\times M_{Nq}$, where $M_{Nq}$ is itself a product of $N$ $q$-dimensional Einstein manifolds. The higher-dimensional action has a cosmological term $\\Lambda$ and a $q$-form flux, which individually wraps each element of the product; the extended dimensions $M_p$ can be anti-de Sitter, Minkowski, or de Sitter. We find the masses of every excitation around this background, as well as the conditions under which these solutions are stable. This generalizes previous work on Freund-Rubin vacua, which focused on the $N=1$ case, in which a $q$-form flux wraps a single $q$-dimensional Einstein manifold. The $N=1$ case can have a classical instability when the $q$-dimensional internal manifold is a product---one of the members of the product wants to shrink while the rest of the manifold expands. Here, we will see that individually wrapping each element of the product with a lower-form flux cures this cycle-collapse instability. ...
A triangulation of a homotopy-Deligne-Mumford compactification of the Moduli of curves
Gadgil, Siddhartha
2010-01-01
We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the compactification we construct to the Deligne-Mumford compactification so that the inverse image of each point is contractible. In particular our compactification is homotopy equivalent to the Deligne-Mumford compactification.
GUT relations from string theory compactifications
Tatar, Radu [Division of Theoretical Physics, Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX (United Kingdom); Watari, Taizan [Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan); Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, Kashiwa-no-ha 5-1-5, 277-8592 (Japan)], E-mail: watari@hep-th.phys.s.u-tokyo.ac.jp
2009-03-21
Wilson line on a non-simply connected manifold is a nice way to break SU(5) unified symmetry, and to solve the doublet-triplet splitting problem. This mechanism also requires, however, that the two Higgs doublets are strictly vector-like under all underlying gauge symmetries, and consequently there is a limit in a class of modes and their phenomenology for which the Wilson line can be used. An alternative is to turn on a non-flat line bundle in the U(1){sub Y} direction on an internal manifold, which does not have to be non-simply connected. The U(1){sub Y} gauge field has to remain in the massless spectrum, and its coupling has to satisfy the GUT relation. In string theory compactifications, however, it is not that easy to satisfy these conditions in a natural way; we call it U(1){sub Y} problem. In this article, we explain how the problem is solved in some parts of moduli space of string theory compactifications. Two major ingredients are an extra strongly coupled U(1) gauge field and parametrically large volume for compactification, which is also essential in accounting for the hierarchy between the Planck scale and the GUT scale. Heterotic M-theory vacua and F-theory vacua are discussed. This article also shows that the toroidal orbifold GUT approach using discrete Wilson lines corresponds to the non-flat line-bundle breaking above when orbifold singularities are blown up. Thus, the orbifold GUT approach also suffers from the U(1){sub Y} problem, and this article shows how to fix it.
Magnetic Flux in Toroidal Type I Compactification
Blumenhagen, R; Körs, B; Lüst, Dieter; Blumenhagen, Ralph; Goerlich, Lars; Kors, Boris; Lust, Dieter
2001-01-01
We discuss the compactification of type I strings on a torus with additional background gauge flux on the D9-branes. The solutions to the cancellation of the RR tadpoles display various phenomenologically attractive features: supersymmetry breaking, chiral fermions and the opportunity to reduce the rank of the gauge group as desired. We also point out the equivalence of the concept of various different background fields and noncommutative deformations of the geometry on the individual D9-branes by constructing the relevant boundary states to describe such objects.
Yukawa couplings in superstring compactification. [in quantum gravity theory
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.
Revisiting eight-manifold flux compactifications of M-theory using geometric algebra techniques
Babalic, Elena-Mirela
2013-01-01
Motivated by open problems in F-theory, we reconsider warped compactifications of M theory on 8-manifolds to AdS3 spaces in the presence of a non-trivial field strength of the M-theory 3-form, studying the most general conditions under which such backgrounds preserve N=2 supersymmetry in three dimensions. In contrast with previous studies, we allow for the most general pair of Majorana generalized Killing pinors on the internal 8-manifold, without imposing any chirality conditions on those pinors. We also show how such pinors can be lifted to the 9-dimensional metric cone over the compactification 8-manifold. We describe the translation of the generalized Killing pinor equations for such backgrounds to a system of differential and algebraic constraints on certain form-valued pinor bilinears and develop techniques through which such equations can be analyzed efficiently.
Wilson lines and UV sensitivity in magnetic compactifications arXiv
Ghilencea, D.M.
We investigate the ultraviolet (UV) behaviour of 6D N=1 supersymmetric effective (Abelian) gauge theories compactified on a two-torus ($T_2$) with magnetic flux. To this purpose we compute offshell the one-loop correction to the Wilson line state self-energy. The offshell calculation is actually necessary to capture the usual effective field theory expansion in powers of $(\\partial/\\Lambda)$. Particular care is paid to the regularization of the (divergent) momentum integrals, which is relevant for identifying the corresponding counterterm(s). We find a counterterm which is a new higher dimensional effective operator of dimension d=6, that is enhanced for a larger compactification area (where the effective theory applies) and is consistent with the symmetries of the theory. Its consequences are briefly discussed and comparison is made with orbifold compactifications without flux.
Compactifications of the Heterotic string with unitary bundles
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
Quotient space of $\\mathcal{LMC}$-compactification as a space of $z-$filters
Tootkaboni, M. Akbari
2010-01-01
The left multiplicative continuous compactification of a semitopological semigroup is the universal semigroup compactification. In this paper an internal construction of a semigroup compactification of a semitopological semigroup is constructed as a space of filters. In \\cite{Akbari}, we described an external construction of a semigroup compactification of a semitopological semigroup.
Special points of inflation in flux compactifications
Iñaki García-Etxebarria
2015-10-01
Full Text Available We study the realization of axion inflation models in the complex structure moduli spaces of Calabi–Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure point and conifold point, but can be of more general nature. In Type IIB and F-theory compactifications the geometric axions receive a scalar potential from a flux-induced superpotential. We find toy variants of various inflationary potentials including the ones for natural inflation of one or multiple axions, or axion monodromy inflation with polynomial potential. Interesting examples are also given by mirror geometries of torus fibrations with Mordell–Weil group of rank N−1 or an N-section, which admit an axion if N>3.
Moduli fixing in semirealistic string compactifications
Ramos-Sanchez, Saul
2011-01-01
Heterotic orbifold compactifications yield a myriad of models that reproduce many properties of the supersymmetric extension of the standard model and provide potential solutions to persisting problems of high energy physics, such as the origin of the neutrino masses and the strong CP problem. However, the details of the phenomenology in these scenarios rely on the assumption of a stable vacuum, characterized by moduli fields. In this note, we drop this assumption and address the problem of moduli stabilization in realistic orbifold models. We study their qualities and their 4D effective action, and discuss how nonperturbative effects indeed lift all bulk moduli directions. The resulting vacua, although still unstable, are typically de Sitter and there are generically some quasi-flat directions which can help to deal with cosmological challenges, such as inflation.
Flux compactifications in Einstein-Born-Infeld theories
Ramadhan, Handhika S; Iqbal, Muhammad
2015-01-01
We investigate the flux compactification mechanism in simple toy models of Einstein-Born-Infeld theories. These are the direct generalizations of the Einstein-Maxwell flux compactifications that recently gained fame as a toy model for tunneling in the landscape. Our investigation reveals that the Born-Infeld form does not significantly modify the qualitative result of the Einstein-Maxwell theory. for the case of Einstein-Higgs theory, however, we found that the effect of Born-Infeld nonlinearity is to render all q>1 extradimensional compactification unstable against semiclassical tunneling to nothing.
The Spectra of Type IIB Flux Compactifications at Large Complex Structure
Brodie, Callum
2015-01-01
We compute the spectra of the Hessian matrix, ${\\cal H}$, and the matrix ${\\cal M}$ that governs the critical point equation of the low-energy effective supergravity, as a function of the complex structure and axio-dilaton moduli space in type IIB flux compactifications at large complex structure. We find both spectra analytically in an $h^{1,2}_-+3$ real-dimensional subspace of the moduli space, and show that they exhibit a universal structure with highly degenerate eigenvalues, independently of the choice of flux, the details of the compactification geometry, and the number of complex structure moduli. In this subspace, the spectrum of the Hessian matrix contains no tachyons, but there are also no critical points. We show numerically that the spectra of ${\\cal H}$ and ${\\cal M}$ remain highly peaked over a large fraction of the sampled moduli space of explicit Calabi-Yau compactifications with 2 to 5 complex structure moduli. In these models, the scale of the supersymmetric contribution to the scalar masses...
Dynamics of warped flux compactifications with backreacting anti-branes
Junghans, Daniel
2014-01-01
We revisit the effective low-energy dynamics of the volume modulus in warped flux compactifications with anti-D3-branes in order to analyze the prospects for meta-stable de Sitter vacua and brane inflation along the lines of KKLT/KKLMMT. At the level of the 10d supergravity solution, anti-branes in flux backgrounds with opposite charge are known to source singular terms in the energy densities of the bulk fluxes, which led to a debate on the consistency of such constructions in string theory. A straightforward yet non-trivial check of the singular solution is to verify that its dimensional reduction in the large-volume limit reproduces the 4d low-energy dynamics expected from known results where the anti-branes are treated as a probe. Taking into account the anti-brane backreaction in the effective scalar potential, we find that both the volume scaling and the coefficient of the anti-brane uplift term are in exact agreement with the probe potential if the singular fluxes satisfy a certain near-brane boundary ...
Generating Small Numbers by Tunneling in Multi-Throat Compactifications
Silverstein, Eva M
2001-07-25
A generic F-theory compactification containing many D3 branes develops multiple brane throats. The interaction of observers residing inside different throats involves tunneling suppression and, as a result, is very weak. This suggests a new mechanism for generating small numbers in Nature. One application is to the hierarchy problem: large supersymmetry breaking near the unification scale inside a shallow throat causes TeV-scale SUSY-breaking inside the standard-model throat. Another application, inspired by nuclear-decay, is in designing naturally long-lived particles: a cold dark matter particle residing near the standard model brane decays to an approximate CFT-state of a longer throat within a Hubble time. This suggests that most of the mass of the universe today could consist of CFT-matter and may soften structure formation at sub-galactic scales. The tunneling calculation demonstrates that the coupling between two throats is dominated by higher dimensional modes and consequently is much larger than a naive application of holography might suggest.
Gravity of a noncanonical global monopole: conical topology and compactification
Prasetyo, Ilham
2015-01-01
We obtain solutions of Einstein's equations describing gravitational field outside a noncanonical global monopole with cosmological constant. In particular, we consider two models of k-monopoles: the Dirac-Born-Infeld (DBI) and the power-law types, and study their corresponding exterior gravitational fields. For each model we found two types of solutions. The first of which are global k-monopole black hole with conical global topology. These are generalizations of the Barriola-Vilenkin solution of global monopole. The appearance of noncanonical kinetic terms does not modify the critical symmetry-breaking scale, $\\eta_{crit}$, but it does affect the corresponding horizon(s). The second type of solution is compactification, whose topology is a product of two $2$-dimensional spaces with constant curvatures; ${\\mathcal Y}_4\\rightarrow {\\mathcal Z}_2\\times S^2$, with ${\\mathcal Y}, {\\mathcal Z}$ can be de Sitter, Minkowski, or Anti-de Sitter, and $S^2$ is the $2$-sphere. We investigate all possible compactificatio...
New class of de Sitter vacua in string theory compactifications
Achúcarro, Ana; Ortiz, Pablo; Sousa, Kepa
2016-10-01
String theory contains few known working examples of de Sitter vacua, four-dimensional universes with a positive cosmological constant. A notorious obstacle is the stabilization of a large number—sometimes hundreds—of moduli fields that characterize the compact dimensions. We study the stability of a class of supersymmetric moduli (the complex structure moduli and dilaton in type-IIB flux compactifications) in the regime where the volume of the compact space is large but not exponentially large. We show that, if the number of moduli is very large, random matrix theory provides a new stability condition, a lower bound on the volume. We find a new class of stable vacua where the mass spectrum of these supersymmetric moduli is gapped, without requiring a large mass hierarchy between moduli sectors or any fine-tuning of the superpotential. We provide the first explicit example of this class of vacua in the P[1,1 ,1 ,6 ,9 ] 4 model. A distinguishing feature is that all fermions in the supersymmetric sector are lighter than the gravitino.
Spontaneous Compactification to Robertson-Walker Universe Due To Dynamical Torsion
Malyshenko, V O; Malyshenko, Viktoria; Ricoy, Domingo Marin
1997-01-01
We investigate multidimensional gravity with the Gauss-Bonnet term and with torsion on the space of extra dimensions chosen to be the group manifold of a simple Lie group. We take the Robertson-Walker ansatz for the 4-dimensional space-time and study the potential of a dilaton and torsion fields. It is shown that for certain values of the parameters of the initial theory the potential has classically stable minima, corresponding to the spontaneous compactification of the extra dimensions. However, these minima have zero torsion.
Warping the Kähler potential of F-theory/IIB flux compactifications
Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei' , Università di Padova,and INFN - Sezione di Padova,Via Marzolo 8, 35131 Padova (Italy)
2015-03-13
We identify the low-energy Kähler potential of warped F-theory/IIB flux compactifications whose light spectrum includes universal, Kähler, axionic and mobile D3-brane moduli. The derivation is based on four-dimensional local superconformal symmetry and holomorphy of brane instanton contributions and it reproduces and generalises previous partial results. We compute the resulting kinetic terms, which show their explicit dependence on the warping. The Kähler potential satisfies the no-scale condition and produces, at leading order in the large volume expansion, a specific correction to the unwarped Kähler potential.
Topologically subordered rectifiable spaces and compactifications
Lin, Fucai
2011-01-01
A topological space $G$ is said to be a {\\it rectifiable space} provided that there are a surjective homeomorphism $\\phi :G\\times G\\rightarrow G\\times G$ and an element $e\\in G$ such that $\\pi_{1}\\circ \\phi =\\pi_{1}$ and for every $x\\in G$ we have $\\phi (x, x)=(x, e)$, where $\\pi_{1}: G\\times G\\rightarrow G$ is the projection to the first coordinate. In this paper, we mainly discuss the rectifiable spaces which are suborderable, and show that if a rectifiable space is suborderable then it is metrizable or a totally disconnected P-space, which improves a theorem of A.V. Arhangel'ski\\v\\i\\ in \\cite{A20092}. As an applications, we discuss the remainders of the Hausdorff compactifications of GO-spaces which are rectifiable, and we mainly concerned with the following statement, and under what condition $\\Phi$ it is true. Statement: Suppose that $G$ is a non-locally compact GO-space which is rectifiable, and that $Y=bG\\setminus G$ has (locally) a property-$\\Phi$. Then $G$ and $bG$ are separable and metrizable. Moreo...
Backreaction of Localised Sources in String Compactifications
Junghans, Daniel
2013-01-01
Localised sources such as D-branes or orientifold planes play an important role in many string compactifications that are relevant for phenomenology. The presence of these objects typically induces complicated dynamics in the compact dimensions such that a full solution to the 10d equations of motion is often out of reach. In order to still be able to make statements about the 4d effective theory arising in the low-energy limit, the equations of motion are usually only solved in an integrated sense, while the backreaction of the localised sources on the internal fields is neglected. This simplification is often referred to as smearing. In this work, we investigate to what extent smearing may affect observables in the effective low-energy theory and whether it may lead to fake solutions that would cease to exist once the backreaction is properly taken into account. We analyse explicit examples for which smeared solutions exist and find that the reliability of the smeared approximation appears to depend on whet...
The Scherk-Schwarz mechanism as a flux compactification with internal torsion
Andrianopoli, Laura [Centro E. Fermi, Compendio Viminale, I-00184 Rome (Italy); Lledo, Maria A. [Departament de FIsica Teorica, Universitat de Valencia and IFIC, C/Dr. Moliner, 50, E-46100 Burjassot (Valencia) (Spain); Trigiante, Mario [Dipartimento di Fisica, Politecnico di Torino, C. so Duca degli Abruzzi, 24 I-10129 Torino (Italy)
2005-05-01
The aim of this paper is to make progress in the understanding of the Scherk-Schwarz dimensional reduction in terms of a compactification in the presence of background fluxes and torsion. From the eleven dimensional supergravity point of view, we find that a general E{sub 6(6)} S-S phase may be obtained by turning on an appropriate background torsion, together with suitable fluxes, some of which can be directly identified with certain components of the four-form field-strength. Furthermore, we introduce a novel (four dimensional) approach to the study of dualities between flux/torsion compactifications of type II/M-theory. This approach defines the action that duality should have on the background quantities, in order for the E{sub 7(7)} invariance of the field equations and Bianchi identities to be restored also in the presence of fluxes/torsion. This analysis further implies the interpretation of the torsion flux as the T-dual of the NS three-form flux.
Compactification of a Drinfeld Period Domain over a Finite Field
Pink, Richard
2010-01-01
We study a certain compactification of the Drinfeld period domain over a finite field which arises naturally in the context of Drinfeld moduli spaces. Its boundary is a disjoint union of period domains of smaller rank, but these are glued together in a way that is dual to how they are glued in the compactification by projective space. This compactification is normal and singular along all boundary strata of codimension~$\\ge2$. We study its geometry from various angles including the projective coordinate ring with its Hilbert function, the cohomology of twisting sheaves, the dualizing sheaf, and give a modular interpretation for it. We construct a natural desingularization which is smooth projective and whose boundary is a divisor with normal crossings. We also study its quotients by certain finite groups.
Warped Strings: Self-dual Flux and Contemporary Compactifications
Frey, A R
2003-01-01
I review type IIB string compactifications in which the three-form field strengths satisfy a self-duality condition on the internal manifold. I begin with an overview of the models, giving preliminary formulae and several points of view from which they can be understood. Then I describe windows into the small radius behavior of the compactifications, which is more complicated than compactifications without fluxes. I discuss details of the flux-generated potential and nonperturbative corrections to it. These nonperturbative corrections allow a discussion of the cosmological constant and possible mechanisms for the universe to decay from one energy state to another. I conclude with comments on related topics and interesting directions for future study. As this review is a PhD dissertation, I will indicate my own contributions to the subject. However, it is my hope that this document will be a useful and relatively comprehensive review, especially to graduate students. In particular, the early part of the docume...
The Cross-ratio Compactification of the Configuration Space of Ordered Points on (C)
Risako FUNAHASHI; Masahiko TANIGUCHI
2012-01-01
A natural compactification of the virtual configuration space of N points on the Riemann sphere (C) is constructed by using cross-ratios.We show that this compactification is homeomorphic to the Bers' compactification of the virtual moduli space of a punctured Riemann sphere of type N.In particular,the system of global and explicit coordinates of this standard compactification is given by cross-ratios.
Calabi-Yau compactifications of non-supersymmetric heterotic string theory
Blaszczyk, Michael [Mainz Univ. (Germany). PRISMA Cluster of Excellence and Inst. fuer Physik (WA THEP); Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Loukas, Orestis [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; National Technical Univ. Athens (Greece). School of Electrical and Computer Engineering; Ruehle, Fabian [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2015-07-15
Phenomenological explorations of heterotic strings have conventionally focused primarily on the E{sub 8} x E{sub 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{sub 8} x E{sub 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.
Nonuniversal gaugino masses in a magnetized toroidal compactification of SYM theories
Sumita, Keigo
2015-10-01
This paper proposes a concrete model of nonuniversal gaugino masses on the basis of higher-dimensional supersymmetric Yang-Mills theories compactified on a magnetized factorizable torus, and we estimate the gauge coupling constants and gaugino masses in the model. In the magnetized toroidal compactifications, the four-dimensional effective action can be obtained analytically identifying its dependence on moduli fields, where the magnetic fluxes are able to yield the flavor structure of the minimal supersymmetric standard model (MSSM). The obtained gauge kinetic functions contains multi moduli fields and their dependence is nonuniversal for the three gauge fields. The nonuniversal gauge kinetic functions can lead to nonuniversal gaugino masses at a certain high energy scale (e.g. compactification scale). Our numerical analysis of them shows that, particular ratios of gaugino masses, which were found to enhance the Higgs boson mass and lead to "natural supersymmetry" in the MSSM, can be realized in our model, while the gauge couplings are unified as is achieved in the MSSM.
A No-go theorem for de Sitter compactifications?
Dass, N D H
2002-01-01
A general framework for studying compactifications in supergravity and string theories was introduced by Candelas, Horowitz, Strominger and Witten. This was further generalised to take into account the warp factor by de Wit, Smit and Hari Dass. Though the prime focus of the latter was to find solutions with nontrivial warp factors (shown not to exist under a variety of circumstances), it was shown there that de Sitter compactifications are generically disfavoured. In this note we place these results in the context of a revived interest in de Sitter spacetimes .
Gauge fluxes in F-theory compactifications
Lin, Ling
2016-07-13
In this thesis, we study the geometry and physics of gauge fluxes in F-theory compactifications to four dimensions. Motivated by the phenomenological requirement of chiral matter in realistic model building scenarios, we develop methods for a systematic analysis of primary vertical G{sub 4}-fluxes on torus-fibred Calabi-Yau fourfolds. In particular, we extend the well-known description of fluxes on elliptic fibrations with sections to the more general set-up of genus-one fibrations with multi-sections. The latter are known to give rise to discrete abelian symmetries in F-theory. We test our proposal for constructing fluxes in such geometries on an explicit model with SU(5) x Z{sub 2} symmetry, which is connected to an ordinary elliptic fibration with SU(5) x U(1) symmetry by a conifold transition. With our methods we systematically verify anomaly cancellation and tadpole matching in both models. Along the way, we find a novel way of understanding anomaly cancellation in 4D F-theory in purely geometric terms. This observation is further strengthened by a similar analysis of an SU(3) x SU(2) x U(1){sup 2} model. The obvious connection of this particular model with the Standard Model is then investigated in a more phenomenologically motivated survey. There, we will first provide possible matchings of the geometric spectrum with the Standard Model states, which highlights the role of the additional U(1) factor as a selection rule. In a second step, we then utilise our novel methods on flux computations to set up a search algorithm for semi-realistic chiral spectra in our Standard- Model-like fibrations over specific base manifolds B. As a demonstration, we scan over three choices P{sup 3}, Bl{sub 1}P{sup 3} and Bl{sub 2}P{sup 3} for the base. As a result we find a consistent flux that gives the chiral Standard Model spectrum with a vector-like triplet exotic, which may be lifted by a Higgs mechanism.
Supersymmetric compactifications of heterotic strings with fluxes and condensates
Manousselis, Pantelis [Department of Engineering Sciences, University of Patras, GR-26110 Patras (Greece)]. E-mail: pantelis@upatras.gr; Prezas, Nikolaos [Institut de Physique, Universite de Neuchatel, CH-2000 Neuchatel (Switzerland)]. E-mail: nikolaos.prezas@unine.ch; Zoupanos, George [Physics Department, National Technical University of Athens, GR-15780 University Campus, Athens (Greece)]. E-mail: zoupanos@mail.cern.ch
2006-04-03
We discuss supersymmetric compactifications of heterotic strings in the presence of H-flux and general condensates using the formalism of G-structures and intrinsic torsion. We revisit the examples based on nearly-Kaehler coset spaces and show that supersymmetric solutions, where the Bianchi identity is satisfied, can be obtained when both gaugino and dilatino condensates are present.
Right-handed neutrinos in F-theory compactifications
Tatar, Radu [Division of Theoretical Physics, Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 3BX, England (United Kingdom); Tsuchiya, Yoichi [Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan); Watari, Taizan [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwano-ha 5-1-5, 277-8592 (Japan)], E-mail: taizan.watari@ipmu.jp
2009-12-11
F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-handed neutrinos are in F-theory compactifications and how their Majorana mass terms are generated together with developing a theoretical framework where effective Yukawa couplings involving both SU(5)-neutral and charged fields can be calculated. We find that the complex structure moduli chiral multiplets of F-theory compactifications are good candidates to be right-handed neutrinos, and that their Majorana masses are automatically generated in flux compactifications. The mass scale is predicted to be somewhat below the GUT scale, which is in nice agreement with the {delta}m{sup 2} of the atmospheric neutrino oscillation through the see-saw mechanism. We also discuss various scenarios of solving the dimension-4 proton decay problem in supersymmetric F-theory compactifications, along with considering the consequences of those scenarios in the nature of right-handed neutrinos.
Equivariant K-theory of regular compactifications: further developments
Uma, V.
2016-04-01
We describe the \\widetilde G× \\widetilde G-equivariant K-ring of X, where \\widetilde G is a factorial covering of a connected complex reductive algebraic group G, and X is a regular compactification of G. Furthermore, using the description of K\\widetilde G×\\widetilde G(X), we describe the ordinary K-ring K(X) as a free module (whose rank is equal to the cardinality of the Weyl group) over the K-ring of a toric bundle over G/B whose fibre is equal to the toric variety \\overline{T}+ associated with a smooth subdivision of the positive Weyl chamber. This generalizes our previous work on the wonderful compactification (see [1]). We also give an explicit presentation of K\\widetilde G×\\widetilde G(X) and K(X) as algebras over K\\widetilde G×\\widetilde G(\\overline{G\\operatorname{ad}}) and K(\\overline{G\\operatorname{ad}}) respectively, where \\overline{G\\operatorname{ad}} is the wonderful compactification of the adjoint semisimple group G\\operatorname{ad}. In the case when X is a regular compactification of G\\operatorname{ad}, we give a geometric interpretation of these presentations in terms of the equivariant and ordinary Grothendieck rings of a canonical toric bundle over \\overline{G\\operatorname{ad}}.
Metastable Vacua in Flux Compactifications and Their Phenomenology
Lebedev, O; Mambrini, Y; Nilles, H P; Ratz, M; L\\"owen, Val\\'eri; Lebedev, Oleg; Mambrini, Yann; Nilles, Hans Peter; Ratz, Michael
2007-01-01
In the context of flux compactifications, metastable vacua with a small positive cosmological constant are obtained by combining a sector where supersymmetry is broken dynamically with the sector responsible for moduli stabilization, which is known as the F-uplifting. We analyze this procedure in a model-independent way and study phenomenological properties of the resulting vacua.
The Geometry on Smooth Toroidal Compactifications of Siegel varieties
Yau, Shing-Tung
2012-01-01
This is a part of our joint program. The purpose of this paper is to study smooth toroidal compactifications of Siegel varieties and their applications, we also try to understand the K\\"ahler-Einstein metrics on Siegel varieties through the compactifications. Let $A_{g,\\Gamma}:=H_g/\\Gamma$ be a Siegel variety, where $H_g$ is the genus-$g$ Siegel space and $\\Gamma$ is an arithmetic subgroup in $\\Aut(H_g)$. There are four aspects of this paper : 1.There is a correspondence between the category of degenerations of Abelian varieties and the category of limits of weight one Hodge structures. We show that any cusp of Siegel space $\\frak{H}_g$ can be identified with the set of certain weight one polarized mixed Hodge structures. 2.In general, the boundary of a smooth toroidal compactification $\\bar{A}_{g,\\Gamma}$ of $A_{g,\\Gamma}$ has self-intersections.For most geometric applications, we would like to have a nice toroidal compactification such that the added infinity boundary $D_\\infty =\\bar{A}_{g,\\Gamma}-A_{g,\\Gam...
Socorro, J.; Toledo Sesma, L.
2016-03-01
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus without the contributions of fluxes as first approximation. This approach is applied to anisotropic cosmological Bianchi type II model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Also, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology and we claim that these quantum solution are generic in the moduli scalar field for all Bianchi Class A models. Also we give the relation to these solutions for asymptotic behavior to large argument in the corresponding quantum solution in the gravitational variables and compare with Bohm's solutions, finding that this corresponds to the lowest-order WKB approximation.
Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory
Ho, Pei-Ming; Shiba, Shotaro
2009-01-01
We construct a class of Lie 3-algebras with an arbitrary number of pairs of generators with Lorentzian signature metric. Some examples are given and corresponding BLG models are studied. We show that such a system in general describes a supersymmetric massive vector multiplets after the ghost fields are Higgsed. Simple systems with nontrivial interaction are realized by infinite dimensional Lie 3-algebras associated with the loop algebras. The massive fields are then naturally identified with the Kaluza-Klein modes by the toroidal compactification triggered by the ghost fields. For example, Dp-brane with an (infinite dimensional) affine Lie algebra symmetry $\\hat g$ can be identified with D(p+1)-brane with gauge symmetry $g$.
L. Toledo Sesma
2016-01-01
Full Text Available We construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. This approach is applied to anisotropic cosmological Bianchi type I model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Under this approach, we present an isotropization mechanism for the Bianchi I cosmological model through the analysis of the ratio between the anisotropic parameters and the volume of the Universe which in general keeps constant or runs into zero for late times. We also find that the presence of extra dimensions in this model can accelerate the isotropization process depending on the momenta moduli values. Finally, we present some solutions to the corresponding Wheeler-DeWitt (WDW equation in the context of standard quantum cosmology.
The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications
Halverson, James
2016-01-01
We study seven-branes in $O(10^{15})$ four-dimensional F-theory compactifications where seven-brane moduli must be tuned in order to achieve non-abelian gauge symmetry. The associated compact spaces $B$ are the set of all smooth weak Fano toric threefolds. By a study of fine star regular triangulations of three dimensional reflexive polytopes, the number of such spaces is estimated to be $5.8\\times 10^{14}\\lesssim N_\\text{bases}\\lesssim 1.8\\times 10^{17}$. Typically hundreds or thousands of moduli must be tuned to achieve symmetry for $h^{11}(B)<10$, but the average number drops sharply into the range $O(25)$-$O(200)$ as $h^{11}(B)$ increases. For some low rank groups, such as $SU(2)$ and $SU(3)$, there exist examples where only a few moduli must be tuned in order to achieve seven-brane gauge symmetry.
Socorro, J
2015-01-01
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus without the contributions of fluxes as first approximation. This approach is applied to anisotropic cosmological Bianchi type II model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Also, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology and we claim that these quantum solution are generic in the moduli scalar field for all Bianchi Class A models. Also we gives the relation to these solutions for asymptotic behavior to large argument in the corresponding quantum solution in the gravitational variables and is compared with the Bohm's solutions, finding that this corresponds to lowest-order WKB approximation.
Flux Formulation of DFT on Group Manifolds and Generalized Scherk-Schwarz Compactifications
Bosque, Pascal du; Lust, Dieter
2015-01-01
A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a $2D$-dimensional, pseudo Riemannian manifold, which is isomorphic to a Lie group embedded into O($D,D$). All fields and parameters of generalized diffeomorphisms are supported on this manifold, whose metric is spanned by the background vielbein $E_A{}^I \\in$ GL($2D$). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, $E_A{}^I$ is identified with the left invariant Maurer-Cartan form on the group manifo...
Flux formulation of DFT on group manifolds and generalized Scherk-Schwarz compactifications
Bosque, Pascal du [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Fakultät für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Hassler, Falk [University of North Carolina, Department of Physics and Astronomy,Phillips Hall, CB #3255, 120 E. Cameron Ave., Chapel Hill, NC 27599-3255 (United States); City University of New York, The Graduate Center,365 Fifth Avenue, New York, NY 10016 (United States); Columbia University, Department of Physics,Pupin Hall, 550 West 120th St., New York, NY 10027 (United States); Lüst, Dieter [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Fakultät für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany)
2016-02-04
A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a 2D-dimensional, pseudo Riemannian manifold, which is isomorphic to a Lie group embedded into O(D,D). All fields and parameters of generalized diffeomorphisms are supported on this manifold, whose metric is spanned by the background vielbein E{sub A}{sup I}∈ GL(2D). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, E{sub A}{sup I} is identified with the left invariant Maurer-Cartan form on the group manifold, in the same way as it is done in geometric Scherk-Schwarz reductions. We show in detail how the Maurer-Cartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3,3), we calculate E{sub A}{sup I}.
Balanced metrics and phenomenological aspects of heterotic string compactifications
Brelidze, Tamaz
This thesis mainly focuses on numerical methods for studying Calabi-Yau manifolds. Such methods are instrumental in linking models inspired by the microscopic physics of string theory and the observable four dimensional world. In particular, it is desirable to compute Yukawa and gauge couplings. However, only for a relatively small class of geometries can those be computed exactly using the rather involved tools of algebraic geometry and topological string theory. Numerical methods provide one of the alternatives to go beyond these limitations. In this work we describe numerical procedures for computing Calabi-Yau metrics on complete intersections and free quotients of complete intersections. This is accomplished using the balanced metrics approach and enhancing its previous implementations with tools from Invariant Theory. In particular, we construct these metrics on generic quintics, four-generation quotients of the quintic, Schoen Calabi-Yau complete intersections and the quotient of a Schoen manifold with the Z3xZ 3 fundamental group that was previously used to construct a heterotic standard model. We also investigate the dependence of Donaldson's algorithm on the integration scheme, as well as on the Kahler and complex moduli. We then construct a numerical algorithm for explicitly computing the spectrum of the Laplace-Beltrami operator on Calabi-Yau threefolds. One of the inputs of this algorithm is the Calabi-Yau metric. To illustrate our algorithm, the eigenvalues and eigenfunctions of the Laplacian are computed numerically on two different quintic hypersurfaces, some Z5xZ 5 quotients of quintics, and the Calabi-Yau threefold with the Z3xZ 3 fundamental group of the heterotic standard model. We then explain the degeneracies of the eigenvalues in terms of the irreducible representations of the finite symmetry groups of the threefolds. We also study the cosmic string solutions in softly broken N = 1 supersymmetric theories that arise from heterotic string
Strongly Zero-Dimensional Locales
KOU Hui; LUO Mao Kang
2002-01-01
New kinds of strongly zero-dimensional locales are introduced and characterized, whichare different from Johnstone's, and almost all the topological properties for strongly zero-dimensionalspaces have the pointless localic forms. Particularly, the Stone-Cech compactification of a stronglyzero-dimensional locale is stongly zero-dimensional.
Darabi, F
2009-01-01
We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors $a$ and $R$, corresponding to $D$-dimensional internal space and 4-dimensional universe, respectively. By introducing an exotic matter in the form of perfect fluid with an special equation of state, as the space-time part of the higher dimensional energy-momentum tensor, a four dimensional effective decaying cosmological term appears as $\\lambda \\sim R^{-m}$ with $0 \\leq m\\leq 2$, playing the role of an evolving dark energy in the universe. By taking $m=2$, which has some interesting implications in reconciling observations with inflationary models and is consistent with quantum tunneling, the resulting Einstein's field equations yield the exponential solutions for the scale factors $a$ and $R$. These exponential behaviors may account for the dynamical compactification of extra dimensions and the accelerating expansion of the 4-dimensional universe in terms of Hubble parameter, $H$. The accelerat...
Threshold corrections and symmetry enhancement in string compactifications
Lópes-Cardoso, G; Mohaupt, T; Cardoso, Gabriel Lopes; Lust, Dieter; Mohaupt, Thomas
1994-01-01
We present the computation of threshold functions for Abelian orbifold compactifications. Specifically, starting from the massive, moduli-dependent string spectrum after compactification, we derive the threshold functions as target space duality invariant free energies (sum over massive string states). In particular we work out the dependence on the continuous Wilson line moduli fields. In addition we concentrate on the physically interesting effect that at certain critical points in the orbifold moduli spaces additional massless states appear in the string spectrum leading to logarithmic singularities in the threshold functions. We discuss this effect for the gauge coupling threshold corrections; here the appearance of additional massless states is directly related to the Higgs effect in string theory. In addition the singularities in the threshold functions are relevant for the loop corrections to the gravitational coupling constants.
Ubiquity of non-geometry in heterotic compactifications
García-Etxebarria, Iñaki; Massai, Stefano; Mayrhofer, Christoph
2016-01-01
We study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest non-trivial elliptic fibration the effect is quite dramatic: the $I_1$ degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the $T^2$. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety due to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.
Distribution of the number of generations in flux compactifications
Braun, Andreas P.; Watari, Taizan
2014-12-01
Flux compactification of string theory generates an ensemble with a large number of vacua, called the landscape. By using the statistics of various properties of low-energy effective theories in the string landscape, one can therefore hope to provide a scientific foundation to the notion of naturalness. This article discusses how to answer such questions of practical interest by using flux compactification of F-theory. It is found that the distribution is approximately in a factorized form given by distribution on the choice of 7-brane gauge group, that on the number of generations Ngen and that on effective coupling constants. The distribution on Ngen is approximately Gaussian for the range |Ngen|≲10 . The statistical cost of higher-rank gauge group is also discussed.
Distribution of the Number of Generations in Flux Compactifications
Braun, Andreas P
2014-01-01
Flux compactification of string theory generates an ensemble with a large number of vacua called the landscape. By using the statistics of various properties of low-energy effective theories in the string landscape, one can therefore hope to provide a scientific foundation to the notion of naturalness. This article discusses how to answer such questions of practical interest by using flux compactification of F-theory. It is found that the distribution is approximately in a factorized form given by the distribution of the choice of 7-brane gauge group, that of the number of generations $N_{\\rm gen}$ and that of effective coupling constants. The distribution of $N_{\\rm gen}$ is approximately Gaussian for the range $|N_{\\rm gen}| \\lesssim 10$. The statistical cost of higher-rank gauge groups is also discussed.
Negative Energy Density in Calabi-Yau Compactifications
Hertog, Thomas; Horowitz, Gary T.; Maeda, Kengo
2003-01-01
We show that a large class of supersymmetric compactifications, including all simply connected Calabi-Yau and G_2 manifolds, have classical configurations with negative energy density as seen from four dimensions. In fact, the energy density can be arbitrarily negative -- it is unbounded from below. Nevertheless, positive energy theorems show that the total ADM energy remains positive. Physical consequences of the negative energy density include new thermal instabilities, and possible violati...
A compactification of the Bruhat-Tits building
Landvogt, Erasmus
1996-01-01
The aim of this work is the definition of the polyhedral compactification of the Bruhat-Tits building of a reductive group over a local field. In addition, an explicit description of the boundary is given. In order to make this work as self-contained as possible and also accessible to non-experts in Bruhat-Tits theory, the construction of the Bruhat-Tits building itself is given completely.
Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
Cassani, Davide
2007-01-01
We consider compactifications of type II string theory on general SU(3) x SU(3) structure backgrounds allowing for a very large set of fluxes, possibly nongeometric ones. We study the effective 4d low energy theory which is a gauged N=2 supergravity, and discuss how its data are obtained from the formalism of the generalized geometry on T+T*. In particular we relate Hitchin's special Kaehler metrics on the spaces of even and odd pure spinors to the metric on the supergravity moduli space of internal metric and B-field fluctuations. We derive the N=1 vacuum conditions from this N=2 effective action, as well as from its N=1 truncation. We prove a direct correspondence between these conditions and an integrated version of the pure spinor equations characterizing the N=1 backgrounds at the ten dimensional level.
Standard Model Compactifications of IIA Z3 x Z3 Orientifolds from Intersecting D6-branes
Kokorelis, C E
2004-01-01
We discuss the construction of chiral four dimensional T^6/(Z3 x Z3) orientifold compactifications of IIA theory, using D6-branes intersecting at angles and not aligned with the orientifold O6 planes. Cancellation of mixed U(1) anomalies requires the presence of a generalized Green-Schwarz mechanism mediated by RR partners of closed string untwisted moduli. As expected all complex moduli fields get stabilized naturally in these constructions by the orbifold symmetry. In this respect we describe the appearance of three quark and lepton family SU(3)_C x SU(2)_L x U(1)_Y non-supersymmetric orientifold models with only the massless spectrum of the SM at low energy that can have either no exotics present and three families of $\
Anagnostopoulos, Konstantinos N; Nishimura, Jun
2012-01-01
The IKKT or IIB matrix model has been postulated to be a non perturbative definition of superstring theory. It has the attractive feature that spacetime is dynamically generated, which makes possible the scenario of dynamical compactification of extra dimensions, which in the Euclidean model manifests by spontaneously breaking the SO(10) rotational invariance (SSB). In this work we study using Monte Carlo simulations the 6 dimensional version of the Euclidean IIB matrix model. Simulations are found to be plagued by a strong complex action problem and the factorization method is used for effective sampling and computing expectation values of the extent of spacetime in various dimensions. Our results are consistent with calculations using the Gaussian Expansion method which predict SSB to SO(3) symmetric vacua, a finite universal extent of the compactified dimensions and finite spacetime volume.
Right-handed Neutrinos in F-theory Compactifications
Tatar, Radu; Watari, Taizan
2009-01-01
F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-handed neutrinos are in F-theory compactifications and how their Majorana mass terms are generated together with developing a theoretical framework where effective Yukawa couplings involving both SU(5)-neutral and charged fields can be calculated. We find that the complex structure moduli chiral multiplets of F-theory compactifications are good candidates to be right-handed neutrinos, and that their Majorana masses are automatically generated in flux compactifications. The mass scale is predicted to be somewhat below the GUT...
On the existence of Stone-Cech compactification
Curi, Giovanni
2009-01-01
In [G. Curi, "Exact approximations to Stone-Cech compactification'', Ann. Pure Appl. Logic, 146, 2-3, 2007, pp. 103-123] a characterization is obtained of the class of locales of which the Stone-Cech compactification can be defined in constructive type theory CTT, and in the formal system CZF+uREA+DC, a natural extension of Aczel's system for constructive set theory CZF by a strengthening of the Regular Extension Axiom REA and the principle of dependent choice. In this paper we show that this characterization continues to hold over the standard system CZF plus REA, thus removing in particular any dependency from a choice principle. This will follow by a result of independent interest, namely the proof that the class of continuous mappings from a compact regular locale X to a regular a set-presented locale Y is a set in CZF, even without REA. It is then shown that the existence of Stone-Cech compactification of a non-degenerate Boolean locale is independent of the axioms of CZF (+REA), so that the obtained cha...
Shadows of the Planck Scale The Changing Face of Compactification Geometry
Dienes, Keith R; Dienes, Keith R.; Mafi, Arash
2002-01-01
By studying the effects of the shape moduli associated with toroidal compactifications, we demonstrate that Planck-sized extra dimensions can cast significant ``shadows'' over low-energy physics. These shadows can greatly distort our perceptions of the compactification geometry associated with large extra dimensions, and place a fundamental limit on our ability to probe the geometry of compactification simply by measuring Kaluza-Klein states. We also discuss the interpretation of compactification radii and hierarchies in the context of geometries with non-trivial shape moduli. One of the main results of this paper is that compactification geometry is effectively renormalized as a function of energy scale, with ``renormalization group equations'' describing the ``flow'' of geometric parameters such as compactification radii and shape angles as functions of energy.
Softly Broken Supersymmetric Gauge Theories through Compactifications
Takenaga, K
1998-01-01
Effects of boundary conditions of fields for compactified space directions on the supersymmetric gauge theories are discussed. For general and possible boundary conditions the supersymmetry is explicitly broken to yield universal soft supersymmetry breaking terms, and the gauge symmetry of the theory can also be broken through the dynamics of non-integrable phases, depending on number and the representation under the gauge group of matters. The 4-dimensional supersymmetric QCD is studied as a toy model when one of the space coordinates is compactified on $S^1$.
Foliated backgrounds for M-theory compactifications (I)
Babalic, Elena Mirela
2015-01-01
We summarize our geometric and topological description of compact eight-manifolds which arise as internal spaces in ${\\cal N}=1$ flux compactifications of M-theory down to $\\mathrm{AdS}_3$, under the assumption that the internal part of the supersymmetry generator is everywhere non-chiral. Specifying such a supersymmetric background is {\\em equivalent} with giving a certain codimension one foliation defined by a closed one-form and which carries a leafwise $G_2$ structure, a foliation whose topology and geometry we characterize rigorously.
The alpha'-Expansion of Calabi-Yau Compactifications
Becker, Katrin; Robbins, Daniel
2015-01-01
We consider alpha'-corrections to Calabi-Yau compactifications of type II string theory. These were discussed from the string worldsheet approach many years ago in terms of supersymmetric non-linear sigma-models by Nemeschansky and Sen as well as Gross and Witten. There it was shown that once alpha'-corrections are included, the internal manifold solving the string equations of motion is still Calabi-Yau though not Ricci flat. In this brief note we review these results and compare with a space-time effective field theory approach, in which we show that SU(3)-holonomy manifolds become SU(3)-structure manifolds once such corrections are included.
Soft Supersymmetry Breaking in Anisotropic LARGE Volume Compactifications
Angus, Stephen
2014-01-01
We study soft supersymmetry breaking terms for anisotropic LARGE volume compactifications, where the bulk volume is set by a fibration with one small four-cycle and one large two-cycle. We consider scenarios where D7s wrap either a blow-up cycle or the small fibre cycle. Chiral matter can arise either from modes parallel or perpendicular to the brane. We compute soft terms for this matter and find that for the case where the D7 brane wraps the fibre cycle the scalar masses can be parametrically different, allowing a possible splitting of third-generation soft terms.
Naturally light hidden photons in LARGE volume string compactifications
Goodsell, M. [LPTHE, Univ. Pierre et Marie Curie, Paris (France); Jaeckel, J. [Inst. for Particle Physics Phenomenology, Univ. Durham (United Kingdom); Redondo, J.; Ringwald, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2009-09-15
Extra ''hidden'' U(1) gauge factors are a generic feature of string theory that is of particular phenomenological interest. They can kinetically mix with the Standard Model photon and are thereby accessible to a wide variety of astrophysical and cosmological observations and laboratory experiments. In this paper we investigate the masses and the kinetic mixing of hidden U(1)s in LARGE volume compactifications of string theory. We find that in these scenarios the hidden photons can be naturally light and that their kinetic mixing with the ordinary electromagnetic photon can be of a size interesting for near future experiments and observations. (orig.)
Distribution of rational points of bounded height on equivariant compactifications of PGL 2 I
Takloo-Bighash, Ramin; Tanimoto, Sho
2016-01-01
We study the distribution of rational points of bounded height on a one-sided equivariant compactification of PGL2 using automorphic representation theory of PGL2.......We study the distribution of rational points of bounded height on a one-sided equivariant compactification of PGL2 using automorphic representation theory of PGL2....
Sesma, L Toledo; Loaiza, O
2015-01-01
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. This approach is applied to anisotropic cosmological Bianchi type I model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Under this approach, we present an isotropization mechanism for the Bianchi I cosmological model through the analysis of the ratio between the anisotropic parameters and the volume of the Universe which in general keeps constant or runs into zero for late times. Finally, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology.
Couplings between QCD axion and photon from string compactification
Jihn E. Kim
2016-08-01
Full Text Available The QCD axion couplings of various invisible axion models are presented. In particular, the exact global symmetry U(1PQ in the superpotential is possible for the anomalous U(1 from string compactification, broken only by the gauge anomalies at one loop level, and is shown to have the resultant invisible axion coupling to photon, caγγ≥83−caγγchbr where caγγchbr≃2. However, this bound is not applicable in approximate U(1PQ models with sufficiently suppressed U(1PQ-breaking superpotential terms. We also present a simple method to obtain caγγ0 which is the value obtained above the electroweak scale.
Foliated backgrounds for M-theory compactifications (I)
Babalic, Elena Mirela, E-mail: mbabalic@theory.nipne.ro [Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering Str. Reactorului no.30, P.O.BOX MG-6, Bucharest–Magurele 077125, Romania, Department of Physics, University of Craiova, 13 Al. I. Cuza Str., Craiova 200585 (Romania); Lazaroiu, Calin Iuliu [Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 790-784 (Korea, Republic of)
2015-12-07
Using the theory of foliations, we give a geometric and topological description of compact eight-manifolds which arise as internal spaces in N = 1 flux compactifications of M-theory down to AdS{sub 3}. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation defined by a closed one-form and which carries a leafwise G{sub 2} structure, whose geometry we characterize explicitly. It can be shown that the leaves of this foliation acquire singularities on the chiral locus, which is a set with empty interior when the equations of motion for the supregravity four-form field strength are imposed, but here we concentrate only on the case of an everywhere non-chiral spinor.
Massive IIA string theory and Matrix theory compactification
Lowe, David A. E-mail: lowe@het.brown.edu; Nastase, Horatiu; Ramgoolam, Sanjaye
2003-09-08
We propose a Matrix theory approach to Romans' massive Type IIA supergravity. It is obtained by applying the procedure of Matrix theory compactifications to Hull's proposal of the massive Type IIA string theory as M-theory on a twisted torus. The resulting Matrix theory is a super-Yang-Mills theory on large N three-branes with a space-dependent noncommutativity parameter, which is also independently derived by a T-duality approach. We give evidence showing that the energies of a class of physical excitations of the super-Yang-Mills theory show the correct symmetry expected from massive Type IIA string theory in a lightcone quantization.
A delicate universe: compactification obstacles to D-brane inflation.
Baumann, Daniel; Dymarsky, Anatoly; Klebanov, Igor R; McAllister, Liam; Steinhardt, Paul J
2007-10-01
We investigate whether explicit models of warped D-brane inflation are possible in string compactifications. To this end, we study the potential for D3-brane motion in a warped conifold that includes holomorphically embedded D7-branes involved in moduli stabilization. The presence of the D7-branes significantly modifies the inflaton potential. We construct an example based on a very simple and symmetric embedding due to Kuperstein, z1= const, in which it is possible to fine-tune the potential so that slow-roll inflation can occur. The resulting model is rather delicate: inflation occurs in the vicinity of an inflection point, and the cosmological predictions are extremely sensitive to the precise shape of the potential.
Lectures on Warped Compactifications and Stringy Brane Constructions
Kachru, Shamit
2001-07-26
In these lectures, two different aspects of brane world scenarios in 5d gravity or string theory are discussed. In the first two lectures, work on how warped compactifications of 5d gravity theories can change the guise of the hierarchy problem and the cosmological constant problem is reviewed, and a discussion of several issues which remain unclear in this context is provided. In the next two lectures, microscopic constructions in string theory which involve D-branes wrapped on cycles of Calabi-Yau manifolds are described. The focus is on computing the superpotential in the brane worldvolume field theory. Such calculations may be a necessary step towards understanding e.g. supersymmetry breaking and moduli stabilization in stringy realizations of such scenarios, and are of intrinsic interest as probes of the quantum geometry of the Calabi-Yau space.
Compactification of 5th dimension with usual and phantom scalar fields
Dzhunushaliev, V
2008-01-01
A new compactification mechanism of the 5th dimension in a gravitating system with two scalar fields (one of which is phantom) is proposed. It was shown that such a model has solutions oscillating over an extra coordinate and giving a finite radius of compactification of the 5th dimension. Also a possibility of using the model for a greater number of extra dimensions is pointed out.
Effect of compactification of twisted toroidal extra-dimension on sterile neutrino
Mohanty, Ajit Kumar
2016-01-01
We consider a toroidal extra-dimensional space with shape moduli $\\theta$ which is the angle between the two large extra dimensions $R_1$ and $R_2$ (twisted LED with $\\delta=2$). The Kaluza-Klein (KK) compactification results in a tower of KK bulk neutrinos which are sterile in nature and couple to the active neutrinos in the brane. The active-sterile mixing probability strongly depends on the angle $\\theta$ due to changing pattern of KK mass gaps which leads to level crossing. Considering only the first two lowest KK states in analogy with $(3+2)$ model, it is shown that $|U_{\\alpha 4}| > |U_{\\alpha 5}|$ when $\\theta = \\pi/2$ corresponding to the case of a normal torus. Since $\\Delta_{14}^2 < \\Delta_{15}^2$, this is expected in normal LED model as higher the sterile mass lower is the mixing probability. Contrary to this expectation, it is found that there exists a range in $\\theta$ where $|U_{\\alpha 5}| \\ge |U_{\\alpha 4}|$ even though $\\Delta m_{14}^2 < \\Delta m_{15}^2$ which has been demonstrated qant...
Three-family particle physics models from global F-theory compactifications
Cvetič, Mirjam [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104-6396 (United States); Klevers, Denis [Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland); Peña, Damián Kaloni Mayorga [The Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34151, Trieste (Italy); Oehlmann, Paul-Konstantin; Reuter, Jonas [Bethe Center for Theoretical Physics, Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany)
2015-08-17
We construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and the Trinification Model. These models result from compactification on toric hypersurface fibrations X with the choice of base ℙ{sup 3}. We observe that the F-theory conditions on the G{sub 4}-flux restrict the number of families to be at least three. We comment on the phenomenology of the models, and for Pati-Salam and Trinification models discuss the Higgsing to the Standard Model. A central point of this work is the construction of globally consistent G{sub 4}-flux. For this purpose we compute the vertical cohomology H{sub V}{sup (2,2)}(X) in each case and solve the conditions imposed by matching the M- and F-theoretical 3D Chern-Simons terms. We explicitly check that the expressions found for the G{sub 4}-flux allow for a cancellation of D3-brane tadpoles. We also use the integrality of 3D Chern-Simons terms to ensure that our G{sub 4}-flux solutions are adequately quantized.
Twisted compactifications of 3d N = 4 theories and conformal blocks
Gaiotto, Davide
2016-01-01
Three-dimensional N = 4 supersymmetric quantum field theories admit two topological twists, the Rozansky-Witten twist and its mirror. Either twist can be used to define a supersymmetric compactification on a Riemann surface and a corre- sponding space of supersymmetric ground states. These spaces of ground states can play an interesting role in the Geometric Langlands program. We propose a description of these spaces as conformal blocks for certain non-unitary Vertex Operator Algebras and test our conjecture in some important examples. The two VOAs can be constructed respectively from a UV Lagrangian description of the N = 4 theory or of its mirror. We further conjecture that the VOAs associated to an N = 4 SQFT inherit properties of the theory which only emerge in the IR, such as enhanced global symmetries. Thus knowledge of the VOAs should allow one to compute the spaces of supersymmetric ground states for a theory coupled to supersymmetric background connections for the full symmetry group of the IR SCFT. ...
Gravitational backreaction of anti-D branes in the warped compactification
Koyama, K; Koyama, Kayoko; Koyama, Kazuya
2005-01-01
We derive a low-energy effective theory for gravity with anti-D branes, which are essential to get de Sitter solutions in the type IIB string warped compactification, by taking account of gravitational backreactions of anti-D branes. In order to see the effects of the self-gravity of anti-D branes, a simplified model is studied where a 5-dimensional anti-de Sitter ({\\it AdS}) spacetime is realized by the bulk cosmological constant and the 5-form flux, and anti-D branes are coupled to the 5-form field by Chern-Simon terms. The {\\it AdS} spacetime is truncated by introducing UV and IR cut-off branes like the Randall-Sundrum model. We derive an effective theory for gravity on the UV brane and reproduce the familiar result that the tensions of the anti-D branes give potentials suppressed by the forth-power of the warp factor at the location of the anti-D branes. However, in this simplified model, the potential energy never inflates the UV brane, although the anti-D-branes are inflating. The UV brane is dominated ...
Three-Family Particle Physics Models from Global F-theory Compactifications
Cvetic, Mirjam; Peña, Damián Kaloni Mayorga; Oehlmann, Paul-Konstantin; Reuter, Jonas
2015-01-01
We construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and the Trinification Model. These models result from compactification on toric hypersurface fibrations $X$ with the choice of base $\\mathbb{P}^3$. We observe that the F-theory conditions on the $G_4$-flux restrict the number of families to be at least three. We comment on the phenomenology of the models, and for Pati-Salam and Trinification models discuss the Higgsing to the Standard Model. A central point of this work is the construction of globally consistent $G_4$-flux. For this purpose we compute the vertical cohomology $H_V^{(2,2)}(X)$ in each case and solve the conditions imposed by matching the M- and F-theoretical 3D Chern-Simons terms. We explicitly check that the expressions found for the $G_4$-flux allow for a cancelation of D3-brane tadpoles. We also use the integrality ...
Astrophysical and Cosmological Implications of Large Volume String Compactifications
Conlon, Joseph P
2007-01-01
We study the spectrum, couplings and cosmological and astrophysical implications of the moduli fields for the class of Calabi-Yau IIB string compactifications for which moduli stabilisation leads to an exponentially large volume V ~ 10^{15} l_s^6 and an intermediate string scale m_s ~ 10^{11}GeV, with TeV-scale observable supersymmetry breaking. All K\\"ahler moduli except for the overall volume are heavier than the susy breaking scale, with m ~ ln(M_P/m_{3/2}) m_{3/2} ~ (\\ln(M_P/m_{3/2}))^2 m_{susy} ~ 500 TeV and, contrary to standard expectations, have matter couplings suppressed only by the string scale rather than the Planck scale. These decay to matter early in the history of the universe, with a reheat temperature T ~ 10^7 GeV, and are free from the cosmological moduli problem (CMP). The heavy moduli have a branching ratio to gravitino pairs of 10^{-30} and do not suffer from the gravitino overproduction problem. The overall volume modulus is a distinctive feature of these models and is an M_{planck}-cou...
Type IIA flux compactifications. Vacua, effective theories and cosmological challenges
Koers, Simon
2009-07-30
In this thesis, we studied a number of type IIA SU(3)-structure compactifications with 06-planes on nilmanifolds and cosets, which are tractable enough to allow for an explicit derivation of the low energy effective theory. In particular we calculated the mass spectrum of the light scalar modes, using N = 1 supergravity techniques. For the torus and the Iwasawa solution, we have also performed an explicit Kaluza-Klein reduction, which led to the same result. For the nilmanifold examples we have found that there are always three unstabilized moduli corresponding to axions in the RR sector. On the other hand, in the coset models, except for SU(2) x SU(2), all moduli are stabilized. We discussed the Kaluza-Klein decoupling for the supersymmetric AdS vacua and found that it requires going to the Nearly-Calabi Yau limited. We searched for non-trivial de Sitter minima in the original flux potential away from the AdS vacuum. Finally, in chapter 7, we focused on a family of three coset spaces and constructed non-supersymmetric vacua on them. (orig.)
Foliated eight-manifolds for M-theory compactification
Babalic, Elena Mirela
2014-01-01
We characterize compact eight-manifolds M which arise as internal spaces in N=1 flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part of the supersymmetry generator is everywhere non-chiral. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation of M which carries a leafwise G2 structure, such that the O'Neill-Gray tensors, non-adapted part of the normal connection and torsion classes of the G2 structure are given in terms of the supergravity four-form field strength by explicit formulas which we derive. We discuss the topology of such foliations, showing that the C star algebra of the foliation is a noncommutative torus of dimension given by the irrationality rank of a certain cohomology class constructed from the four-form field strength, which must satisfy the Latour obstruction. We also give a criterion in terms of this class for when such foliations are fibrations over the circle. When t...
Correlation between Dark Matter and Dark Radiation in String Compactifications
Allahverdi, Rouzbeh; Dutta, Bhaskar; Sinha, Kuver
2014-01-01
Reheating in string compactifications is generically driven by the decay of the lightest modulus which produces Standard Model particles, dark matter and light hidden sector degrees of freedom that behave as dark radiation. This common origin allows us to find an interesting correlation between dark matter and dark radiation. By combining present upper bounds on the effective number of neutrino species N_eff with lower bounds on the reheating temperature as a function of the dark matter mass m_DM from Fermi data, we obtain strong constraints on the (N_eff,m_DM)-plane. Most of the allowed region in this plane corresponds to non-thermal scenarios with Higgsino-like dark matter. Thermal dark matter can be allowed only if N_eff tends to its Standard Model value. We show that the above situation is realised in models with perturbative moduli stabilisation where the production of dark radiation is unavoidable since bulk closed string axions remain light and do not get eaten up by anomalous U(1)s.
Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications
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.)
Compactification of Drinfeld modular varieties and Drinfeld Modular Forms of Arbitrary Rank
Pink, Richard
2010-01-01
We give an abstract characterization of the Satake compactification of a general Drinfeld modular variety. We prove that it exists and is unique up to unique isomorphism, though we do not give an explicit stratification by Drinfeld modular varieties of smaller rank which is also expected. We construct a natural ample invertible sheaf on it, such that the global sections of its $k$-th power form the space of (algebraic) Drinfeld modular forms of weight~$k$. We show how the Satake compactification and modular forms behave under all natural morphisms between Drinfeld modular varieties; in particular we define Hecke operators. We give explicit results in some special cases.
Astrophysical and cosmological implications of large volume string compactifications
Conlon, Joseph P.; Quevedo, Fernando
2007-08-01
We study the spectrum, couplings and cosmological and astrophysical implications of the moduli fields for the class of Calabi Yau IIB string compactifications for which moduli stabilisation leads to an exponentially large volume \\mathcal {V} \\sim 10^{15} l_{\\mathrm {s}}^6 and an intermediate string scale ms~1011 GeV, with TeV-scale observable supersymmetry breaking. All Kähler moduli except for the overall volume are heavier than the susy (supersymmetry) breaking scale, with m~ln(MP/m3/2)m3/2~(ln(MP/m3/2))2msusy~500 TeV and, contrary to standard expectations, have matter couplings suppressed only by the string scale rather than the Planck scale. These decay to matter early in the history of the universe, with a reheat temperature T~107 GeV, and are free from the cosmological moduli problem (CMP). The heavy moduli have a branching ratio to gravitino pairs of 10-30 and do not suffer from the gravitino overproduction problem. The overall volume modulus is a distinctive feature of these models and is an Mplanck-coupled scalar of mass m~1 MeV and subject to the CMP. A period of thermal inflation may help relax this problem. This field has a lifetime τ~1024 s and can contribute to dark matter. It may be detected through its decays to γγ or e+e-. If accessible the e+e- decay mode dominates, with \\mathrm {Br}(\\chi \\to \\gamma \\gamma) suppressed by a factor (ln(MP/m3/2))2. We consider the potential for detection of this field through different astrophysical sources: the Milky Way halo, the diffuse cosmic background and nearby galaxy clusters and find that the observed gamma ray background constrains \\Omega_{\\chi } \\lesssim 10^{-4} . The decays of this field may generate the 511 keV emission line from the galactic centre observed by INTEGRAL/SPI.
Fibre inflation: observable gravity waves from IIB string compactifications
Cicoli, M.; Quevedo, F. [DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Burgess, C.P., E-mail: M.Cicoli@damtp.cam.ac.uk, E-mail: cburgess@perimeterinstitute.ca, E-mail: F.Quevedo@damtp.cam.ac.uk [Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5 (Canada)
2009-03-15
We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential V = V{sub 0}(3-4e{sup -{phi}/(3){sup 1{sup /{sup 2}}}}). Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient V{sub 0}, and in particular do not enter into the slow-roll parameters. Consequently these are determined purely by the number of e -foldings, N{sub e}, and so are not independent: {epsilon} {approx_equal} 3/2{eta}{sup 2}. This implies similar relations among observables like the primordial scalar-to-tensor amplitude, r, and the scalar spectral tilt, n{sub s}: r {approx_equal} 6(n{sub s}-1){sup 2}. N{sub e} is itself more model-dependent since it depends partly on the post-inflationary reheat history. In a simple reheating scenario a reheating temperature of T{sub rh} {approx_equal} 10{sup 9} GeV gives N{sub e} {approx_equal} 58, corresponding to n{sub s} {approx_equal} 0.970 and r {approx_equal} 0.005, within reach of future observations. The model is an example of a class that arises naturally in the context of type IIB string compactifications with large-volume moduli stabilisation, and takes advantage of the generic existence there of Kaehler moduli whose dominant appearance in the scalar potential arises from string loop corrections to the Kaehler potential. The inflaton field is a combination of Kaehler moduli of a K3-fibered Calabi-Yau manifold. We believe there are likely to be a great number of models in this class-''high-fibre models''-in which the inflaton starts off far enough up the fibre to produce observably large primordial gravity waves.
Five Dimensional f(R) Braneworld Models
da Silva, J M Hoff
2011-01-01
After incorporating the f(R) gravity into the general braneworld sum rules scope, it is shown that some particular class of warped five dimensional nonlinear braneworld models, which may be interesting for the hierarchy problem solution, still require a negative tension brane. For other classes of warp factors (suitable and not suitable for approaching the hierarchy problem) it is not necessary any negative brane tension in the compactification scheme. In this vein, it is argued that in the bulk f(R) gravity context, some types of warp factors may be useful for approaching the hierarchy problem and for evading the necessity of a negative brane tension in the compactification scheme.
Non-commutative multi-dimensional cosmology
Khosravi, N; Sepangi, H R
2006-01-01
A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these problems find natural solutions in a universe described by an increasing time parameter.
Dimensional reduction for D3-brane moduli
Cownden, Brad; Frey, Andrew R.; Marsh, M. C. David; Underwood, Bret
2016-12-01
Warped string compactifications are central to many attempts to stabilize moduli and connect string theory with cosmology and particle phenomenology. We present a first-principles derivation of the low-energy 4D effective theory from dimensional reduction of a D3-brane in a warped Calabi-Yau compactification of type IIB string theory with imaginary self-dual 3-form flux, including effects of D3-brane motion beyond the probe approximation, and find the metric on the moduli space of brane positions, the universal volume modulus, and axions descending from the 4-form potential. As D3-branes may be considered as carrying either electric or magnetic charges for the self-dual 5-form field strength, we present calculations in both duality frames. Our results are consistent with, but extend significantly, earlier results on the low-energy effective theory arising from D3-branes in string compactifications.
Dimensional Reduction for D3-brane Moduli
Cownden, Brad; Marsh, M C David; Underwood, Bret
2016-01-01
Warped string compactifications are central to many attempts to stabilize moduli and connect string theory with cosmology and particle phenomenology. We present a first-principles derivation of the low-energy 4D effective theory from dimensional reduction of a D3-brane in a warped Calabi-Yau compactification of type IIB string theory with imaginary self-dual 3-form flux, including effects of D3-brane motion beyond the probe approximation, and find the metric on the moduli space of brane positions, the universal volume modulus, and axions descending from the 4-form potential. As D3-branes may be considered as carrying either electric or magnetic charges for the self-dual 5-form field strength, we present calculations in both duality frames. Our results are consistent with, but extend significantly, earlier results on the low-energy effective theory arising from D3-branes in string compactifications.
Exact two-dimensional superconformal R symmetry and c extremization.
Benini, Francesco; Bobev, Nikolay
2013-02-08
We uncover a general principle dubbed c extremization, which determines the exact R symmetry of a two-dimensional unitary superconformal field theory with N=(0,2) supersymmetry. To illustrate its utility, we study superconformal theories obtained by twisted compactifications of four-dimensional N=4 super-Yang-Mills theory on Riemann surfaces and construct their gravity duals.
Coset space dimensional reduction of Einstein-Yang-Mills theory
Chatzistavrakidis, A. [Institute of Nuclear Physics, NCSR Demokritos, 15310 Athens (Greece); Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Manousselis, P. [Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Department of Engineering Sciences, University of Patras, 26110 Patras (Greece); Prezas, N. [Theory Unit, Physics Department, 1211 Geneva (Switzerland); Zoupanos, G.
2008-04-15
In the present contribution we extend our previous work by considering the coset space dimensional reduction of higher-dimensional Einstein-Yang-Mills theories including scalar fluctuations as well as Kaluza-Klein excitations of the compactification metric and we describe the gravity-modified rules for the reduction of non-abelian gauge theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Parabolic Bundles on Algebraic Surfaces I -- The Donaldson-Uhlenbeck Compactification
V Balaji; A Dey; R Parthasarathi
2008-02-01
The aim of this paper is to construct the parabolic version of the Donaldson-Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algebraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non-emptiness of the moduli space of parabolic stable bundles of rank 2.
Kaehler potentials of chiral matter fields for Calabi-Yau string compactifications
Conlon, Joseph P.; Cremades, Daniel; Quevedo, Fernando [DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2007-01-15
The Kaehler potential is the least understood part of effective N = 1 supersymmetric theories derived from string compactifications. Even at tree-level, the Kaehler potential for the physical matter fields, as a function of the moduli fields, is unknown for generic Calabi-Yau compactifications and has only been computed for simple toroidal orientifolds. In this paper we describe how the modular dependence of matter metrics may be extracted in a perturbative expansion in the Kaehler moduli. Scaling arguments, locality and knowledge of the structure of the physical Yukawa couplings are sufficient to find the relevant Kaehler potential. Using these techniques we compute the 'modular weights' for bifundamental matter on wrapped D7 branes for large-volume IIB Calabi-Yau flux compactifications. We also apply our techniques to the case of toroidal compactifications, obtaining results consistent with those present in the literature. Our techniques do not provide the complex structure moduli dependence of the Kaehler potential, but are sufficient to extract relevant information about the canonically normalised matter fields and the soft supersymmetry breaking terms in gravity mediated scenarios.
The Principle of Equivalence as a Guide towards Matrix Theory Compactifications
Peñalba, J P
1998-01-01
The principle of equivalence is translated into the language of the world-volume field theories that define matrix and string theories. This idea leads to explore possible matrix descriptions of M-theory compactifications. An interesting case is the relationship between D=6 N=1 U(M) SYM and Matrix Theory on K3.
Twisted compactification of N=2 5D SCFTs to three and two dimensions from F(4) gauged supergravity
Karndumri, Parinya
2015-01-01
We study supersymmetric $AdS_4\\times \\Sigma_2$ and $AdS_3\\times \\Sigma_3$ solutions in half-maximal gauged supergravity in six dimensions with $SU(2)_R\\times SU(2)$ gauge group. The gauged supergravity is obtained by coupling three vector multiplets to the pure $F(4)$ gauged supergravity. The $SU(2)_R$ R-symmetry together with the $SO(3)\\sim SU(2)$ symmetry of the vector multiplets are gauged. The resulting gauged supergravity admits supersymmetric $AdS_6$ critical points with $SO(4)\\sim SU(2)\\times SU(2)$ and $SO(3)\\sim SU(2)_{\\textrm{diag}}$ symmetries. The former corresponds to five-dimensional $N=2$ superconformal field theories (SCFTs) with $E_1\\sim SU(2)$ symmetry. We find new classes of supersymmetric $AdS_4\\times \\Sigma_2$ and $AdS_3\\times \\Sigma_3$ solutions with $\\Sigma_{2,3}$ being $S^{2,3}$ and $H^{2,3}$. These solutions describe SCFTs in three and two dimensions obtained from twisted compactifications of the aforementioned five-dimensional SCFTs with different numbers of unbroken supersymmetry an...
Non-standard compactifications with mass gaps and Newton's law
Brandhuber, A
1999-01-01
The four-dimensional Minkowski space-time is considered as a three-brane embedded in five dimensions using solutions of five-dimensional supergravity. These backgrounds have a string theoretical interpretation in terms of D3-brane distributions. By studying linear fluctuations of the graviton we find a zero-mode representing the massless graviton in four-dimensional space-time. The novelty of our models is that the graviton spectrum has a genuine mass gap above the zero-mode or it is discrete. Hence, an effective four-dimensional theory on a brane that includes the massless graviton mode is well defined. The gravitational force between point particles deviates from the Newton law by Yukawa-type corrections, which we compute explicitly. We show that the parameters of our solutions can be chosen such that these corrections lie within experimental bounds.
Deconfinement in Yang-Mills Theory through Toroidal Compactification
Simic, Dusan; Unsal, Mithat; /Stanford U., Phys. Dept. /SLAC
2011-08-12
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory on R{sup 2} x S{sub L}{sup 1} x S{sub {beta}}{sup 1}. At large N, fixed-L, and arbitrary {beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.
${\\cal N}=2$ heterotic string compactifications on orbifolds of $K3\\times T^2$
Chattopadhyaya, Aradhita
2016-01-01
We study ${\\cal N}=2$ compactifications of $E_8\\times E_8$ heterotic string theory on orbifolds of $K3 \\times T^2$ by $g'$ which acts as an $\\mathbb{Z}_N$ automorphism of $K3$ together with a$1/N$ shift on a circle of $T^2$. The orbifold action $g'$ corresponds to the $26$ conjugacy classes of the Mathieu group $M_{24}$. We show that for the standard embedding the new supersymmetric index for these compactifications can always be decomposed into the elliptic genus of $K3$ twisted by $g'$. The difference in one-loop corrections to the gauge couplings are captured by automorphic forms obtained by the theta lifts of the elliptic genus of $K3$ twisted by $g'$. We work out in detail the case for which $g'$ belongs to the equivalence class $2B$. We then investigate all the non-standard embeddings for$K3$ realized as a $T^4/\\mathbb{Z}_\
A new class of de Sitter vacua in String Theory Compactifications
Achúcarro, Ana; Sousa, Kepa
2015-01-01
We revisit the stability of the complex structure moduli in the large volume regime of type-IIB flux compactifications. We argue that when the volume is not exponentially large, such as in K\\"ahler uplifted dS vacua, the quantum corrections to the tree-level mass spectrum can induce tachyonic instabilities in this sector. We discuss a Random Matrix Theory model for the classical spectrum of the complex structure fields, and derive a new stability bound involving the compactification volume and the (very large) number of moduli. We also present a new class of vacua for this sector where the mass spectrum presents a finite gap, without invoking large supersymmetric masses. At these vacua the complex structure sector is protected from tachyonic instabilities even at non-exponential volumes. A distinguishing feature is that all fermions in this sector are lighter than the gravitino.
Dressed elliptic genus of heterotic compactifications with torsion and general bundles
Israel, Dan
2016-01-01
We define and compute the dressed elliptic genus of N = 2 heterotic compactifications with torsion that are principal two-torus bundles over a K3 surface. We consider the most general gauge bundle compatible with supersymmetry, a stable holomorphic vector bundle over the base together with an Abelian bundle over the total space, generalizing the computation previously done by the authors in the absence of the latter. Starting from a (0,2) gauged linear sigma-model with torsion we use supersymmetric localization to obtain the result. We provide also a mathematical definition of the dressed elliptic genus as a modified Euler characteristic and prove that both expressions agree for hypersurfaces in weighted projective spaces. Finally we show that it admits a natural decomposition in terms of N = 4 superconformal characters, that may be useful to investigate moonshine phenomena for this wide class of N = 2 vacua, that includes K3*T2 compactifications as special cases.
Conformal anomaly and compactification of Kaluza--Klein models
Vasilevich, D.V.; Shtykov, N.N.
1988-10-01
An O (d)-invariant regularization of d-dimensional Kaluza--Klein models with scalar and fermion fields is proposed. The regularization preserves the power divergences and does not give inverse powers of the cutoff parameter in the conformal anomaly. The one-loop corrections to the trace of the energy--momentum tensor are calculated for internal spaces S/sup 2/, S/sup 4/, and S/sup 6/.
Jing Wen LUAN; Fu Liu ZHU
2005-01-01
In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.
Finite Temperature and Density Effects in Higher Dimensions with and without Compactifications
Shiraishi, Kiyoshi
2012-01-01
Expressions for the thermodynamic potential of a Dirac fermion gas are represented at finite temperature with the chemical potential in an ultrastatic space $R^d\\times S^N$. The high- and low- temperature expansions for the thermodynamic potential are obtained and, in particular, strongly degenerate fermi gas is investigated. For the Candelas-Weinberg model, sufficiently high "charge" density prevents the compactification of the extra space.
Cosmological constant problem in a scenario with compactifications (RS-I model)
Martinez-Robles, C
2016-01-01
In this letter, we apply the Randall-Sundrum (RS) model, a scenario based on compactifications, to control the UV divergence of the zero-point energy density equation for the vacuum fluctuations, which has been unsuccessfully addressed to the cosmological constant (CC) due to a heavy discrepancy between theory and observation. Historically, the problem of CC has been shelved in the RS point of view, having few or non literature on the subject. In this sense and as done with the hierarchy problem, we apply the RS model to solve this difference via extra dimensions; we also describe how brane effects could be the solution to this substantial difference. It should be noticed that this problem is studied assuming first Minkoswki type branes, and then followed by cosmologically more realistic FLRW type branes. We finally find some remarkably interesting consequences in the RS scenario: The CC problem can be solved via compactification of the extra dimension and the compactification radius turns out to be approxima...
Aspects of compactifications and black holes in four-dimensional supergravity
Looijestijn, H.T.
2010-01-01
In the 20th century, theoretical physics has seen the development of General Relativity and the Standard Model of elementary particles. These theories describe, with great precision, gravity and all known matter, respectively. However, it is not possible to unite them into one, single theory. We nee
Sharpening the weak gravity conjecture with dimensional reduction
Heidenreich, Ben; Reece, Matthew; Rudelius, Tom
2016-02-01
We investigate the behavior of the Weak Gravity Conjecture (WGC) under toroidal compactification and RG flows, finding evidence that WGC bounds for single photons become weaker in the infrared. By contrast, we find that a photon satisfying the WGC will not necessarily satisfy it after toroidal compactification when black holes charged under the Kaluza-Klein photons are considered. Doing so either requires an infinite number of states of different charges to satisfy the WGC in the original theory or a restriction on allowed compactification radii. These subtleties suggest that if the Weak Gravity Conjecture is true, we must seek a stronger form of the conjecture that is robust under compactification. We propose a "Lattice Weak Gravity Conjecture" that meets this requirement: a superextremal particle should exist for every charge in the charge lattice. The perturbative heterotic string satisfies this conjecture. We also use compactification to explore the extent to which the WGC applies to axions. We argue that gravitational instanton solutions in theories of axions coupled to dilaton-like fields are analogous to extremal black holes, motivating a WGC for axions. This is further supported by a match between the instanton action and that of wrapped black branes in a higher-dimensional UV completion.
Testing string vacua in the lab. From a hidden CMB to dark forces in flux compactifications
Cicoli, Michele; Goodsell, Mark; Ringwald, Andreas [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany). Theory Group; Jaeckel, Joerg [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenolgy
2011-03-15
We perform a detailed analysis of the phenomenological properties of hidden Abelian gauge bosons with a kinetic mixing with the ordinary photon within type IIB flux compactifications. We study the interplay between moduli stabilisation and the Green-Schwarz mechanism that gives mass to the hidden photon paying particular attention to the role of D-terms. We present two generic classes of explicit Calabi-Yau examples with an isotropic and an anisotropic shape of the extra dimensions showing how the last case turns out to be very promising to make contact with current experiments. In fact, anisotropic compactifications lead naturally to a GeV-scale hidden photon (''dark forces'' that can be searched for in beam dump experiments) for an intermediate string scale; or even to an meV-scale hidden photon (which could lead to a ''hidden CMB'' and can be tested by light-shining-through-a-wall experiments) in the case of TeV-scale strings. (orig.)
N =2 heterotic string compactifications on orbifolds of K3 × T 2
Chattopadhyaya, Aradhita; David, Justin R.
2017-01-01
We study N = 2 compactifications of E 8 × E 8 heterotic string theory on orbifolds of K3 × T 2 by g ' which acts as an {Z}_N automorphism of K3 together with a 1 /N shift on a circle of T 2. The orbifold action g ' corresponds to the 26 conjugacy classes of the Mathieu group M 24. We show that for the standard embedding the new supersymmetric index for these compactifications can always be decomposed into the elliptic genus of K3 twisted by g '. The difference in one-loop corrections to the gauge couplings are captured by automorphic forms obtained by the theta lifts of the elliptic genus of K3 twisted by g '. We work out in detail the case for which g ' belongs to the equivalence class 2 B. We then investigate all the non-standard embeddings for K3 realized as a {T}^4/{Z}_{ν } orbifold with ν = 2 ,4 and g ' the 2 A involution. We show that for non-standard embeddings the new supersymmetric index as well as the difference in one-loop corrections to the gauge couplings are completely characterized by the instanton numbers of the embeddings together with the difference in number of hypermultiplets and vector multiplets in the spectrum.
Cvetic, Mirjam; Piragua, Hernan
2013-01-01
We study F-theory compactifications with U(1)xU(1) gauge symmetry on elliptically fibered Calabi-Yau manifolds with a rank two Mordell-Weil group. We find that the natural presentation of an elliptic curve E with two rational points and a zero point is the generic Calabi-Yau onefold in dP_2. We determine the birational map to its Tate and Weierstrass form and the coordinates of the two rational points in Weierstrass form. We discuss its resolved elliptic fibrations over a general base B and classify them in the case of B=P^2. A thorough analysis of the generic codimension two singularities of these elliptic Calabi-Yau manifolds is presented. This determines the general U(1)xU(1)-charges of matter in corresponding F-theory compactifications. The matter multiplicities for the fibration over P^2 are determined explicitly and shown to be consistent with anomaly cancellation. Explicit toric examples are constructed, both with U(1)xU(1) and SU(5)xU(1)xU(1) gauge symmetry. As a by-product, we prove the birational eq...
The twelve dimensional super (2+2)-brane
Hewson, S F
1996-01-01
We discuss supersymmetry in twelve dimensions and present a covariant supersymmetric action for a brane with worldsheet signature (2,2), called a super (2+2)-brane, propagating in the osp(64,12) superspace. This superspace is explicitly constructed, and is trivial in the sense that the spinorial part is a trivial bundle over spacetime, unlike the twisted superspace of usual Poincare supersymmetry. For consistency, it is necessary to take a projection of the superspace. This is the same as the projection required for worldvolume supersymmetry. Upon compactification of this superspace, a torsion is naturally introduced and we produce the membrane and type IIB string actions in 11 and 10 dimensional Minkowski spacetimes. In addition, the compactification of the twelve dimensional supersymmetry algebra produces the correct algebras for these theories, including central charges. These considerations thus give the type IIB string and M-theory a single twelve dimensional origin.
BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications
Govindarajan, Suresh; Krishna, K Gopala
2011-01-01
We study the degeneracy of quarter BPS dyons in N =4 type II compactifications of string theory. We find that the genus-two Siegel modular forms generating the degeneracies of the quarter BPS dyons in the type II theories can be expressed in terms of the genus-two Siegel modular forms generating the degeneracies of quarter BPS dyons in the CHL theories and the heterotic string. This helps us in understanding the algebra structure underlying the degeneracy of the quarter BPS states. The Conway group, Co_1, plays a role similar to Mathieu group, M_{24}, in the CHL models with eta quotients appearing in the place of eta products. We construct BKM Lie superalgebra structures corresponding to Z_N (for N=2,3,4) orbifolds of the type II string compactified on a six-torus.
Towards unity of families: anti-SU(7) from Z 12- I orbifold compactification
Kim, Jihn E.
2015-06-01
The problem of families, "Why are there three families of fermions?", is a long awaited question to be answered within a reasonable framework. We propose anti-SU( N ) groups for the unification of families in grand unification (GUT) groups, where the separation of color and weak gauge groups in the GUT is achieved by antisymmetric tensor Brout-Englert-Higgs boson instead of an adjoint representation. Theories of anti-SU( N )'s are proposed for the unification of families. The minimal model is found as SU(7)anti2 GUT with the fermion representation . We present an example in a Z 12-I orbifold compactification, where the missing partner mechanism is also realized.
Compactifications of F-Theory on Calabi-Yau Threefolds at Constant Coupling
Ahn, C; Ahn, Changhyun; Nam, Soonkeon
1998-01-01
Generalizing the work of Sen, we analyze special points in the moduli space of the compactification of the F-theory on elliptically fibered Calabi-Yau threefolds where the coupling remains constant. These contain points where they can be realized as orbifolds of six torus $T^6$ by $Z_m \\times Z_n (m, n=2, 3, 4, 6)$. At various types of intersection points of singularities, we find that the enhancement of gauge symmetries arises from the intersection of two kinds of singularities. We also argue that when we take the Hirzebruch surface as a base for the Calabi-Yau threefold, the condition for constant coupling corresponds to the case where the point like instantons coalesce, giving rise to enhanced gauge group of $Sp(k)$.
Bainbridge, Matthew; Möller, Martin
of the field F satisfying a strong geometry of numbers type restriction. We apply this computation to give evidence for the conjecture that there are only finitely many algebraically primitive Teichmueller curves in M_3. In particular, we prove that there are only finitely many algebraically primitive......In the moduli space M_g of genus g Riemann surfaces, consider the locus RM_O of Riemann surfaces whose Jacobians have real multiplication by the order O in a totally real number field F of degree g. If g = 2 or 3, we compute the closure of RM_O in the Deligne-Mumford compactification of M...... Teichmueller curves generated by a one-form having two zeros of order 3 and 1. We also present the results of a computer search for algebraically primitive Teichmueller curves generated by a one-form having a single zero....
Compactification and inflation in the superstring theory from the condensation of gravitino pairs
Pollock, M. D.
1987-12-01
We discuss the possibility that inflation can occur in the E8×E8' heterotic superstring theory, if there is a pair condensation of the gravitino field ψA and also of the Majorana-Weyl spinor λ, as suggested by the Helayël-Neto and Smith. In the absence of a condensation of the anti-symmetric tensor field HMNP, then the associated potential V(θ,φ) is bounded from below and independent of the dilaton field φ. It can be made to vanish at the minimum, where the compactification scale θ is fixed. Alternatively, a small cosmological constant may remain (ultimately to be cancelled by radiative corrections at the lower energy scale of the gaugino condensation), which could in principle lead to inflation. Present address: Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Bombay 400 005, India.
Shah, Peter Jivan; Mouritsen, Ole G.
1990-01-01
with couplings leading to twofold-degenerate as well as fourfold-degenerate ordering. The models are quenched into a phase-separation region, which makes it possible for both types of ordering to observe the following scenario of ordering processes: (i) early-time nucleation and growth of ordered domains, (ii...... and compactification via coalescence. The domain-size distribution function, which is approximately log-normal, is shown to obey dynamical scaling over a substantial time range for both types of ordering. The growth for the pure systems is found to be described by a power law with the classical growth exponent n=1....... The results of the model study are relevant for the interpretation of experiments on ordering in impure systems and off-stochiometric alloys, grain growth in radiation-damaged materials, and may also shed light on aspects of sintering processes. The finding of a crossover from an algebraic growth law...
Soft SUSY breaking terms for chiral matter in IIB string compactifications
Conlon, Joseph P.; Abdussalam, Shehu S.; Quevedo, Fernando; Suruliz, Kerim [DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2007-01-15
This paper develops the computation of soft supersymmetry breaking terms for chiral D7 matter fields in IIB Calabi-Yau flux compactifications with stabilised moduli. We determine explicit expressions for soft terms for the single-modulus KKLT scenario and the multiple-moduli large volume scenario. In particular we use the chiral matter metrics for Calabi-Yau backgrounds recently computed in hep-th/0609180. These differ from the better understood metrics for non-chiral matter and therefore give a different structure of soft terms. The soft terms take a simple form depending explicitly on the modular weights of the corresponding matter fields. For the large-volume case we find that in the simplest D7 brane configuration, scalar masses, gaugino masses and A-terms are very similar to the dilaton-dominated scenario. Although all soft masses are suppressed by ln (M{sub P}/m{sub 3/2}) compared to the gravitino mass, the anomaly-mediated contributions do not compete, being doubly suppressed and thus subdominant to the gravity-mediated tree-level terms. Soft terms are flavour-universal to leading order in an expansion in inverse Kaehler moduli. They also do not introduce extra CP violating phases to the effective action. We argue that soft term flavour universality should be a property of the large-volume compactifications, and more generally IIB flux models, in which flavour is determined by the complex structure moduli while supersymmetry is broken by the Kaehler moduli. For the simplest large-volume case we run the soft terms to low energies and present some sample spectra and a basic phenomenological analysis.
Bianchi, M
1998-01-01
We show that various disconnected components of the moduli space of superstring vacua with 16 supercharges admit a rationale in terms of type I toroidal compactifications with constant non-vanishing but quantized vacuum expectation values of the NS-NS antisymmetric tensor. These include heterotic vacua with reduced rank, known as CHL strings, and their dual type II models below D=6. Type I vacua without open strings allow for an interpretation of the non-perturbative heterotic vacua related to type II models without D-branes and their U-duals. We also comment on the relation between some of these vacua and compactifications of the putative M-theory on unorientable manifolds as well as F-theory vacua.
$S^1/T^2$ Compactifications of 6d $\\mathcal{N}=(1,0)$ Theories and Brane Webs
Ohmori, Kantaro
2015-01-01
We consider the circle and torus compactification of a certain subclass of 6d $\\mathcal{N}=(1,0)$ SCFTs which are Higgsable to the higher rank E-string theories. Using the T-duality between Type I' and Type IIB, we found that the $S^1$ compactification of the theories can be realized by 5-brane webs describing the 5d uplifting of a specified class S theory, generalizing the result by Benini, Benvenuti and Tachikawa. We checked the above result by calculating conformal and flavor central charges of the 4d torus compactified theory both from the tensor branch structure of the 6d theory and from the predicted class S description.
Klemm, A D; Klemm, Albrecht; Theisen, Stefan
1993-01-01
We consider Calabi-Yau compactifications with one K\\"ahler modulus. Following the method of Candelas et al. we use the mirror hypothesis to solve the quantum theory exactly in dependence of this modulus by performing the calculation for the corresponding complex structure deformation on the mirror manifold. Here the information is accessible by techniques of classical geometry. It is encoded in the Picard-Fuchs differential equation which has to be supplemented by requirements on the global properties of its solutions.
Applications of the D-instanton calculus in type IIB orientifold compactifications
Moster, Sebastian
2010-06-22
In this thesis string compactifications are studied in the formalism of the large-volume type IIB string theory. This class of compactifications possesses an in various regards phenomenologically interesting effective low-energy field theory. Theme of this thesis is the further development of these models motivated by recent knowledges in the D-brane instanton calculus of the string theory. After a short, general introduction in the string theory and especially in type IIB orbifolds and their consistency conditions the large-volume models are extensively presented and the hitherto knowledges on their phenomenology - like scale hierarchies, gauge couplings, supersymmetry breaking, and cosmological questions - discussed. An essential part in the construction of the large-volume models is the stabilizing of moduli fields by means of nonperturbative contribution to the superpotential in the effective low-energy field theory, which are caused by D-brane instantons or gaugino condensates. With recent knowledges in the D-brane instanton calculus it is shown that the moduli stabilization with the hitherto applied mechanism is not compatible with the existence of chiral fermions, as they occur in the standard model of elementary particle physics. A modified mechanism is proposed, in which the moduli fields are stabilized by additions of D-terms. Then by so-called ''polyinstanton corrections'' for the gauge-kinetic function a new large-volume scenario is constructed, in which the string scale without fine tuning lies not in an as in these model usual intermediate range of about 10{sup 11} GeV, but at 10{sup 16} GeV. By this this construction becomes interesting also for grand unified theories with SU(5) or SO(10) gauge groups. This is demonstrated on explicit models. Finally supersymmetry breaking is treated in large-volume scenarios. By the new mechanism for the moduli stabilization it is suggested that the supersymmetry breaking is caused by a
Kaluza-Klein graviton phenomenology for warped compactifications, and the 750 GeV diphoton excess
Giddings, Steven B.; Zhang, Hao
2016-06-01
A generic prediction of scenarios with extra dimensions accessible in TeV-scale collisions is the existence of Kaluza-Klein excitations of the graviton. For a broad class of strongly warped scenarios one expects to initially find an isolated resonance, whose phenomenology in the simplest cases is described by a simplified model with two parameters, its mass, and a constant Λ with units of mass parametrizing its coupling to the Standard Model stress tensor. These parameters are in turn determined by the geometrical configuration of the warped compactification. We explore the possibility that the 750 GeV excess recently seen in 13 TeV data at ATLAS and CMS could be such a warped Kaluza-Klein graviton, and find a best-fit value Λ ≈60 TeV . We find that while there is some tension between this interpretation and data from 8 TeV and from the dilepton channel at 13 TeV, it is not strongly excluded. However, in the simplest scenarios of this kind, such a signal should soon become apparent in both diphoton and dilepton channels.
Kaluza-Klein graviton phenomenology for warped compactifications, and the 750 GeV diphoton excess
Giddings, Steven B
2016-01-01
A generic prediction of scenarios with extra dimensions accessible in TeV-scale collisions is the existence of Kaluza-Klein excitations of the graviton. For a broad class of strongly-warped scenarios one expects to initially find an isolated resonance, whose phenomenology in the simplest cases is described by a simplified model with two parameters, its mass, and a constant $\\Lambda$ with units of mass parameterizing its coupling to the Standard Model stress tensor. These parameters are in turn determined by the geometrical configuration of the warped compactification. We explore the possibility that the 750 GeV excess recently seen in 13 TeV data at ATLAS and CMS could be such a warped Kaluza-Klein graviton, and find a best-fit value $\\Lambda\\approx 60$ TeV. We find that while there is some tension between this interpretation and data from 8 TeV and from the dilepton channel at 13 TeV, it is not strongly excluded. However, in the simplest scenarios of this kind, such a signal should soon become apparent in bo...
Extra-dimensional models on the lattice
Knechtli, Francesco
2016-01-01
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergencies by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include non-perturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.
Implementing odd-axions in dimensional oxidation of non-geometric type IIB action
Shukla, Pramod
2016-01-01
In a setup of type IIB string compactification on an orientifold of a ${\\mathbb T}^6/{\\mathbb Z}_4$ sixfold, the presence of geometric flux ($\\omega$) and non-geometric fluxes ($Q, R$) is implemented along with the standard NS-NS and RR three-form fluxes ($H, F$). After computing the F/D-term contributions to the ${\\cal N}=1$ four dimensional effective scalar potential, we rearrange the same into `suitable' pieces by using a set of new generalized flux orbits. Subsequently, we dimensionally oxidize the various pieces of the total four dimensional scalar potential to guess their ten-dimensional origin.
Five-dimensional Nernst branes from special geometry
Dempster, P.; Errington, D.; Gutowski, J.; Mohaupt, T.
2016-11-01
We construct Nernst brane solutions, that is black branes with zero entropy density in the extremal limit, of FI-gauged minimal five-dimensional supergravity coupled to an arbitrary number of vector multiplets. While the scalars take specific constant values and dynamically determine the value of the cosmological constant in terms of the FI-parameters, the metric takes the form of a boosted AdS Schwarzschild black brane. This metric can be brought to the Carter-Novotný-Horský form that has previously been observed to occur in certain limits of boosted D3-branes. By dimensional reduction to four dimensions we recover the four-dimensional Nernst branes of arXiv:1501.07863 and show how the five-dimensional lift resolves all their UV singularities. The dynamics of the compactification circle, which expands both in the UV and in the IR, plays a crucial role. At asymptotic infinity, the curvature singularity of the four-dimensional metric and the run-away behaviour of the four-dimensional scalar combine in such a way that the lifted solution becomes asymptotic to AdS5. Moreover, the existence of a finite chemical potential in four dimensions is related to fact that the compactification circle has a finite minimal value. While it is not clear immediately how to embed our solutions into string theory, we argue that the same type of dictionary as proposed for boosted D3-branes should apply, although with a lower amount of supersymmetry.
Walter, M.G.A.
2004-02-01
We consider several examples of a special class of heterotic compactifications, i.e. heterotic E{sub 8} x E{sub 8} orbifolds with Wilson line backgrounds. By developing a local perspective we show that a brane world like picture emerges. As an important result we prove that the local massless spectrum at such a brane can always be traced back to the global spectrum of a (different) orbifold without Wilson lines. One particular implication of this result is that the use of (discrete) Wilson lines for the construction of phenomenologically interesting models has to be rethought. We show that stringy constraints render the brane spectra consistent. Using our local picture we are able to compute the local anomalies appearing at the different branes for our examples and show that they can all be cancelled by a local version of the Green-Schwarz mechanism at the same time. (orig.)
Kaluza--Klein Cosmology from five-dimensional Lovelock--Cartan Theory
Castillo-Felisola, Oscar; del Pino, Simón; Ramírez, Francisca
2016-01-01
We study the Kaluza-Klein dimensional reduction of the Lovelock-Cartan theory in five-dimensional spacetime, with a compact dimension of $S^1$ topology. We find cosmological solutions of the Friedmann-Robertson-Walker class in the reduced spacetime. The torsion and the fields arising from the dimensional reduction induce a nonvanishing energy-momentum tensor in four dimensions. We find solutions describing expanding, contracting and bouncing universes. The model shows a dynamical compactification of the extra dimension in some regions of the parameter space.
Sigma models for bundles on Calabi-Yau: a proposal for matrix string compactifications
Hofman, C.; Park, J.-S.
2001-01-01
W e describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite dimensional space of bundles on a Calabi-Y au 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped around the Calabi-Yau. We propose that this model can be us
Deconfinement in Yang-Mills theory through toroidal compactification with deformation
Simic, Dusan
2010-01-01
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double- trace deformation of toroidally compactified Yang-Mills theory on R2 \\times S1_L \\times S1_{\\beta}. At large N, fixed-L, and arbitrary {\\beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {\\beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic comp...
Non-supersymmetric flux compactifications of heterotic string- and M-theory
Held, Johannes Georg Joseph
2012-05-08
This dissertation is concerned with non-supersymmetric vacua of string theory in the supergravity (SUGRA) approach. This approach is the effective description of string theory at low energies. The concrete field of research that is treated here is heterotic E{sub 8} x E{sub 8} string theory at weak and at strong coupling, respectively. In the strong coupling limit the theory is described by eleven-dimensional SUGRA with two ten-dimensional boundaries (heterotic M-Theory). The transition to the weak coupling limit is governed by the restricted space dimension, whose length tends to zero for weak coupling such that the two boundaries get identified with each other. The resulting theory is ten-dimensional E{sub 8} x E{sub 8} SUGRA. In the context of this heterotic SUGRA, at first six of the former nine space-dimensions are compactified, and then, in the presence of non-vanishing background flux, conditions for unbroken supersymmetry (SUSY) in four space-time dimensions are analyzed. Afterwards, a violation of one of the necessary SUSY conditions is allowed. An essential ingredient, necessary for this to work, is the presence of flux. This kind of SUSY-breaking leads to severe constraints on the compact six-dimensional manifold, which can be satisfied by fiber bundles with two-dimensional fiber and four-dimensional base. In simple examples one can stabilize the expectation value of the dilaton as well as the volume of the fiber, whereas the volume of the base remains undetermined. Furthermore, the effect of a fermionic condensate is analyzed. The expected additional SUSY-breaking can be observed, and it is shown that the breaking induced by the flux can not be canceled by the contributions from the condensate. The end of this thesis is concerned with the discussion of the strong coupling limit of the previously found examples. To analyze this, it is necessary to rewrite the action of heterotic M-theory as a sum of quadratic terms, which vanish once SUSY is imposed
Topological phase transitions in Calabi-Yau compactifications of M-theory
Saueressig, F. [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, 07743 Jena (Germany)
2005-01-14
In this thesis we construct five-dimensional gauged supergravity actions which describe flop and conifold transitions in M-theory compactified on Calabi-Yau threefolds. While the vector multiplet sector is determined exactly, we use the Wolf spaces X(1+N) = (U(1+N,2))/(U(1+N)xU(2)) to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of M2-branes. After specifying the hypermultiplet sector the actions are uniquely determined by M-theory. As an application we consider five-dimensional Kasner cosmologies. Including the dynamics of the winding modes, we find smooth cosmological solutions which undergo flop and conifold transitions. Instead of the usual runaway behavior the scalar fields of these solutions generically stabilize in the transition region where they oscillate around the transition locus. The scalar potential thereby induces short episodes of accelerated expansion in the space-time. (Abstract Copyright [2005], Wiley Periodicals, Inc.)
Effective action of heterotic compactification on K3 with non-trivial gauge bundles
Schasny, Martin
2012-10-15
In this thesis we study the heterotic string compactified on K3 with non-trivial gauge bundles. We focus on two backgrounds, the well-known standard embedding and abelian line bundles. Using a Kaluza-Klein reduction, the six-dimensional effective action is computed up to terms of order {alpha}'{sup 2} with special attention on the hypermultiplet sector. We compute the moduli dependent couplings of the matter fields and analyze the geometry of the hyperscalar sigma model. Moreover, we prove the consistency with six-dimensional supergravity and derive the appropriate D-term scalar potential. For the line bundle backgrounds we show that the gauge flux stabilizes some geometrical moduli and renders some abelian vector multiplets massive.
A pure Dirac's analysis for a four dimensional BF-like theory with a compact dimension
Escalante, Alberto
2013-01-01
In the context of extra dimensions, we perform a detailed Dirac's canonical analysis for a topological four dimensional BF-like theory. By performing the compactification process a la Kaluza-Klein, we find out the relevant symmetries of the theory, namely, the full structure of the constraints and the extended action. We show that the extended Hamiltonian is a linear combination of first class constraints, which means that the general covariance of the theory is not affected by the compactification process. Furthermore, in order to carry out the correct counting of physical degrees of freedom, we show that must be taken into account the reducibility conditions among the first class constraints associated to the excited KK modes. Finally, we perform the Hamiltonian analysis of Maxwell theory written as a $BF$-like theory, we analyze the constraints of the theory and the results obtained are compared with those found in the literature.
Jacobi Forms of Higher Index and Paramodular Groups in N=2, D=4 Compactifications of String Theory
Nazaroglu, Caner
2013-01-01
We associate a Jacobi form over a rank s lattice to N=2, D=4 heterotic string compactifications which have s Wilson lines at a generic point in the vector multiplet moduli space. Jacobi forms of index m=1 and m=2 have appeared earlier in the context of threshold corrections to heterotic string couplings. We emphasize that higher index Jacobi forms as well as Jacobi forms of several variables over more generic even lattices also appear and construct models in which they arise. In particular, we construct an orbifold model which can be connected to models that give index m=3, 4 or 5 Jacobi forms through the Higgsing process. Constraints from being a Jacobi form are then employed to get threshold corrections using only partial information on the spectrum. We apply this procedure for index m=3, 4 or 5 Jacobi form examples and also for Jacobi forms over A_2 and A_3 root lattices. Examples with a single Wilson line are examined in detail and we display the relation of Siegel forms over a paramodular group \\Gamma_m ...
Heterotic compactifications with principal bundles for general groups and general levels
Distler, J
2007-01-01
We examine to what extent heterotic string worldsheets can describe arbitrary E8xE8 gauge fields. The traditional construction of heterotic strings builds each E8 via a Spin(16)/Z2 subgroup, typically realized as a current algebra by left-moving fermions, and as a result, only E8 gauge fields reducible to Spin(16)/Z2 gauge fields are directly realizable in standard constructions. However, there exist perturbatively consistent E8 gauge fields which can not be reduced to Spin(16)/Z2, and so cannot be described within standard heterotic worldsheet constructions. A natural question to then ask is whether there exists any (0,2) SCFT that can describe such E8 gauge fields. To answer this question, we first show how each ten-dimensional E8 partition function can be built up using other subgroups than Spin(16)/Z2, then construct ``fibered WZW models'' which allow us to explicitly couple current algebras for general groups and general levels to heterotic strings. This technology gives us a very general approach to han...
Misra, Aalok; Shukla, Pramod
2010-03-01
We consider type IIB large volume compactifications involving orientifolds of the Swiss Cheese Calabi-Yau WCP[1,1,1,6,9] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the “big” divisor ΣB (as opposed to the “small” divisor usually done in the literature thus far) as well as supporting D7-brane fluxes. After reviewing our proposal of [1] (Misra and Shukla, 2010) for resolving a long-standing tension between large volume cosmology and phenomenology pertaining to obtaining a 10 GeV gravitino in the inflationary era and a TeV gravitino in the present era, and summarizing our results of [1] (Misra and Shukla, 2010) on soft supersymmetry breaking terms and open-string moduli masses, we discuss the one-loop RG running of the squark and slepton masses in mSUGRA-like models (using the running of the gaugino masses) to the EW scale in the large volume limit. Phenomenological constraints and some of the calculated soft SUSY parameters identify the D7-brane Wilson line moduli as the first two generations/families of squarks and sleptons and the D3-brane (restricted to the big divisor) position moduli as the two Higgses for MSSM-like models at TeV scale. We also discuss how the obtained open-string/matter moduli make it easier to impose FCNC constraints, as well as RG flow of off-diagonal squark mass(-squared) matrix elements.
Higher-dimensional gauge theories from string theory
Tomasiello, Alessandro [Dipartimento di Fisica, Universita di Milano-Bicocca, Milano (Italy); INFN, Sezione di Milano-Bicocca, Milano (Italy)
2016-04-15
We review some recent developments regarding supersymmetric field theories in six and five dimensions. In particular, we will describe the classification of supersymmetric six-dimensional theories with a holographic IIA dual; they are ''linear quivers'' consisting of chains of many SU (or SO/Sp) gauge groups connected by hypermultiplets and tensor multiplets. We will also describe the wider classification of supersymmetric six-dimensional theories that can be engineered in F-theory; these are also chains, but they include exceptional gauge groups and copies of a more exotic ''E-string'' theory with a single tensor and E{sub 8} flavor symmetry. Finally we discuss some properties of these theories under compactification to lower dimensions. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Special properties of five-dimensional BPS rotating black holes
Herdeiro, C.A.R. E-mail: car26@damtp.cam.ac.uk
2000-08-28
Supersymmetric, rotating, asymptotically flat black holes with a regular horizon are rare configurations in string theory. One example is known in five spacetime dimensions, within the toroidal compactification of type IIB string theory. The existence of such special solution is allowed by the existence of a Chern-Simons coupling in the supergravity theory and by the possibility of imposing a self duality condition on the 'rotation 2-form'. We further exemplify the use of such duality condition by finding a new Brinkmann wave solution in D=6 simple gravity, possessing Killing spinors. We then explore three peculiar features of the aforementioned black holes: (1) Oxidising to D=10 the five-dimensional configuration may be interpreted as a system of D1-D5 branes with a Brinkmann wave propagating along their worldvolume. Unlike its five-dimensional Kaluza-Klein compactification, the universal covering space of this manifold has no causality violations. In other words, causal anomalies can be solved in higher dimensions. From the dual SCFT viewpoint, the causality bound for the compactified spacetime arises as the unitarity bound; (2) The vanishing of the scattering cross section for uncharged scalars and sufficiently high angular momentum of the background is shown still to hold at the level of charged interactions. The same is verified when a non-minimal coupling to the geometry is used. Therefore, the 'repulson' behaviour previously found is universal for non accelerated observers; (3) The solutions are shown to have a non-standard gyromagnetic ratio of g=3. In contrast, the superpartners of a static, BPS, five-dimensional black hole have g=1. At the semi-classical level, we find that a Dirac fermion propagating in the rotating hole background has g=2{+-}1, depending on the spinor direction of the fermion being parallel to Killing or 'anti-Killing' spinors.
Five-dimensional Nernst branes from special geometry
Dempster, P; Gutowski, J; Mohaupt, T
2016-01-01
We construct Nernst brane solutions, that is black branes with zero entropy density in the extremal limit, of FI-gauged minimal five-dimensional supergravity coupled to an arbitrary number of vector multiplets. While the scalars take specific constant values and dynamically determine the value of the cosmological constant in terms of the FI-parameters, the metric takes the form of a boosted AdS Schwarzschild black brane. This metric can be brought to the Carter-Novotny-Horsky form that has previously been observed to occur in certain limits of boosted D3-branes. By dimensional reduction to four dimensions we recover the four-dimensional Nernst branes of arXiv:1501.07863 and show how the five-dimensional lift resolves all their UV singularities. The dynamics of the compactification circle, which expands both in the UV and in the IR, plays a crucial role. At asymptotic infinity, the curvature singularity of the four-dimensional metric and the run-away behaviour of the four-dimensional scalar combine in such a w...
Six-dimensional origin of gravity mediated brane to brane supersymmetry breaking
Diamandis, G A; Kouroumalou, P; Lahanas, A B
2013-01-01
Four dimensional supergravities may be the right framework to describe particle physics at low energies. Its connection to the underlying string theory can be implemented through higher dimensional supergravities which bear special characteristics. Their reduction to four dimensions breaks supersymmetry whose magnitude depends both on the compactifying manifold and the mechanism that generates the breaking. In particular compactifications, notably on a $S_1/Z_2$ orbifold, the breaking of supersymmetry occuring on a hidden brane, residing at one end of $S_1/Z_2$, is communicated to the visible brane which lies at the other end, via gravitational interactions propagating in the bulk. This scenario has been exemplified in the framework of the $N=2$, $D=5$ supergravity. In this note, motivated by the recent developments in the field, related to the six-dimensional description of the supergravity theory, we study the $N=2$, $D=5$ supergravity theory as originating from a $D=6$ supergravity which, in addition to th...
Gauge invariance and radiative corrections in an extra dimensional model
Novales-Sánchez, H
2011-01-01
The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold $S^1/Z_2$, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the exci...
Gauge invariance and radiative corrections in an extra dimensional theory
Novales-Sánchez, H.; Toscano, J. J.
2011-04-01
The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S1 /Z2, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU4(N). A calculation of the one-loop contributions of the excited KK modes of the SUL(2) gauge group on the off-shell W+W-V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.
Mass spectrum in d = 11 supergravity with SU(3) x U(1)/U(1) x U(1) compactification
Lyakhovskii-breve, V.D.; Shtykov, N.N.
1987-07-01
The mass spectrum of excited states is calculated in the model of 11-dimensional supergravity over the AdS x SU(3) x U(1)/U(1) x U(1) vacuum configuration, where the internal space is characterized by five parameters. It is shown that for certain values of the parameters the massless sector of the model exhibits an appreciable number of excitations with various spins, which are not predicted by the supersymmetry of the vacuum state.
Rapport med bidrag fra symposiet Nye Dimensioner 24.-26. nov. 2011 samt nye selvstændige bidrag......Rapport med bidrag fra symposiet Nye Dimensioner 24.-26. nov. 2011 samt nye selvstændige bidrag...
A symplectic rearrangement of the four dimensional non-geometric scalar potential
Shukla, Pramod
2015-01-01
We present a symplectic rearrangement of the effective four-dimensional non-geometric scalar potential resulting from the type IIB superstring compactification on Calabi Yau orientifolds. The strategy has two main steps. In the first step, we rewrite the four dimensional scalar potential utilizing some interesting flux combinations which we call {\\it new generalized flux orbits}. After invoking a couple of non-trivial symplectic relations, in the second step, we further rearrange all the pieces of scalar potential into a completely `symplectic-formulation' which involves only the symplectic ingredients (such as period matrix etc.) without the need of knowing Calabi Yau metric. Moreover, the scalar potential under consideration is induced by a generic tree level K\\"{a}hler potential and (non-geometric) flux superpotential for arbitrary numbers of complex structure moduli, K\\"ahler moduli and odd-axions. Finally, we exemplify our symplectic formulation for the two well known toroidal examples based on type IIB ...
Warped Brane Worlds in Six Dimensional Supergravity
Aghababaie, Y; Cline, J M; Firouzjahi, H; Parameswaran, S L; Quevedo, Fernando; Tasinato, G; Zavala, I
2003-01-01
We present warped compactification solutions of six-dimensional supergravity, which are generalizations of the Randall-Sundrum warped brane world to codimension two and to a supersymmetric context. In these solutions the dilaton varies over the extra dimensions, and this makes the electroweak hierarchy only power-law sensitive to the proper radius of the extra dimensions (as opposed to being exponentially sensitive as in the RS model). Warping changes the phenomenology of these models because the Kaluza-Klein gap can be much larger than the internal space's inverse proper radius. We provide examples both for Romans' nonchiral supergravity and Salam-Sezgin chiral supergravity, and in both cases the solutions break all of the supersymmetries of the models. We interpret the solution as describing the fields sourced by a 3-brane and a boundary 4-brane (Romans' supergravity) or by one or two 3-branes (Salam-Sezgin supergravity), and we identify the topological constraints which are required by this interpretation....
张丽丽
2012-01-01
In this paper, our aim is to discuss the topological place of the space of fuzzy compacta in its Naturnal Hilbert cube compactification. By using the topological characterization of the pseudoboundary in the Hilbert cube, we show that the space of fuzzy compacta is a pseudointerior of its Hilbert cube compact if ication.%以讨论模糊紧空间在其一个自然的Hilbert方体紧化中的拓扑位置为目的,利用Hilbert方体中伪边界的拓扑刻画,得出模糊紧空间是其Hilbert方体紧化的伪内部.
Akal, Ibrahim; Müller, Carsten; Villalba-Chávez, Selym
2016-01-01
The production of particle-antiparticle pairs from the quantum field theoretic ground state in the presence of an external electric field is studied. Starting with the quantum kinetic Boltzmann-Vlasov equation in four-dimensional spacetime, we obtain the corresponding equations in lower dimensionalities by way of spatial compactification. Our outcomes in $2+1$-dimensions are applied to bandgap graphene layers, where the charge carriers have the particular property of behaving like light massive Dirac fermions. We calculate the single-particle distribution function for the case of an electric field oscillating in time and show that the creation of particle-hole pairs in this condensed matter system closely resembles electron-positron pair production by the Schwinger effect.
n-dimensional isotropic Finch-Skea stars
Chilambwe, Brian; Hansraj, Sudan
2015-02-01
We study the impact of dimension on the physical properties of the Finch-Skea astrophysical model. It is shown that a positive definite, monotonically decreasing pressure and density are evident. A decrease in stellar radius emerges as the order of the dimension increases. This is accompanied by a corresponding increase in energy density. The model continues to display the necessary qualitative features inherent in the 4-dimensional Finch-Skea star and the conformity to the Walecka theory is preserved under dimensional increase. The causality condition is always satisfied for all dimensions considered resulting in the proposed models demonstrating a subluminal sound speed throughout the interior of the distribution. Moreover, the pressure and density decrease monotonically outwards from the centre and a pressure-free hypersurface exists demarcating the boundary of the perfect-fluid sphere. Since the study of the physical conditions is performed graphically, it is necessary to specify certain constants in the model. Reasonable values for such constants are arrived at on examining the behaviour of the model at the centre and demanding the satisfaction of all elementary conditions for physical plausibility. Finally two constants of integration are settled on matching of our solutions with the appropriate Schwarzschild-Tangherlini exterior metrics. Furthermore, the solution admits a barotropic equation of state despite the higher dimension. The compactification parameter as well as the density variation parameter are also computed. The models satisfy the weak, strong and dominant energy conditions in the interior of the stellar configuration.
Carlsen, Bent Erik; Jensen, Bjarne Chr.; Olesen, Frits Bolonius;
Indholdet af nærværende rapport, er identisk med den indstilling, som pr. 1. september 1977 er afgivet til Dansk Ingeniør-forening, Normstyrelsen, af det i forsommeren 1976 nedsatte udvalg vedrørende brandteknisk dimensionering. Indstillingen, hvis primære formål har været at give Normstyrelsen et...... grundlag for at vurdere, om - og i givet fald hvordan - brandteknisk dimensionering af bærende konstruktioner vil kunne indføres i DIF's konstruktionsnormer, indeholder et skitseforslag til, efter hvilke principper dette vil kunne gøres. Men derudover har udvalget i fire dataoplæg (rapportens bilag 1...
Dimensional deconstruction and Wess-Zumino-Witten terms
Hill, Christopher T.; /Fermilab; Zachos, Cosmas K.; /Argonne
2004-11-01
A new technique is developed for the derivation of the Wess-Zumino-Witten terms of gauged chiral lagrangians. We start in D = 5 with a pure (mesonless) Yang-Mills theory, which includes relevant gauge field Chern-Simons terms. The theory is then compactified, and the effective D = 4 lagrangian is derived using lattice techniques, or ''deconstruction'', where pseudoscalar mesons arise from the lattice Wilson links. This yields the WZW term with the correct Witten coefficient by way of a simple heuristic argument. We discover a novel WZW term for singlet currents, that yields the full Goldstone-Wilczek current, and a U(1) axial current for the skyrmion, with the appropriate anomaly structures. A more detailed analysis is presented of the dimensional compactification of Yang-Mills in D = 5 into a gauged chiral lagrangian in D = 4, heeding the consistency of the D = 4 and D = 5 Bianchi identities. These dictate a novel covariant derivative structure in the D = 4 gauge theory, yielding a field strength modified by the addition of commutators of chiral currents. The Chern-Simons term of the pure D = 5 Yang-Mills theory then devolves into the correct form of the Wess-Zumino-Witten term with an index (the analogue of N{sub colors} = 3) of N = D = 5. The theory also has a Skyrme term with a fixed coefficient.
Non-constant volume exponential solutions in higher-dimensional Lovelock cosmologies
Chirkov, Dmitry; Toporensky, Alexey
2015-01-01
In this paper we propose a scheme which allows one to find all possible exponential solutions of special class -- non-constant volume solutions -- in Lovelock gravity in arbitrary number of dimensions and with arbitrate combinations of Lovelock terms. We apply this scheme to (6+1)- and (7+1)-dimensional flat anisotropic cosmologies in Einstein-Gauss-Bonnet and third-order Lovelock gravity to demonstrate how our scheme does work. In course of this demonstration we derive all possible solutions in (6+1) and (7+1) dimensions and compare solutions and their abundance between cases with different Lovelock terms present. As a special but more "physical" case we consider spaces which allow three-dimensional isotropic subspace for they could be viewed as examples of compactification schemes. Our results suggest that the same solution with three-dimensional isotropic subspace is more "probable" to occur in the model with most possible Lovelock terms taken into account, which could be used as kind of anthropic argument...
Green, Daniel; /SLAC /Stanford U., Phys. Dept.; Lawrence, Albion; /Brandeis U.; McGreevy, John; /MIT, LNS; Morrison, David R.; /Duke U., CGTP /UC, Santa Barbara; Silverstein,; /SLAC /Stanford U., Phys. Dept.
2007-05-18
We show that string theory on a compact negatively curved manifold, preserving a U(1)b1 winding symmetry, grows at least b1 new effective dimensions as the space shrinks. The winding currents yield a ''D-dual'' description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b{sub 1}-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.
Five dimensional cosmological traversable wormhole
Najafi, S.; Rostami, T., E-mail: t_rostami@sbu.ac.ir; Jalalzadeh, S., E-mail: s-jalalzadeh@sbu.ac.ir
2015-03-15
In this paper, a traversable wormhole in the Friedmann–Lemaître–Robertson–Walker (FLRW) model with one extra spacelike compact dimension is studied. We have chosen dynamical compactification as the evolution of the fifth dimension. In this respect, we study how the existence of the extra dimension affects the behavior of the energy density, the shape function and the scale factor. It is shown that the total matter can be non-exotic and the violation of the weak energy condition can be avoided.
Five dimensional cosmological traversable wormhole
Najafi, S; Jalalzadeh, S
2015-01-01
In this paper, a traversable wormhole in the Friedmann-Lema\\^{\\i}tre-Robertson-Walker (FLRW) model with one extra spacelike compact dimension is studied. We have chosen dynamical compactification as the evolution of the fifth dimension. In this respect, we study how the existence of the extra dimension, affect the behavior of the energy density, the shape function and the scale factor. It is shown that the total matter can be non-exotic and the violation of the weak energy condition can be avoided.
Two dimensional fermions in three dimensional YM
Narayanan, R
2010-01-01
Dirac fermions in the fundamental representation of $SU(N)$ live on the surface of a cylinder embedded in $R^3$ and interact with a three dimensional $SU(N)$ Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the circumference of the cylinder is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit at a typical bulk scale. Replacing three dimensional YM by four dimensional YM introduces non-trivial renormalization effects.
Zhou, Tianci; Faulkner, Thomas; Fradkin, Eduardo
2016-01-01
We investigate the entanglement entropy (EE) of circular entangling cuts in the 2+1-dimensional quantum Lifshitz model, whose ground state wave function is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose weight is the Gibbs weight of 2D Euclidean free boson. We show that the finite subleading corrections of EE to the area-law term as well as the mutual information are conformal invariants and calculate them for cylinder, disk-like and spherical manifolds with various spatial cuts. The subtlety due to the boson compactification in the replica trick is carefully addressed. We find that in the geometry of a punctured plane with many small holes, the constant piece of EE is proportional to the number of holes, indicating the ability of entanglement to detect topological information of the configuration. Finally, we compare the mutual information of two small distant disks with Cardy's relativistic CFT scaling proposal. We find that in the quantum Lifshitz model, the mutual information al...
Dimensional Enhancement via Supersymmetry
M. G. Faux
2011-01-01
of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.
Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx; Zarate, Moises, E-mail: mzarate@ifuap.buap.mx
2015-02-15
A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac’s analysis of the theory; we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza–Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev–Jackiw quantization for the theory under study, and we calculate the generalized Faddeev–Jackiw brackets, we show that both the Faddeev–Jackiw and Dirac’s brackets are the same. Finally we discuss some remarks and prospects. - Highlights: • Dirac’s method for 5D Stueckelberg theory with a compact dimension is performed. • By fixing the gauge in the effective theory we find present pseudo-Goldstone bosons. • Dirac’s brackets are constructed for the zero-modes and the kk-excitations. • The Faddeev–Jackiw quantization is performed. • The equivalence between generalized Faddeev–Jackiw and Dirac’s brackets is shown.
Two dimensional fermions in four dimensional YM
Narayanan, R
2009-01-01
Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in $R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the size of the torus in units of $\\frac{1}{\\Lambda_{SU(N)}}$ is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit.
Clustering high dimensional data
Assent, Ira
2012-01-01
High-dimensional data, i.e., data described by a large number of attributes, pose specific challenges to clustering. The so-called ‘curse of dimensionality’, coined originally to describe the general increase in complexity of various computational problems as dimensionality increases, is known...... to render traditional clustering algorithms ineffective. The curse of dimensionality, among other effects, means that with increasing number of dimensions, a loss of meaningful differentiation between similar and dissimilar objects is observed. As high-dimensional objects appear almost alike, new approaches...
Modular Constraints on Calabi-Yau Compactifications
Keller, Christoph A
2012-01-01
We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primary states whose total conformal weights are less than 0.656. Moreover, the number of such primary states grows at least linearly in the total Hodge number. We discuss implications of these results for Calabi-Yau geometry.
Calabi–Yau metrics and string compactification
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.
Special points of inflation in flux compactifications
Garcia-Etxebarria, Inaki; Grimm, Thomas W.; Valenzuela, Irene
2015-01-01
We study the realization of axion inflation models in the complex structure moduli spaces of Calabi-Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure p
Dynamical Symmetry Breaking in Warped Compactifications
Rius, N
2001-01-01
We study dynamical electroweak symmetry breaking in the Randall-Sundrum scenario. We show that one extra dimension is enough to give the correct pattern of electroweak symmetry breaking in a simple model with gauge bosons and the right-handed top quark in the bulk. The top quark mass is also in agreement with experiment. Furthermore, we propose an extended scenario with all Standard Model gauge bosons and fermions propagating in the bulk, which naturally accommodates the fermion mass hierarchies. No new fields or interactions beyond the observed in the Standard Model are required.
Compactification of nonlinear patterns and waves.
Rosenau, Philip; Kashdan, Eugene
2008-12-31
We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.
Wonderful Compactifications in Quantum Field Theory
Berghoff, Marko
2014-01-01
This article reviews the use of DeConcini-Procesi wonderful models in renormalization of ultraviolet divergences in position space as introduced by Bergbauer, Brunetti and Kreimer. In contrast to the exposition there we employ a slightly different approach; instead of the subspaces in the arrangement of divergent loci, we use the poset of divergent subgraphs as the main tool to describe the whole renormalization process. This is based on an article by Feichtner, where wonderful models were st...
Calabi-Yau metrics and string compactification
Douglas, Michael R
2015-01-01
Yau proved an existence theorem for Ricci-flat K\\"ahler metrics in the 1970's, 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.
Calabi-Yau metrics and string compactification
Douglas, Michael R.
2015-09-01
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.
Signatures of extra dimensional sterile neutrinos
Werner Rodejohann
2014-10-01
Full Text Available We study a large extra dimension model with active and sterile Dirac neutrinos. The sterile neutrino masses stem from compactification of an extra dimension with radius R and are chosen to have masses around eV or keV, in order to explain short-baseline anomalies or act as warm dark matter candidates. We study the effect of the sterile neutrino Kaluza–Klein tower in short-baseline oscillation experiments and in the beta spectrum as measurable by KATRIN-like experiments.
Signatures of extra dimensional sterile neutrinos
Rodejohann, Werner, E-mail: werner.rodejohann@mpi-hd.mpg.de; Zhang, He, E-mail: he.zhang@mpi-hd.mpg.de
2014-10-07
We study a large extra dimension model with active and sterile Dirac neutrinos. The sterile neutrino masses stem from compactification of an extra dimension with radius R and are chosen to have masses around eV or keV, in order to explain short-baseline anomalies or act as warm dark matter candidates. We study the effect of the sterile neutrino Kaluza–Klein tower in short-baseline oscillation experiments and in the beta spectrum as measurable by KATRIN-like experiments.
Three dimensional strained semiconductors
Voss, Lars; Conway, Adam; Nikolic, Rebecca J.; Leao, Cedric Rocha; Shao, Qinghui
2016-11-08
In one embodiment, an apparatus includes a three dimensional structure comprising a semiconductor material, and at least one thin film in contact with at least one exterior surface of the three dimensional structure for inducing a strain in the structure, the thin film being characterized as providing at least one of: an induced strain of at least 0.05%, and an induced strain in at least 5% of a volume of the three dimensional structure. In another embodiment, a method includes forming a three dimensional structure comprising a semiconductor material, and depositing at least one thin film on at least one surface of the three dimensional structure for inducing a strain in the structure, the thin film being characterized as providing at least one of: an induced strain of at least 0.05%, and an induced strain in at least 5% of a volume of the structure.
Dimensional Enhancement via Supersymmetry
Faux, M G; Landweber, G D
2009-01-01
We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describe "shadows" of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can "enhance" to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of "phantoms" which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.
Dimensional comparison theory.
Möller, Jens; Marsh, Herb W
2013-07-01
Although social comparison (Festinger, 1954) and temporal comparison (Albert, 1977) theories are well established, dimensional comparison is a largely neglected yet influential process in self-evaluation. Dimensional comparison entails a single individual comparing his or her ability in a (target) domain with his or her ability in a standard domain (e.g., "How good am I in math compared with English?"). This article reviews empirical findings from introspective, path-analytic, and experimental studies on dimensional comparisons, categorized into 3 groups according to whether they address the "why," "with what," or "with what effect" question. As the corresponding research shows, dimensional comparisons are made in everyday life situations. They impact on domain-specific self-evaluations of abilities in both domains: Dimensional comparisons reduce self-concept in the worse off domain and increase self-concept in the better off domain. The motivational basis for dimensional comparisons, their integration with recent social cognitive approaches, and the interdependence of dimensional, temporal, and social comparisons are discussed.
Dimensional regularization is generic
Fujikawa, Kazuo
2016-01-01
The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the dimensional regularization, we illustrate how to reproduce the results of the dimensional regularization for the $\\lambda\\phi^{4}$ theory in the more conventional regularization such as the higher derivative regularization; the basic postulate involved is that the quadratically divergent induced mass, which is independent of the scale change of the physical mass, is kinematical and unphysical. This is consistent with the derivation of the Callan-Symanzik equation, which is a comparison of two theories with slightly different masses, for the $\\lambda\\phi^{4}$ theory without encountering the quadratic divergence. We thus suggest that the dimensional regularization is generic in a bottom-up approach starting with a successful low-energy theory. We also define a modified version of t...
Experimental higher dimensional entanglement
Richart, Daniel L.; Wieczorek, Witlef; Weinfurter, Harald [MPI fuer Quantenoptik, Hans Kopfermannstr. 1, 85748 Garching (Germany); Ludwig-Maximilians-Universitaet, Schellingstr. 4, D-80797 Muenchen (Germany)
2009-07-01
Higher dimensional states (qudits) allow to implement quantum communication schemes of increasing complexity, as e.g. superdense coding. Similarly, qudits allow further research into the fundaments of quantum theory. Here we report on first steps towards the implementation of states with correlated photon pairs in a 2 x 8 dimensional Hilbert space. To this end the photon pairs are prepared in the energy-time basis, as initially proposed in: Using unbalanced interferometers, information can be encoded in the different arrival times of the photon pairs, early and late, as was experimentally realized in. Here, we extend this scheme by proposing and characterizing a scalable multiple time delay interferometer. This interferometer system allows an exponential increase in the dimensionality of the entangled state with only a linear increase in the optical components used. Using the proposed interferometer system, first experimental tests on a two-dimensional state yielded a violation of a Bell inequality by four standard deviations.
On the four-dimensional formulation of dimensionally regulated amplitudes
Fazio, A.R. [Universidad Nacional de Colombia, Departamento de Fisica, Bogota (Colombia); Mastrolia, P. [Universita di Padova, Dipartimento di Fisica e Astronomia, Padua (Italy); Max-Planck-Institut fuer Physik, Munich (Germany); INFN, Padova (Italy); Mirabella, E. [Max-Planck-Institut fuer Physik, Munich (Germany); Torres Bobadilla, W.J. [Universidad Nacional de Colombia, Departamento de Fisica, Bogota (Colombia); Universita di Padova, Dipartimento di Fisica e Astronomia, Padua (Italy); INFN, Padova (Italy)
2014-12-01
Elaborating on the four-dimensional helicity scheme, we propose a pure four-dimensional formulation (FDF) of the d-dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are represented by massive internal states regulating the divergences. The latter obey Feynman rules containing multiplicative selection rules which automatically account for the effects of the extra-dimensional regulating terms of the amplitude. We present explicit representations of the polarization and helicity states of the four-dimensional particles propagating in the loop. They allow for a complete, four-dimensional, unitarity-based construction of d-dimensional amplitudes. Generalized unitarity within the FDF does not require any higher-dimensional extension of the Clifford and the spinor algebra. Finally we show how the FDF allows for the recursive construction of d-dimensional one-loop integrands, generalizing the four-dimensional open-loop approach. (orig.)
Three-Dimensional Complex Variables
Martin, E. Dale
1988-01-01
Report presents new theory of analytic functions of three-dimensional complex variables. While three-dimensional system subject to more limitations and more difficult to use than the two-dimensional system, useful in analysis of three-dimensional fluid flows, electrostatic potentials, and other phenomena involving harmonic functions.
Bruce, Duncan W; O'Hare, Dermot
2010-01-01
With physical properties that often may not be described by the transposition of physical laws from 3D space across to 2D or even 1D space, low-dimensional solids exhibit a high degree of anisotropy in the spatial distribution of their chemical bonds. This means that they can demonstrate new phenomena such as charge-density waves and can display nanoparticulate (0D), fibrous (1D) and lamellar (2D) morphologies. Low-Dimensional Solids presents some of the most recent research into the synthesis and properties of these solids and covers: Metal Oxide Nanoparticles; Inorganic Nanotubes and Nanowir
Dimensional Metrology for Microtechnology
Bariani, Paolo
2005-01-01
of the (large) CMM positioning errors. A geometrical (three dimensional) model, for the Large range AFM was produced and calibration issues discussed following the three dimensional approach. Furthermore, a novel measuring procedure, based on two images, for eliminating the effects of vertical drift...... of one percent, with this instrument. Uncertainty is dominated by residual non linearity after off line correction. SEM based stereo-photogrammetry was also studied. A commercially available software package was purchased. The working hypothesis for the package in use was eucentric tilting. This is only...
Three-dimensional photovoltaics
Myers, Bryan; Bernardi, Marco; Grossman, Jeffrey C.
2010-03-01
The concept of three-dimensional (3D) photovoltaics is explored computationally using a genetic algorithm to optimize the energy production in a day for arbitrarily shaped 3D solar cells confined to a given area footprint and total volume. Our simulations demonstrate that the performance of 3D photovoltaic structures scales linearly with height, leading to volumetric energy conversion, and provides power fairly evenly throughout the day. Furthermore, we show that optimal 3D shapes are not simple box-like shapes, and that design attributes such as reflectivity can be optimized in new ways using three-dimensionality.
Dimensionality Reduction Mappings
Bunte, Kerstin; Biehl, Michael; Hammer, Barbara
2011-01-01
A wealth of powerful dimensionality reduction methods has been established which can be used for data visualization and preprocessing. These are accompanied by formal evaluation schemes, which allow a quantitative evaluation along general principles and which even lead to further visualization schem
Larsen, Mihail
De fire dimensioner er en humanistisk håndbog beregnet især på studerende og vejledere inden for humaniora, men kan også læses af andre med interesse for, hvad humanistisk forskning er og kan. Den er blevet til over et langt livs engageret forskning, uddannelse og formidling på Roskilde Universitet...... og udgør på den måde også et bidrag til universitetets historie, som jeg var med til at grundlægge. De fire dimensioner sætter mennesket i centrum. Men det er et centrum, der peger ud over sig selv; et centrum, hvorfra verden anskues, erfares og forstås. Alle mennesker har en forhistorie og en...... fremtid, og udstrakt mellem disse punkter i tiden tænker og handler de i rummet. Den menneskelige tilværelse omfatter alle fire dimensioner. De fire dimensioner udgør derfor også et forsvar for en almen dannelse, der gennemtrænger og kommer kulturelt til udtryk i vores historie, viden, praksis og kunst....
Larsen, Mihail
De fire dimensioner er en humanistisk håndbog beregnet især på studerende og vejledere inden for humaniora, men kan også læses af andre med interesse for, hvad humanistisk forskning er og kan. Den er blevet til over et langt livs engageret forskning, uddannelse og formidling på Roskilde Universitet...... og udgør på den måde også et bidrag til universitetets historie, som jeg var med til at grundlægge. De fire dimensioner sætter mennesket i centrum. Men det er et centrum, der peger ud over sig selv; et centrum, hvorfra verden anskues, erfares og forstås. Alle mennesker har en forhistorie og en...... fremtid, og udstrakt mellem disse punkter i tiden tænker og handler de i rummet. Den menneskelige tilværelse omfatter alle fire dimensioner. De fire dimensioner udgør derfor også et forsvar for en almen dannelse, der gennemtrænger og kommer kulturelt til udtryk i vores historie, viden, praksis og kunst....
Dimensional characteristics of low-dimensional structures
Blood, Peter
2000-07-01
The purpose of this paper is to examine the dimensional aspects of the optical properties of quantum well and dot systems, without assuming that the carriers are localized to the geometrical extent of the confining potential. We show that optical absorption normal to the plane of a well cannot be expressed as an absorption coefficient but should be specified as a fraction of light transmitted or absorbed per well. The modal gain for light propagating along the plane of a well does not scale with well width and the variation of the material gain inversely proportional to the well width is a consequence of the definition of the confinement factor and has no independent physical significance. Optical absorption by quantum dots should be expressed as a cross section per dot. The radiative recombination rate is correctly expressed in terms of a 2D recombination coefficient and use of an equivalent 3D coefficient introduces an artificial dependence on well width which can lead to errors in the comparison of quantum well systems.
Two-dimensional optical spectroscopy
Cho, Minhaeng
2009-01-01
Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.
Dimensionally regulated pentagon integrals
Bern, Z; Kosower, D A
1994-01-01
We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4-2 epsilon dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O(epsilon) corrections, a result which is the dimensionally-regulated version of a D=4 result of Melrose, and of van Neerven and Vermaseren. We obtain and solve differential equations for various dimensionally-regulated box integrals with massless internal lines, which appear in one-loop n-point calculations in QCD. We give a procedure for constructing the tensor pentagon integrals needed in gauge theory, again through O(epsilon^0).
Dimensional Metrology for Microtechnology
Bariani, Paolo
2005-01-01
This ph. D. project was aimed at developing and validating techniques for dimensional metrology of: miniaturized items, microsystem components, and surfaces. In particular the study was focused on techniques based on: AFM-CMM integration and Scanning Electron Microscopy (SEM). Development...... was proposed and the principle demonstrated on software gauges. Simulations of Surface Mapping were done, based on the model developed. Direct performance verification of the Large Range AFM was eventually carried out, and lateral metrology was possible, in the millimeter range, with accuracy in the order...... at high magnifications was, proposed and this has resulted into a patent application. The final part of the thesis is devoted to applications of dimensional metrology to case studies. Three applications are presented, two of them are investigations of surface metrology, while the third is about extraction...
Kerstein, A.R. [Sandia National Lab., Livermore, CA (United States)
1996-12-31
One-Dimensional Turbulence is a new turbulence modeling strategy involving an unsteady simulation implemented in one spatial dimension. In one dimension, fine scale viscous and molecular-diffusive processes can be resolved affordably in simulations at high turbulence intensity. The mechanistic distinction between advective and molecular processes is thereby preserved, in contrast to turbulence models presently employed. A stochastic process consisting of mapping {open_quote}events{close_quote} applied to a one-dimensional velocity profile represents turbulent advection. The local event rate for given eddy size is proportional to the velocity difference across the eddy. These properties cause an imposed shear to induce an eddy cascade analogous in many respects to the eddy cascade in turbulent flow. Many scaling and fluctuation properties of self-preserving flows, and of passive scalars introduced into these flows, are reproduced.
Dimensional analysis for engineers
Simon, Volker; Gomaa, Hassan
2017-01-01
This monograph provides the fundamentals of dimensional analysis and illustrates the method by numerous examples for a wide spectrum of applications in engineering. The book covers thoroughly the fundamental definitions and the Buckingham theorem, as well as the choice of the system of basic units. The authors also include a presentation of model theory and similarity solutions. The target audience primarily comprises researchers and practitioners but the book may also be suitable as a textbook at university level.
3 - Dimensional Body Measurement Technology
ZHOU Xu-dong; LI Yan-mei
2002-01-01
3 - dimensional body measurement technology, the basis of developing high technology in industry, accelerates digital development of aplparel industry. This paper briefly introduces the history of 3 - dimensional body measurement technology, and recounts the principle and primary structure of some types of 3 - dimensional automatic body measurement system. With this understanding, it discusses prospect of 3- dimensional CAD and virtual technology used in apparel industry.
Friederike Helm
2016-05-01
Full Text Available Dimensional comparison theory (DCT defines dimensional comparisons as intraindividual comparisons that a person draws between his or her own achievements in two domains or subjects. DCT assumes that dimensional comparisons influence students’ academic self-concepts, causing stronger self-concept differences between subjects perceived as dissimilar, such as math and English, than between subjects perceived as more similar, like math and physics. However, there have been no experimental studies testing the causal effect of perceived subject similarity on domain-specific self-concepts. In the present research, three experimental studies analyzed the effects of experimentally induced higher or lower perceived subject similarity on academic self-concept differences: Study 1 (N = 351, with math and German; Study 2a (N = 148, with math and physics; and Study 2b (N = 161, with English and German, show that, in line with expectations, induced lower perceived subject similarity led to stronger self-concept differences than did higher perceived similarity. Some implications of the results for DCT are discussed.
One-Dimensionality and Whiteness
Calderon, Dolores
2006-01-01
This article is a theoretical discussion that links Marcuse's concept of one-dimensional society and the Great Refusal with critical race theory in order to achieve a more robust interrogation of whiteness. The author argues that in the context of the United States, the one-dimensionality that Marcuse condemns in "One-Dimensional Man" is best…
One-Dimensionality and Whiteness
Calderon, Dolores
2006-01-01
This article is a theoretical discussion that links Marcuse's concept of one-dimensional society and the Great Refusal with critical race theory in order to achieve a more robust interrogation of whiteness. The author argues that in the context of the United States, the one-dimensionality that Marcuse condemns in "One-Dimensional Man" is best…
Zhou, Tianci; Chen, Xiao; Faulkner, Thomas; Fradkin, Eduardo
2016-09-01
We investigate the entanglement entropy (EE) of circular entangling cuts in the 2 + 1-dimensional quantum Lifshitz model. The ground state in this model is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose amplitude is the Gibbs weight of 2D Euclidean free boson. We show that the finite subleading corrections of EE to the area-law term, as well as the mutual information, are conformal invariants and calculate them for cylinder, disk-like and spherical manifolds with various spatial cuts. The subtlety due to the boson compactification in the replica trick is carefully addressed. We find that in the geometry of a punctured plane with many small holes, the constant piece of EE is proportional to the number of holes, indicating the ability of entanglement to detect topological information of the configuration. Finally, we compare the mutual information of two small distant disks with Cardy’s relativistic CFT scaling proposal. We find that in the quantum Lifshitz model, the mutual information also scales at long distance with a power determined by the lowest scaling dimension local operator in the theory.
Three-dimensional ultrasound scanning.
Fenster, Aaron; Parraga, Grace; Bax, Jeff
2011-08-06
The past two decades have witnessed developments of new imaging techniques that provide three-dimensional images about the interior of the human body in a manner never before available. Ultrasound (US) imaging is an important cost-effective technique used routinely in the management of a number of diseases. However, two-dimensional viewing of three-dimensional anatomy, using conventional two-dimensional US, limits our ability to quantify and visualize the anatomy and guide therapy, because multiple two-dimensional images must be integrated mentally. This practice is inefficient, and may lead to variability and incorrect diagnoses. Investigators and companies have addressed these limitations by developing three-dimensional US techniques. Thus, in this paper, we review the various techniques that are in current use in three-dimensional US imaging systems, with a particular emphasis placed on the geometric accuracy of the generation of three-dimensional images. The principles involved in three-dimensional US imaging are then illustrated with a diagnostic and an interventional application: (i) three-dimensional carotid US imaging for quantification and monitoring of carotid atherosclerosis and (ii) three-dimensional US-guided prostate biopsy.
Higher (odd dimensional quantum Hall effect and extended dimensional hierarchy
Kazuki Hasebe
2017-07-01
Full Text Available We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1 monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy
Hasebe, Kazuki
2017-07-01
We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Dimensional Equations of Entropy
Sparavigna, Amelia Carolina
2015-01-01
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the entropy of some physical systems.
Three-dimensional metamaterials
Burckel, David Bruce [Albuquerque, NM
2012-06-12
A fabrication method is capable of creating canonical metamaterial structures arrayed in a three-dimensional geometry. The method uses a membrane suspended over a cavity with predefined pattern as a directional evaporation mask. Metallic and/or dielectric material can be evaporated at high vacuum through the patterned membrane to deposit resonator structures on the interior walls of the cavity, thereby providing a unit cell of micron-scale dimension. The method can produce volumetric metamaterial structures comprising layers of such unit cells of resonator structures.
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
Juday, Richard D. (Inventor)
1992-01-01
A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.
Javidi, Bahram; Andres, Pedro
2014-01-01
Provides a broad overview of advanced multidimensional imaging systems with contributions from leading researchers in the field Multi-dimensional Imaging takes the reader from the introductory concepts through to the latest applications of these techniques. Split into 3 parts covering 3D image capture, processing, visualization and display, using 1) a Multi-View Approach and 2.) a Holographic Approach, followed by a 3rd part addressing other 3D systems approaches, applications and signal processing for advanced 3D imaging. This book describes recent developments, as well as the prospects and
Dimensional analysis made simple
Lira, Ignacio
2013-11-01
An inductive strategy is proposed for teaching dimensional analysis to second- or third-year students of physics, chemistry, or engineering. In this strategy, Buckingham's theorem is seen as a consequence and not as the starting point. In order to concentrate on the basics, the mathematics is kept as elementary as possible. Simple examples are suggested for classroom demonstrations of the power of the technique and others are put forward for homework or experimentation, but instructors are encouraged to produce examples of their own.
Three dimensional system integration
Papanikolaou, Antonis; Radojcic, Riko
2010-01-01
Three-dimensional (3D) integrated circuit (IC) stacking is the next big step in electronic system integration. It enables packing more functionality, as well as integration of heterogeneous materials, devices, and signals, in the same space (volume). This results in consumer electronics (e.g., mobile, handheld devices) which can run more powerful applications, such as full-length movies and 3D games, with longer battery life. This technology is so promising that it is expected to be a mainstream technology a few years from now, less than 10-15 years from its original conception. To achieve thi
QCD and dimensional deconstruction
Son, D T
2003-01-01
Motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge/gravity duality, we consider the model of an "open moose". Such a model has a large number K of hidden gauge groups as well as a global chiral symmetry. In the continuum limit K->infinity the model becomes a 4+1 dimensional theory of a gauge field propagating in a dilaton background and an external space-time metric with two boundaries. We show that the model reproduces several well known phenomenological and theoretical aspects of low-energy hadron dynamics. We derive the general formulas for the mass spectrum, the decay constants of the pion and vector mesons, and the couplings between mesons. We then consider two simple realizations, one with a flat metric and another with a "cosh" metric interpolating between two AdS boundaries. For the pion form-factor, the single pole rho-meson dominance is exact in the latter case and approximate in the former case. We discover that an AdS/CFT-like pres...
A Note on Fluxes in Six-Dimensional String Theory Backgrounds
Becker, K; Becker, Katrin; Tseng, Li-Sheng
2004-01-01
We study the structure of warped compactifications of type IIB string theory to six space-time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kahler manifold, in contrast with the heterotic case where the four-manifold must be conformally Calabi-Yau.
Some exact results in four-dimensional non-perturbative string theory
Robles-Llana, D.; Rocek, M.; Saueressig, Frank; Theis, U.; Vandoren, S.
2007-01-01
We find the D(−1) and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi–Yau threefolds. These combine with known perturbative and worldsheet instanton corrections into a single modular invariant function that determines the hypermultip
ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES
Nikola Stefanović
2007-06-01
Full Text Available In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic leadership style, leadership theory researchers use two dimensional matrices. The two-dimensional matrices define leadership styles on the basis of different parameters. By using these parameters, one can identify two-dimensional styles.
Dimensional crossover in semiconductor nanostructures
McDonald, Matthew P.; Chatterjee, Rusha; Si, Jixin; Jankó, Boldizsár; Kuno, Masaru
2016-08-01
Recent advances in semiconductor nanostructure syntheses provide unprecedented control over electronic quantum confinement and have led to extensive investigations of their size- and shape-dependent optical/electrical properties. Notably, spectroscopic measurements show that optical bandgaps of one-dimensional CdSe nanowires are substantially (approximately 100 meV) lower than their zero-dimensional counterparts for equivalent diameters spanning 5-10 nm. But what, exactly, dictates the dimensional crossover of a semiconductor's electronic structure? Here we probe the one-dimensional to zero-dimensional transition of CdSe using single nanowire/nanorod absorption spectroscopy. We find that carrier electrostatic interactions play a fundamental role in establishing dimensional crossover. Moreover, the critical length at which this transition occurs is governed by the aspect ratio-dependent interplay between carrier confinement and dielectric contrast/confinement energies.
One Dimensional Ballistic Electron Transport
Thomas K J
2009-10-01
Full Text Available Research in low-dimensional semiconductor systems over the last three decades has been largely responsible for the current progress in the areas of nanoscience and nanotechnology. The ability to control and manipulate the size, the carrier density, and the carrier type in two-, one-, and zero- dimensional structures has been widely exploited to study various quantum transport phenomena. In this article, a brief introduction is given to ballistic electron transport in one-dimensional quantum wires.
Dimensional Reduction for Conformal Blocks
Hogervorst, Matthijs
2016-01-01
We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d-1 dimensions. In particular, we obtain a formula for 3d conformal blocks as an infinite sum over 2F1 hypergeometric functions with closed-form coefficients.
Erbach, G
1994-01-01
In this paper, we present an alternative approach to multiple inheritance for typed feature structures. In our approach, a feature structure can be associated with several types coming from different hierarchies (dimensions). In case of multiple inheritance a type has supertypes from different hierarchies. We contrast this approach with approaches based on a single type hierarchy where a feature structure has only one unique most general type, and multiple inheritance involves computation of greatest lower bounds in the hierarchy. The proposed approach supports current linguistic analyses in constraint-based formalisms like HPSG, inheritance in the lexicon, and knowledge representation for NLP systems. Finally, we show that multi-dimensional inheritance hierarchies can be compiled into a Prolog term representation, which allows to compute the conjunction of two types efficiently by Prolog term unification.
Higher dimensional nonlinear massive gravity
Do, Tuan Q
2016-01-01
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constant-like behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini-(A)dS metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity will be figured out consistently.
Two-Dimensional Chirality in Three-Dimensional Chemistry.
Wintner, Claude E.
1983-01-01
The concept of two-dimensional chirality is used to enhance students' understanding of three-dimensional stereochemistry. This chirality is used as a key to teaching/understanding such concepts as enaniotropism, diastereotopism, pseudoasymmetry, retention/inversion of configuration, and stereochemical results of addition to double bonds. (JN)
Analysis of one dimensional and two dimensional fuzzy controllers
Ban Xiaojun; Gao Xiaozhi; Huang Xianlin; Wu Tianbao
2006-01-01
The analytical structures and the corresponding mathematical properties of the one dimensional and two dimensional fuzzy controllers are first investigated in detail.The nature of these two kinds of fuzzy controllers is next probed from the perspective of control engineering. For the one dimensional fuzzy controller, it is concluded that this controller is a combination of a saturation element and a nonlinear proportional controller, and the system that employs the one dimensional fuzzy controller is the combination of an open-loop control system and a closedloop control system. For the latter case, it is concluded that it is a hybrid controller, which comprises the saturation part, zero-output part, nonlinear derivative part, nonlinear proportional part, as well as nonlinear proportional-derivative part, and the two dimensional fuzzy controller-based control system is a loop-varying system with varying number of control loops.
Low-dimensional molecular metals
Toyota, Naoki; Muller, Jens
2007-01-01
Assimilating research in the field of low-dimensional metals, this monograph provides an overview of the status of research on quasi-one- and two-dimensional molecular metals, describing normal-state properties, magnetic field effects, superconductivity, and the phenomena of interacting p and d electrons.
Constructing higher dimensional local fields
Morrow, Matthew
2012-01-01
This note is a gentle introduction to higher dimensional local fields, with the motivating problem being the standard geometric "localisation-completion" process by which they can be constructed. A direct proof of the behaviour of this construction, which is the simplest part of the theory of higher dimensional adeles, will hopefully be useful to both specialists and newcomers.
Three dimensional Dirac semimetals
Zaheer, Saad
We extend the physics of graphene to three dimensional systems by showing that Dirac points can exist on the Fermi surface of realistic materials in three dimensions. Many of the exotic electronic properties of graphene can be ascribed to the pseudorelativistic behavior of its charge carriers due to two dimensional Dirac points on the Fermi surface. We show that certain nonsymmorphic spacegroups exhibit Dirac points among the irreducible representations of the appropriate little group at high symmetry points on the surface of the Brillouin zone. We provide a list of all Brillouin zone momenta in the 230 spacegroups that can host Dirac points. We describe microscopic considerations necessary to design materials in one of the candidate spacegroups such that the Dirac point appears at the Fermi energy without any additional non-Dirac-like Fermi pockets. We use density functional theory based methods to propose six new Dirac semimetals: BiO 2 and SbO2 in the beta-cristobalite lattice (spacegroup 227), and BiCaSiO4, BiMgSiO4, BiAlInO 4, and BiZnSiO4 in the distorted spinels lattice (spacegroup 74). Additionally we derive effective Dirac Hamiltonians given group representative operators as well as tight binding models incorporating spin-orbit coupling. Finally we study the Fermi surface of zincblende (spacegroup 216) HgTe which is effectively point-like at Gamma in the Brillouin zone and exhibits accidental degeneracies along a threefold rotation axis. Whereas compressive strain gaps the band structure into a topological insulator, tensile strain shifts the accidental degeneracies away from Gamma and enlarges the Fermi surface. States on the Fermi surface exhibit nontrivial spin texture marked by winding of spins around the threefold rotation axis and by spin vortices indicating a change in the winding number. This is confirmed by microscopic calculations performed in tensile strained HgTe and Hg0.5Zn 0.5 Te as well as k.p theory. We conclude with a summary of recent
Higher dimensional loop quantum cosmology
Zhang, Xiangdong
2016-07-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology.
Drissi, L B; Bousmina, M
2011-01-01
Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD given in ref.[5] by using the hidden SU(5) symmetry of the 4D hyperdiamond lattice H_4. We first study the link between the H_4 and SU(5); then we refine the BBTW 4D lattice action by using the weight vectors \\lambda_1, \\lambda_2, \\lambda_3, \\lambda_4, \\lambda_5 of the 5-dimensional representation of SU(5) satisfying {\\Sigma}_i\\lambda_i=0. After that we study explicitly the solutions of the zeros of the Dirac operator D in terms of the SU(5) simple roots \\alpha_1, \\alpha_2, \\alpha_3, \\alpha_4 generating H_4; and its fundamental weights \\omega_1, \\omega_2, \\omega_3, \\omega_4 which generate the reciprocal lattice H_4^\\ast. It is shown, amongst others, that these zeros live at the sites of H_4^\\ast; and the continuous limit D is given by ((id\\surd5)/2) \\gamma^\\muk_\\mu with d, \\gamma^\\mu and k_\\mu standing respectively for the lattice parameter of H_4, the usual 4 Dirac matrices and the 4D wave vector. Other features such as differences ...
Drissi, L. B.; Saidi, E. H.; Bousmina, M.
2011-07-01
Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD given in [P. F. Bedaque , Phys. Rev. DPRVDAQ1550-7998 78, 017502 (2008)10.1103/PhysRevD.78.017502] by using the hidden SU(5) symmetry of the 4D hyperdiamond lattice H4. We first study the link between the H4 and SU(5); then we refine the BBTW 4D lattice action by using the weight vectors λ1, λ2, λ3, λ4, and λ5 of the five-dimensional representation of SU(5) satisfying ∑iλi=0. After that, we study explicitly the solutions of the zeros of the Dirac operator D in terms of the SU(5) simple roots α1, α2, α3, and α4 generating H4; and its fundamental weights ω1, ω2, ω3 ω4 which generate the reciprocal lattice H4*. It is shown, among others, that these zeros live at the sites of H4*; and the continuous limit D is given by (id5)/(2) γμkμ with d, γμ, and kμ standing, respectively, for the lattice parameter of H4, the usual 4 Dirac matrices and the 4D wave vector. Other features, such as differences with BBTW model as well as the link between the Dirac operator following from our construction and the one suggested by Creutz using quaternions, are also given.
Three-dimensional echocardiography
Buck, Thomas [University Hospital Essen (Germany). West German Heart Center; Franke, Andreas [Klinikum Region Hannover - Klinikum Siloah, Hannover (Germany). Dept. of Cardiology, Angiology and Intensive Care Medicine; Monaghan, Mark J. (eds.) [King' s College Hospital, London (United Kingdom)
2011-07-01
Presents tips and tricks for beginners and experts Provides educational material for 3D training courses Features comprehensively illustrated cases Includes an accompanying DVD with video clips of all sample cases Three-dimensional echocardiography is the most recent fundamental advancement in echocardiography. Since real-time 3D echocardiography became commercially available in 2002, it has rapidly been accepted in echo labs worldwide. This book covers all clinically relevant aspects of this fascinating new technology, including a comprehensive explanation of its basic principles, practical aspects of clinical application, and detailed descriptions of specific uses in the broad spectrum of clinically important heart disease. The book was written by a group of well-recognized international experts in the field, who have not only been involved in the scientific and clinical evolution of 3D echocardiography since its inception but are also intensively involved in expert training courses. As a result, the clear focus of this book is on the practical application of 3D echocardiography in daily clinical routine with tips and tricks for both beginners and experts, accompanied by more than 150 case examples comprehensively illustrated in more than 800 images and more than 500 videos provided on a DVD. In addition to an in-depth review of the most recent literature on real-time 3D echocardiography, this book represents an invaluable reference work for beginners and expert users of 3D echocardiography. - Tips and tricks for beginners and experts - Educational material for 3D training courses - Comprehensively illustrated cases - DVD with video clips of all sample cases.
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Relations between two-dimensional models from dimensional reduction
Amaral, R.L.P.G.; Natividade, C.P. [Universidade Federal Fluminense, Niteroi, RJ (Brazil). Inst. de Fisica
1998-12-31
In this work we explore the consequences of dimensional reduction of the 3D Maxwell-Chern-Simons and some related models. A connection between topological mass generation in 3D and mass generation according to the Schwinger mechanism in 2D is obtained. Besides, a series of relationships are established by resorting to dimensional reduction and duality interpolating transformations. Nonabelian generalizations are also pointed out. (author) 10 refs.
Understanding high-dimensional spaces
Skillicorn, David B
2012-01-01
High-dimensional spaces arise as a way of modelling datasets with many attributes. Such a dataset can be directly represented in a space spanned by its attributes, with each record represented as a point in the space with its position depending on its attribute values. Such spaces are not easy to work with because of their high dimensionality: our intuition about space is not reliable, and measures such as distance do not provide as clear information as we might expect. There are three main areas where complex high dimensionality and large datasets arise naturally: data collected by online ret
Fermion masses from dimensional reduction
Kapetanakis, D. (National Research Centre for the Physical Sciences Democritos, Athens (Greece)); Zoupanos, G. (European Organization for Nuclear Research, Geneva (Switzerland))
1990-10-11
We consider the fermion masses in gauge theories obtained from ten dimensions through dimensional reduction on coset spaces. We calculate the general fermion mass matrix and we apply the mass formula in illustrative examples. (orig.).
Physical model of dimensional regularization
Schonfeld, Jonathan F.
2016-12-15
We explicitly construct fractals of dimension 4-ε on which dimensional regularization approximates scalar-field-only quantum-field theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and we argue that there probably is no Lorentz-invariant fractal of dimension greater than 2. We derive dimensional regularization's power-law screening first for fractals obtained by removing voids from 3-dimensional Euclidean space. The derivation applies techniques from elementary dielectric theory. Surprisingly, fractal geometry by itself does not guarantee the appropriate power-law behavior; boundary conditions at fractal voids also play an important role. We then extend the derivation to 4-dimensional Minkowski space. We comment on generalization to non-scalar fields, and speculate about implications for quantum gravity. (orig.)
Dimensional scaling in chemical physics
Avery, John; Goscinski, Osvaldo
1993-01-01
Dimensional scaling offers a new approach to quantum dynamical correlations. This is the first book dealing with dimensional scaling methods in the quantum theory of atoms and molecules. Appropriately, it is a multiauthor production, derived chiefly from papers presented at a workshop held in June 1991 at the Ørsted Institute in Copenhagen. Although focused on dimensional scaling, the volume includes contributions on other unorthodox methods for treating nonseparable dynamical problems and electronic correlation. In shaping the book, the editors serve three needs: an introductory tutorial for this still fledgling field; a guide to the literature; and an inventory of current research results and prospects. Part I treats basic aspects of dimensional scaling. Addressed to readers entirely unfamiliar with the subject, it provides both a qualitative overview, and a tour of elementary quantum mechanics. Part II surveys the research frontier. The eight chapters exemplify current techniques and outline results. Part...
Mixed-dimensional Bose polaron
Loft, Niels Jakob Søe; Wu, Zhigang; Bruun, G. M.
2017-09-01
A new generation of cold atom experiments trapping atomic mixtures in species-selective optical potentials opens up the intriguing possibility to create systems in which different atoms live in different spatial dimensions. Inspired by this, we investigate a mixed-dimensional Bose polaron consisting of an impurity particle moving in a two-dimensional (2D) layer immersed in a 3D Bose-Einstein condensate (BEC), using a theory that includes the mixed-dimensional vacuum scattering between the impurity and the bosons exactly. We show that similarly to the pure 3D case, this system exhibits a well-defined polaron state for attractive boson-impurity interaction that evolves smoothly into a mixed-dimensional dimer for strong attraction, as well as a well-defined polaron state for weak repulsive interaction, which becomes overdamped for strong interaction. We furthermore find that the properties of the polaron depend only weakly on the gas parameter of the BEC as long as the Bogoliubov theory remains a valid description for the BEC. This indicates that higher-order correlations between the impurity and the bosons are suppressed by the mixed-dimensional geometry in comparison to a pure 3D system, which led us to speculate that the mixed-dimensional polaron has universal properties in the unitarity limit of the impurity-boson interaction.
Three-dimensional versus two-dimensional vision in laparoscopy
Sørensen, Stine Maya Dreier; Savran, Mona M; Konge, Lars;
2016-01-01
BACKGROUND: Laparoscopic surgery is widely used, and results in accelerated patient recovery time and hospital stay were compared with laparotomy. However, laparoscopic surgery is more challenging compared with open surgery, in part because surgeons must operate in a three-dimensional (3D) space...... through a two-dimensional (2D) projection on a monitor, which results in loss of depth perception. To counter this problem, 3D imaging for laparoscopy was developed. A systematic review of the literature was performed to assess the effect of 3D laparoscopy. METHODS: A systematic search of the literature...
The Dimensional Reduction and K\\"ahler Metric of Forms In Flux and Warping
Frey, Andrew R
2013-01-01
We present a first-principles derivation of the K\\"ahler metric for axion-like moduli of conformally Calabi-Yau compactifications of IIB string theory with imaginary self-dual 3-form flux at the classical level. We find that the warp factor and flux modify the moduli space metric and therefore K\\"ahler potential even in classical supergravity, with the modifications scaling as (volume)$^{-2/3}$ in the large-volume limit. Our derivation emphasizes the role of constraints from 10D gauge symmetries and highlights metric formality as a geometric property that protects the moduli space of highly supersymmetric toroidal orientifolds. Our results have important quantitative implications for nonperturbative moduli stabilization, phenomenology, and cosmology in flux compactifications.
Dimensional micro and nano metrology
Hansen, Hans Nørgaard; da Costa Carneiro, Kim; Haitjema, Han
2006-01-01
The need for dimensional micro and nano metrology is evident, and as critical dimensions are scaled down and geometrical complexity of objects is increased, the available technologies appear not sufficient. Major research and development efforts have to be undertaken in order to answer these chal......The need for dimensional micro and nano metrology is evident, and as critical dimensions are scaled down and geometrical complexity of objects is increased, the available technologies appear not sufficient. Major research and development efforts have to be undertaken in order to answer...... these challenges. The developments have to include new measuring principles and instrumentation, tolerancing rules and procedures as well as traceability and calibration. The current paper describes issues and challenges in dimensional micro and nano metrology by reviewing typical measurement tasks and available...
-Dimensional Fractional Lagrange's Inversion Theorem
F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Multi-Dimensional Path Queries
Bækgaard, Lars
1998-01-01
We present the path-relationship model that supports multi-dimensional data modeling and querying. A path-relationship database is composed of sets of paths and sets of relationships. A path is a sequence of related elements (atoms, paths, and sets of paths). A relationship is a binary path...... to create nested path structures. We present an SQL-like query language that is based on path expressions and we show how to use it to express multi-dimensional path queries that are suited for advanced data analysis in decision support environments like data warehousing environments...
Vejbefæstelsers dimensionering
Bolet, Lars; Busch, Christian
Undervisningsnoten giver en introduktion til vejbygningsmaterialer og til design og dimensionering af vejbefæstelser med udgangspunkt i den mekanistisk-empiriske dimensioneringsmetode. Papiret er rettet mod studerende på Aalborg Universitets bacheloruddannelser i Byggeri og Anlæg.......Undervisningsnoten giver en introduktion til vejbygningsmaterialer og til design og dimensionering af vejbefæstelser med udgangspunkt i den mekanistisk-empiriske dimensioneringsmetode. Papiret er rettet mod studerende på Aalborg Universitets bacheloruddannelser i Byggeri og Anlæg....
Reduction of infinite dimensional equations
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
5-Dimensional Extended Space Model
Tsipenyuk, D. Yu.; Andreev, V. A.
2006-01-01
We put forward an idea that physical phenomena have to be treated in 5-dimensional space where the fifth coordinate is the interval S. Thus, we considered the (1+4) extended space G(T;X,Y,Z,S). In addition to Lorentz transformations (T;X), (T;Y), (T;Z) which are in (1+3)-dimensional Minkowski space, in the proposed (1+4)d extended space two other types of transformations exist in planes (T,S); (X,S), (Y,S), (Z,S) that converts massive particles into massless and vice versa. We also consider e...
Four-dimensional Calabi-Yau Black holes and their entropies.
Lust, D.
The author considers extremal black hole solutions of N = 2 supergravity which arise in the context of type II superstring compactification on Calabi-Yau 3-folds. In particular he shows how the entropies of these black holes depend on the topological data of the Calabi-Yau spaces; he also constructs massless black holes which are relevant for the conifold transition among different Calabi-Yau vacua.
Finite-dimensional (*)-serial algebras
无
2010-01-01
Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain suficient and necessary conditions for an associative algebra to be (*)-serial.
Dimensionality and the sample unit
Francis A. Roesch
2009-01-01
The sample unit and its implications for the Forest Service, U.S. Department of Agriculture's Forest Inventory and Analysis program are discussed in light of a generalized three-dimensional concept of continuous forest inventories. The concept views the sampled population as a spatial-temporal cube and the sample as a finite partitioning of the cube. The sample...
Two-dimensional liquid chromatography
Græsbøll, Rune
of this thesis is on online comprehensive two-dimensional liquid chromatography (online LC×LC) with reverse phase in both dimensions (online RP×RP). Since online RP×RP has not been attempted before within this research group, a significant part of this thesis consists of knowledge and experience gained...
One-dimensional photonic crystals
Shen, Huaizhong; Wang, Zhanhua; Wu, Yuxin; Yang, Bai
2016-01-01
A one-dimensional photonic crystal (1DPC), which is a periodic nanostructure with a refractive index distribution along one direction, has been widely studied by scientists. In this review, materials and methods for 1DPC fabrication are summarized. Applications are listed, with a special emphasis
The Dimensionality of Grammatical Variation
Sankoff, David; Cedergren, Henrietta J.
1976-01-01
Computer-based multidimensional scaling techniques are used to determine the dimensionality of grammatical variation in three large sets of data: Ross' (1973) Noun Phrase and fake Noun Phrase data; Sankoff's (1974) complementizer "que"-deletion (Montreal French) data; and Cedergren's (1973) syllable-final S-reduction (Panamanian Spanish) data. (DB)
Creating Three-Dimensional Scenes
Krumpe, Norm
2005-01-01
Persistence of Vision Raytracer (POV-Ray), a free computer program for creating photo-realistic, three-dimensional scenes and a link for Mathematica users interested in generating POV-Ray files from within Mathematica, is discussed. POV-Ray has great potential in secondary mathematics classrooms and helps in strengthening students' visualization…
6-dimensional brane world model
Kanti, Panagiota; Madden, Richard; Olive, Keith A.
2001-08-15
We consider a 6-dimensional spacetime which is periodic in one of the extra dimensions and compact in the other. The periodic direction is defined by two 4-brane boundaries. Both static and nonstatic exact solutions, in which the internal spacetime has a constant radius of curvature, are derived. In the case of static solutions, the brane tensions must be tuned as in the 5-dimensional Randall-Sundrum model; however, no additional fine-tuning is necessary between the brane tensions and the bulk cosmological constant. By further relaxing the sole fine-tuning of the model, we derive nonstatic solutions, describing de Sitter or anti--de Sitter 4-dimensional spacetimes, that allow for the fixing of the interbrane distance and the accommodation of pairs of positive--negative and positive--positive tension branes. Finally, we consider the stability of the radion field in these configurations by employing small, time-dependent perturbations around the background solutions. In analogy with results drawn in five dimensions, the solutions describing a de Sitter 4-dimensional spacetime turn out to be unstable while those describing an anti--de Sitter geometry are shown to be stable.
Higher dimensional discrete Cheeger inequalities
Anna Gundert
2015-01-01
Full Text Available For graphs there exists a strong connection between spectral and combinatorial expansion properties. This is expressed, e.g., by the discrete Cheeger inequality, the lower bound of which states that $\\lambda(G \\leq h(G$, where $\\lambda(G$ is the second smallest eigenvalue of the Laplacian of a graph $G$ and $h(G$ is the Cheeger constant measuring the edge expansion of $G$. We are interested in generalizations of expansion properties to finite simplicial complexes of higher dimension (or uniform hypergraphs. Whereas higher dimensional Laplacians were introduced already in 1945 by Eckmann, the generalization of edge expansion to simplicial complexes is not straightforward. Recently, a topologically motivated notion analogous to edge expansion that is based on $\\mathbb{Z}_2$-cohomology was introduced by Gromov and independently by Linial, Meshulam and Wallach. It is known that for this generalization there is no direct higher dimensional analogue of the lower bound of the Cheeger inequality. A different, combinatorially motivated generalization of the Cheeger constant, denoted by $h(X$, was studied by Parzanchevski, Rosenthal and Tessler. They showed that indeed $\\lambda(X \\leq h(X$, where $\\lambda(X$ is the smallest non-trivial eigenvalue of the ($(k-1$-dimensional upper Laplacian, for the case of $k$-dimensional simplicial complexes $X$ with complete $(k-1$-skeleton. Whether this inequality also holds for $k$-dimensional complexes with non-com\\-plete$(k-1$-skeleton has been an open question.We give two proofs of the inequality for arbitrary complexes. The proofs differ strongly in the methods and structures employed,and each allows for a different kind of additional strengthening of the original result.
Compactification of gauge models and the effective potential
Shtykov, N.N. (Leningrad State University, Leningrad (SU))
1989-07-01
The one-loop potential for bosons and massive fermions in an Abelian model is obtained on the {ital M}{sup 2}{times}{ital S1}{times}{ital S1} manifold. Stability of the total potential against arbitrary homogeneous deformations of {ital S}{sup 1}{times}{ital S1} is studied. It is shown that attraction or repulsion depends on the relations connecting the radii of the spheres, the fermion masses, and the coupling constant.
Higgs, moduli problem, baryogenesis and large volume compactifications
Higaki, Tetsutaro [RIKEN Nishina Center, Saitama (Japan). Mathematical Physics Lab.; Kamada, Kohei [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Takahashi, Fuminobu [Tohoku Univ., Sendai (Japan). Dept. of Physics
2012-07-15
We consider the cosmological moduli problem in the context of high-scale supersymmetry breaking suggested by the recent discovery of the standard-model like Higgs boson. In order to solve the notorious moduli-induced gravitino problem, we focus on the LARGE volume scenario, in which the modulus decay into gravitinos can be kinematically forbidden. We then consider the Affleck-Dine mechanism with or without an enhanced coupling with the inflaton, taking account of possible Q-ball formation. We show that the baryon asymmetry of the present Universe can be generated by the Affleck-Dine mechanism in LARGE volume scenario, solving the moduli and gravitino problems.
On the Effective Description of Large Volume Compactifications
Gallego, Diego
2011-01-01
We study the reliability of the Two-Step moduli stabilization in the type-IIB Large Volume Scenarios with matter and gauge interactions. The general analysis is based on a family of N=1 Supergravity models with a factorizable invariant Kaehler function, where the decoupling between two sets of fields without a mass hierarchy is easily understood. For the Large Volume Scenario particular analyses are performed for explicit models, one of such developed for the first time here, finding that the simplified version, where the Dilaton and Complex structure moduli are regarded as frozen by a previous stabilization, is a reliable supersymmetric description whenever the neglected fields stand at their leading F-flatness conditions and be neutral. The terms missed by the simplified approach are either suppressed by powers of the Calabi-Yau volume, or are higher order operators in the matter fields, and then irrelevant for the moduli stabilization rocedure. Although the power of the volume suppressing such corrections ...
Right-handed Neutrinos in F-theory Compactifications
Tatar, Radu; Tsuchiya, Yoichi; Watari, Taizan
2009-01-01
F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-han...
Simple compactifications and polar decomposition of homogeneous real spherical spaces
Knop, Friedrich; Krötz, Bernhard; Sayag, Eitan
2015-01-01
Let Z be an algebraic homogeneous space Z = G/H attached to real reductive Lie group G. We assume that Z is real spherical, i.e., minimal parabolic subgroups have open orbits on Z. For such spaces, we investigate their large scale geometry and provide a polar decomposition. This is obtained from...
The Casimir effect in rugby-ball type flux compactifications
Minamitsuji, M.
2008-04-01
We discuss volume stabilization in a 6D braneworld model based on 6D supergravity theory. The internal space is compactified by magnetic flux and contains codimension two 3-branes (conical singularities) as its boundaries. In general the external 4D spacetime is warped and in the unwrapped limit the shape of the internal space looks like a 'rugby ball'. The size of the internal space is not fixed due to the scale invariance of the supergravity theory. We discuss the possibility of volume stabilization by the Casimir effect for a massless, minimally coupled bulk scalar field. The main obstacle in studying this case is that the brane (conical) part of the relevant heat kernel coefficient (a6) has not been formulated. Thus as a first step, we consider the 4D analog model with boundary codimension two 1-branes. The spacetime structure of the 4D model is very similar to that of the original 6D model, where now the relevant heat kernel coefficient is well known. We derive the one-loop effective potential induced by a scalar field in the bulk by employing zeta function regularization with heat kernel analysis. As a result, the volume is stabilized for most possible choices of the parameters. Especially, for a larger degree of warping, our results imply that a large hierarchy between the mass scales and a tiny amount of effective cosmological constant can be realized on the brane. In the non-warped limit the ratio tends to converge to the same value, independently of the bulk gauge coupling constant. Finally, we will analyze volume stabilization in the original model 6D by employing the same mode-sum technique.
Projective BGG equations, algebraic sets, and compactifications of Einstein geometries
Cap, A; Hammerl, M
2010-01-01
For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space. These give preferred local maps to the model projective space that encode geometric contact with the model to a level that is optimal, in a suitable sense. In terms of the trivialisations arising from the special frames, normal solutions of classes of natural linear PDE (so-called first BGG equations) are shown to be necessarily polynomial in the generalised homogeneous coordinates; the polynomial system is the pull back of a polynomial system that solves the corresponding problem on the model. Thus questions concerning the zero locus of solutions, as well as related finer geometric and smooth data, are reduced to a study of the corresponding polynomial systems and algebraic sets. We show that a normal solution determines a canonical manifold stratification that reflects a...
Fibre Inflation: Observable Gravity Waves from IIB String Compactifications
Cicoli, M; Quevedo, Fernando
2009-01-01
We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential V = V_0 (3 - 4 exp{-phi/\\sqrt{3}}). Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient V_0, and in particular do not enter into the slow-roll parameters. Predictions for observables are therefore completely determined by the number of e-foldings (and so are correlated with the post-inflationary reheat temperature, T_r). If the reheat temperature is T_r = 1, 100, 10^{10} or 10^{15} GeV, then N_e = 23, 28, 46 and 58 e-foldings of inflation are required after horizon exit, corresponding to a scalar spectral index n_s = 0.924, 0.937, 0.961 and 0.968, while the ratio of tensor to scalar perturbations becomes r = 0.0264, 0.0189, 0.00797 and 0.00528, withi...
On de Sitter vacua in type IIA orientifold compactifications
Saueressig, Frank [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)]. E-mail: f.s.saueressig@phys.uu.nl; Theis, Ulrich [Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)]. E-mail: ulrich.theis@uni-jena.de; Vandoren, Stefan [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)]. E-mail: s.vandoren@phys.uu.nl
2006-02-02
This Letter discusses the orientifold projection of the quantum corrections to type IIA strings compactified on rigid Calabi-Yau threefolds. It is shown that N=2 membrane instanton effects give a holomorphic contribution to the superpotential, while the perturbative corrections enter into the Kahler potential. At the level of the scalar potential the corrections to the Kahler potential give rise to a positive energy contribution similar to adding anti-D3-branes in the KKLT scenario. This provides a natural mechanism to lift an AdS vacuum to a meta-stable dS vacuum.
Moduli instability in warped compactification - 4D effective theory approach
Arroja, F; Arroja, Frederico; Koyama, Kazuya
2006-01-01
We consider a 5D BPS dilatonic two brane model which reduces to the Randall-Sundrum model or the Horava-Witten theory for a particular choice of parameters. Recently new dynamical solutions were found by Chen et al., which describe a moduli instability of the warped geometry. Using a 4D effective theory derived by solving the 5D equations of motion, based on the gradient expansion method, we show that the exact solution of Chen et. al. can be reproduced within the 4D effective theory and we identify the origin of the moduli instability. We revisit the gradient expansion method with a new metric ansatz to clarify why the 4D effective theory solution can be lifted back to an exact 5D solution. Finally we argue against a recent claim that the 4D effective theory allows a much wider class of solutions than the 5D theory and provide a way to lift solutions in the 4D effective theory to 5D solutions perturbatively in terms of small velocities of the branes.
Non-thermal Dark Matter in String Compactifications
Allahverdi, Rouzbeh; Dutta, Bhaskar; Sinha, Kuver
2013-01-01
Non-thermal cosmological histories are capable of greatly increasing the available parameter space of different particle physics dark matter (DM) models and are well-motivated by the ubiquity of late-decaying gravitationally coupled scalars in UV theories like string theory. A non-thermal DM model is presented in the context of LARGE Volume Scenarios in type IIB string theory. The model is capable of addressing both the moduli-induced gravitino problem as well as the problem of overproduction of axionic dark radiation and/or DM. We show that the right abundance of neutralino DM can be obtained in both thermal under and overproduction cases for DM masses between O(GeV) to O(TeV). In the latter case the contribution of the QCD axion to the relic density is totally negligible, while in the former case it can be comparable to that of the neutralino thus resulting in a multi-component DM scenario.
Non Abelian orbifold compactifications of the heterotic string
Konopka, Sebastian J H
2012-01-01
I consider the construction of heterotic orbifold models having a toroidal orbifold with non Abelian point group. I construct an explicit model based on the point group $S_3$ and calculate the spectrum and remnant symmetries. This model provides a simple example of rank reduction of the Yang--Mills gauge group directly in the string theory rather than in the effective field theory. I check consistency of the construction by verifying that all continous and discrete symmetries are non anomalous.
On Low-Dimensional Projections of High-Dimensional Distributions
Duembgen, Lutz
2011-01-01
Let $P$ be a probability distribution on $q$-dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension $d << q$, most $d$-dimensional projections of $P$ look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension $q$. It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting $\\hat{P}$ be the empirical distribution of $n$ independent random vectors with distribution $P$, we investigate the behavior of the empirical process $\\sqrt{n}(\\hat{P} - P)$ under random projections, conditional on $\\hat{P}$.
4-dimensional spacetimes from 2-dimensional conformal null data
Goswami, Rituparno; Ellis, George F. R.
2017-03-01
In this paper we investigate whether the holographic principle proposed in string theory has a classical counterpart in general relativity theory. We show that there is a partial correspondence: at least in the case of vacuum Petrov type D spacetimes that admit a non-trivial Killing tensor, which encompass all the astrophysical black hole spacetimes, there exists a one-to-one correspondence between gravity in bulk and a 2-dimensional classical conformal scalar field on a null boundary.
ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES
Nikola Stefanović
2007-01-01
In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic ...
High-dimensional covariance estimation with high-dimensional data
Pourahmadi, Mohsen
2013-01-01
Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and mac
Visualizing the quality of dimensionality reduction
Mokbel, Bassam; Lueks, Wouter; Gisbrecht, Andrej; Hammer, Barbara
2013-01-01
The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of formal measures to evaluate the resulting low-dimensional representation independently from the methods' inherent criteria. Many evaluation measures can be summarized base
Las cinco grandes dimensiones de la personalidad
Jan ter Laak
1996-12-01
Full Text Available Este artículo revisa las distintas posiciones teóricas sobre las cinco grandes dimensiones de la personalidad, mostrando las semejanzas y diferencias entre las posturas teóricas. Esta contribución presenta lo siguiente: (a la génesis del contenido y la estructura de las cinco dimensiones; (b la fortaleza de las cinco dimensiones; (e la relación de las cinco grandes dimensiones con otros constructos de personalidad; (d discute el valor predictivo de las puntuaciones del perfil de las cinco dimensiones para criterios pertinentes; (e analiza el estatus teórico de las cinco dimensiones; (f discute críticas históricas sobre las cinco grandes dimensiones y se formulan respuestas a estas críticas; (g hace conjeturas para el futuro de las cinco grandes dimensiones; y (h concluye con algunas conclusiones y comentarios.
Three-dimensional display technologies.
Geng, Jason
2013-01-01
The physical world around us is three-dimensional (3D), yet traditional display devices can show only two-dimensional (2D) flat images that lack depth (i.e., the third dimension) information. This fundamental restriction greatly limits our ability to perceive and to understand the complexity of real-world objects. Nearly 50% of the capability of the human brain is devoted to processing visual information [Human Anatomy & Physiology (Pearson, 2012)]. Flat images and 2D displays do not harness the brain's power effectively. With rapid advances in the electronics, optics, laser, and photonics fields, true 3D display technologies are making their way into the marketplace. 3D movies, 3D TV, 3D mobile devices, and 3D games have increasingly demanded true 3D display with no eyeglasses (autostereoscopic). Therefore, it would be very beneficial to readers of this journal to have a systematic review of state-of-the-art 3D display technologies.
Two-dimensional cubic convolution.
Reichenbach, Stephen E; Geng, Frank
2003-01-01
The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.
Two dimensional unstable scar statistics.
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)
2006-12-01
This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.
Computed tomography for dimensional metrology
Kruth, J.P.; Bartscher, M.; Carmignato, S.;
2011-01-01
metrology, putting emphasis on issues as accuracy, traceability to the unit of length (the meter) and measurement uncertainty. It provides a state of the art (anno 2011) and application examples, showing the aptitude of CT metrology to: (i) check internal dimensions that cannot be measured using traditional...... coordinate measuring machines and (ii) combine dimensional quality control with material quality control in one single quality inspection run....
Juday, Richard D.
1992-01-01
Modified vernier scale gives accurate two-dimensional coordinates from maps, drawings, or cathode-ray-tube displays. Movable circular overlay rests on fixed rectangular-grid overlay. Pitch of circles nine-tenths that of grid and, for greatest accuracy, radii of circles large compared with pitch of grid. Scale enables user to interpolate between finest divisions of regularly spaced rule simply by observing which mark on auxiliary vernier rule aligns with mark on primary rule.
Radon Transform in Finite Dimensional Hilbert Space
Revzen, M.
2012-01-01
Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators are underpinned with finite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite dimensional quantum mechani...
Facial three-dimensional morphometry.
Ferrario, V F; Sforza, C; Poggio, C E; Serrao, G
1996-01-01
Three-dimensional facial morphometry was investigated in a sample of 40 men and 40 women, with a new noninvasive computerized method. Subjects ranged in age between 19 and 32 years, had sound dentitions, and no craniocervical disorders. For each subject, 16 cutaneous facial landmarks were automatically collected by a system consisting of two infrared camera coupled device (CCD) cameras, real time hardware for the recognition of markers, and software for the three-dimensional reconstruction of landmarks' x, y, z coordinates. From these landmarks, 15 linear and 10 angular measurements, and four linear distance ratios were computed and averaged for sex. For all angular values, both samples showed a narrow variability and no significant gender differences were demonstrated. Conversely, all the linear measurements were significantly higher in men than in women. The highest intersample variability was observed for the measurements of facial height (prevalent vertical dimension), and the lowest for the measurements of facial depth (prevalent horizontal dimension). The proportions of upper and lower face height relative to the anterior face height showed a significant sex difference. Mean values were in good agreement with literature data collected with traditional methods. The described method allowed the direct and noninvasive calculation of three-dimensional linear and angular measurements that would be usefully applied in clinics as a supplement to the classic x-ray cephalometric analyses.
Orthogonality preserving infinite dimensional quadratic stochastic operators
Akın, Hasan [Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey); Mukhamedov, Farrukh [Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Assessment of Dimensionality in Social Science Subtest
Ozbek Bastug, Ozlem Yesim
2012-01-01
Most of the literature on dimensionality focused on either comparison of parametric and nonparametric dimensionality detection procedures or showing the effectiveness of one type of procedure. There is no known study to shown how to do combined parametric and nonparametric dimensionality analysis on real data. The current study is aimed to fill…
On the Benefit of Dimensional Comparisons
Pohlmann, Britta; Moller, Jens
2009-01-01
People not only use social comparisons to evaluate their abilities, they also engage in dimensional comparisons, comparing their own achievement in different domains. Processes of dimensional comparison have contrasting effects on subject-specific self-concepts: downward dimensional comparisons result in higher self-concept in the…
Supporting dimensional control by information technology
Wu, R.; Berends, G.; Hoof, P. van; Maas, G.; Tolman, F.P.
1998-01-01
In the building industry, there is a necessity of designing the dimensional control plan before starting construction, for the assurance of the defined dimensional quality. The dimensional control plan provides site personnel with information on, among others, setting out and assembling building com
Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
Classifying Two-dimensional Hyporeductive Triple Algebras
Issa, A Nourou
2010-01-01
Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple systems) and two-dimensional real Bol algebras is given.
Two-dimensional function photonic crystals
Wu, Xiang-Yao; Liu, Xiao-Jing; Liang, Yu
2016-01-01
In this paper, we have firstly proposed two-dimensional function photonic crystals, which the dielectric constants of medium columns are the functions of space coordinates $\\vec{r}$, it is different from the two-dimensional conventional photonic crystals constituting by the medium columns of dielectric constants are constants. We find the band gaps of two-dimensional function photonic crystals are different from the two-dimensional conventional photonic crystals, and when the functions form of dielectric constants are different, the band gaps structure should be changed, which can be designed into the appropriate band gaps structures by the two-dimensional function photonic crystals.
Peterson's Deformations of Higher Dimensional Quadrics
Dinca, Ion I.
2010-01-01
We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in C3 of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere S2 ⊂ C3 to an explicit (n-1)-dimensional family of deformations in C2n-1 of n-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere Sn ⊂ Cn+1 and non-degenerate joined second fundamental forms. It is then proven that this family is maximal.
Samardzija, Nikola
1995-01-01
A simple three dimensional physical model is proposed to qualitatively address a particular type of dynamics evolving on toroidal structures. In the phase space this dynamics creates appearance of a worm-hole through which a chaotic, quasiperiodic and periodic behaviors are formed. An intriguing topological property of such a system is that it possesses no steady state solutions. As such, it opens some interesting questions in the bifurcation theory. The model also offers a novel qualitative tool for explaining some recently reported experimental and simulation results observed in physics, chemistry and biology.
Dimensional Bounds on Vircator Emission
Katz, J I
2016-01-01
Vircators (Virtual Cathode Oscillators) are sources of short-pulsed, high power, microwave (GHz) radiation. An essentially dimensional argument relates their radiated power, pulse energy and oscillation frequency to their driving voltage and fundamental physical constants. For a diode of width and gap 10 cm and for voltages of a few hundred keV the peak radiated power cannot exceed ${\\cal O} (\\text{30 GW})$ and the broad-band single cycle radiated energy cannot exceed ${\\cal O}(\\text{3 J})$. If electrons can be accelerated to relativistic energies higher powers and radiated energies may be possible.
3-Dimensional Response of Composites
1989-01-01
AFWAL-TR-88-4242 3-DIMENSIONAL RESPONSE OF COMPOSITES S.R. Soni S. Chandrashekara G.P. Tandon U. Santhosh Ten-Lu Hsiao CADTECH SYSTEMS RESEARCH INC...Composites 12. PERSONAL AUTHOR(S) S. R. Soni, S. Chandrashekara, G. P. Tandon, U. Santhosh , T. Isiao 13a. TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPRT...Chandrashekara, G.P. Tandon; Mr. U. Santhosh and Mr. Ten-Lu Hsiao. Accesion For NTIS CRAWI DTIC TAB 13 Unaonou,)ced 0 JustfCdtf)In ...._ By .... Di~t ibut;01 I
Emprendimiento sostenible, significado y dimensiones
Rodríguez Moreno, Diana Cristina
2016-01-01
El emprendimiento sostenible es un tema poco explorado, se ha identificado una baja información teórica y empírica especialmente en idioma español, por esta razón este trabajo presenta una revisión de literatura acerca del emprendimiento sostenible, el objetivo es comprender su significado y dimensiones. Para responder a este objetivo se realizó una revisión de literatura, la selección de documentos fue realizada usando Scopus, después se obtuvieron los documentos en science direct. (Ebsco, T...
Quasicrystalline three-dimensional foams
Cox, S. J.; Graner, F.; Mosseri, R.; Sadoc, J.-F.
2017-03-01
We present a numerical study of quasiperiodic foams, in which the bubbles are generated as duals of quasiperiodic Frank–Kasper phases. These foams are investigated as potential candidates to the celebrated Kelvin problem for the partition of three-dimensional space with equal volume bubbles and minimal surface area. Interestingly, one of the computed structures falls close to (but still slightly above) the best known Weaire–Phelan periodic candidate. In addition we find a correlation between the normalized bubble surface area and the root mean squared deviation of the number of faces, giving an additional clue to understanding the main geometrical ingredients driving the Kelvin problem.
Stochastic and infinite dimensional analysis
Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José
2016-01-01
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Two-dimensional liquid chromatography
Græsbøll, Rune
Two-dimensional liquid chromatography has received increasing interest due to the rise in demand for analysis of complex chemical mixtures. Separation of complex mixtures is hard to achieve as a simple consequence of the sheer number of analytes, as these samples might contain hundreds or even...... dimensions. As a consequence of the conclusions made within this thesis, the research group has, for the time being, decided against further development of online LC×LC systems, since it was not deemed ideal for the intended application, the analysis of the polar fraction of oil. Trap-and...
Emprendimiento sostenible, significado y dimensiones
Rodríguez Moreno, Diana Cristina
2016-01-01
El emprendimiento sostenible es un tema poco explorado, se ha identificado una baja información teórica y empírica especialmente en idioma español, por esta razón este trabajo presenta una revisión de literatura acerca del emprendimiento sostenible, el objetivo es comprender su significado y dimensiones. Para responder a este objetivo se realizó una revisión de literatura, la selección de documentos fue realizada usando Scopus, después se obtuvieron los documentos en science direct. (Ebsco, T...
Higher dimensional nonclassical eigenvalue asymptotics
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
Two-dimensional capillary origami
Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu
2016-01-08
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Obtain Lower-Dimensional Turbulence Systems from Higher-Dimensional Lax Integrable Models
LOU Sen-Yue
2001-01-01
Taking the well known (1-+l)-dimensional turbulence system,the Korteweg de-Vries Burgers equation,as a special example,we show that some types of lower-dimensional turbulence systems may be derived from some higherdimensional Lax integrable models,say,the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation.On the other hand,using the Lax pair of the original higher-dimensional integrable model(s),we may obtain higher-dimensional Lax pair(s) for a lower-dimensional turbulence system.``
Cascade Support Vector Machines with Dimensionality Reduction
Oliver Kramer
2015-01-01
Full Text Available Cascade support vector machines have been introduced as extension of classic support vector machines that allow a fast training on large data sets. In this work, we combine cascade support vector machines with dimensionality reduction based preprocessing. The cascade principle allows fast learning based on the division of the training set into subsets and the union of cascade learning results based on support vectors in each cascade level. The combination with dimensionality reduction as preprocessing results in a significant speedup, often without loss of classifier accuracies, while considering the high-dimensional pendants of the low-dimensional support vectors in each new cascade level. We analyze and compare various instantiations of dimensionality reduction preprocessing and cascade SVMs with principal component analysis, locally linear embedding, and isometric mapping. The experimental analysis on various artificial and real-world benchmark problems includes various cascade specific parameters like intermediate training set sizes and dimensionalities.
Dimensional Reduction for Generalized Continuum Polymers
Helmuth, Tyler
2016-10-01
The Brydges-Imbrie dimensional reduction formula relates the pressure of a d-dimensional gas of hard spheres to a model of (d+2)-dimensional branched polymers. Brydges and Imbrie's proof was non-constructive and relied on a supersymmetric localization lemma. The main result of this article is a constructive proof of a more general dimensional reduction formula that contains the Brydges-Imbrie formula as a special case. Central to the proof are invariance lemmas, which were first introduced by Kenyon and Winkler for branched polymers. The new dimensional reduction formulas rely on invariance lemmas for central hyperplane arrangements that are due to Mészáros and Postnikov. Several applications are presented, notably dimensional reduction formulas for (i) non-spherical bodies and (ii) for corrections to the pressure due to symmetry effects.
Teleparallel Gravity in Five Dimensional Theories
Geng, Chao-Qiang; Tseng, Huan-Hsin
2014-01-01
We study teleparallel gravity in five-dimensional space-time with particular discussions on Kaluza-Klein (KK) and braneworld theories. We directly perform the dimensional reduction by differential forms. In the braneworld theory, the teleparallel gravity formalism in the Friedmann-Lema\\^{i}tre-Robertson-Walker cosmology is equivalent to GR due to the same Friedmann equation, whereas in the KK case the reduction of our formulation does not recover the effect as GR of 4-dimensional spacetime.
Hadamard States and Two-dimensional Gravity
Salehi, H
2001-01-01
We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.
Coset space dimensional reduction of gauge theories
Kapetanakis, D. (Physik Dept., Technische Univ. Muenchen, Garching (Germany)); Zoupanos, G. (CERN, Geneva (Switzerland))
1992-10-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.).
Dimensional reduction and the Higgs potential
Farakos, K.; Koutsoumbas, G.; Surridge, M.; Zoupanos, G.
1987-08-17
Dimensional reduction of pure gauge theories over a compact coset space S/R leads to 4-dimensional gauge theories, where Higgs fields and the corresponding potential appear naturally. We derive and examine the Higgs potential in certain classes of dimensionally reduced models. In some of these models with Higgs potential of geometrical origin, the spontaneous symmetry breaking takes us a step closer towards the observed low energy gauge theory.
Three-Dimensional Icosahedral Phase Field Quasicrystal
Subramanian, P.; Archer, A. J.; Knobloch, E.; Rucklidge, A. M.
2016-08-01
We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for three-dimensional soft matter quasicrystal formation.
Topological defects in two-dimensional crystals
Chen, Yong; Qi, Wei-Kai
2008-01-01
By using topological current theory, we study the inner topological structure of the topological defects in two-dimensional (2D) crystal. We find that there are two elementary point defects topological current in two-dimensional crystal, one for dislocations and the other for disclinations. The topological quantization and evolution of topological defects in two-dimensional crystals are discussed. Finally, We compare our theory with Brownian-dynamics simulations in 2D Yukawa systems.
Three Dimensional Confinement WKB Revisited
Sinha, A K
2002-01-01
We develop an alternate formalism for radially confined quantum mechanical systems, in the framework of Wentzel-Kramers-Brillouin (WKB) approximation, without considering the Langer correction for the centrifugal term. Rather, following the analysis the Hainz and Grabert, we expand the centrifugal term perturbatively (in powers of $\\hbar$), decomposing it into 2 terms -- the classical centrifugal potential and a quantum correction. To test the validity of our formalism, we apply it explicitly to study the energy spectrum of certain physically relevant, radially confined quantum mechanical systems, viz., the 3-dimensional harmonic oscillator, the hydrogen atom, and the Hulthen potential. As observed by Hainz and Grabert, this approach gives better estimates than the conventional WKB approximation technique (based on Langer modification), even for spatially confined systems.
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Two-dimensional quantum repeaters
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Two-dimensional capillary origami
Brubaker, N. D.; Lega, J.
2016-01-01
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid.
High-dimensional entanglement certification.
Huang, Zixin; Maccone, Lorenzo; Karim, Akib; Macchiavello, Chiara; Chapman, Robert J; Peruzzo, Alberto
2016-06-17
Quantum entanglement is the ability of joint quantum systems to possess global properties (correlation among systems) even when subsystems have no definite individual property. Whilst the 2-dimensional (qubit) case is well-understood, currently, tools to characterise entanglement in high dimensions are limited. We experimentally demonstrate a new procedure for entanglement certification that is suitable for large systems, based entirely on information-theoretics. It scales more efficiently than Bell's inequality and entanglement witness. The method we developed works for arbitrarily large system dimension d and employs only two local measurements of complementary properties. This procedure can also certify whether the system is maximally entangled. We illustrate the protocol for families of bipartite states of qudits with dimension up to 32 composed of polarisation-entangled photon pairs.
Three-dimensional polarization algebra.
R Sheppard, Colin J; Castello, Marco; Diaspro, Alberto
2016-10-01
If light is focused or collected with a high numerical aperture lens, as may occur in imaging and optical encryption applications, polarization should be considered in three dimensions (3D). The matrix algebra of polarization behavior in 3D is discussed. It is useful to convert between the Mueller matrix and two different Hermitian matrices, representing an optical material or system, which are in the literature. Explicit transformation matrices for converting the column vector form of these different matrices are extended to the 3D case, where they are large (81×81) but can be generated using simple rules. It is found that there is some advantage in using a generalization of the Chandrasekhar phase matrix treatment, rather than that based on Gell-Mann matrices, as the resultant matrices are of simpler form and reduce to the two-dimensional case more easily. Explicit expressions are given for 3D complex field components in terms of Chandrasekhar-Stokes parameters.
Four Dimensional Trace Space Measurement
Hernandez, M.
2005-02-10
Future high energy colliders and FELs (Free Electron Lasers) such as the proposed LCLS (Linac Coherent Light Source) at SLAC require high brightness electron beams. In general a high brightness electron beam will contain a large number of electrons that occupy a short longitudinal duration, can be focused to a small transverse area while having small transverse divergences. Therefore the beam must have a high peak current and occupy small areas in transverse phase space and so have small transverse emittances. Additionally the beam should propagate at high energy and have a low energy spread to reduce chromatic effects. The requirements of the LCLS for example are pulses which contain 10{sup 10} electrons in a temporal duration of 10 ps FWHM with projected normalized transverse emittances of 1{pi} mm mrad[1]. Currently the most promising method of producing such a beam is the RF photoinjector. The GTF (Gun Test Facility) at SLAC was constructed to produce and characterize laser and electron beams which fulfill the LCLS requirements. Emittance measurements of the electron beam at the GTF contain evidence of strong coupling between the transverse dimensions of the beam. This thesis explores the effects of this coupling on the determination of the projected emittances of the electron beam. In the presence of such a coupling the projected normalized emittance is no longer a conserved quantity. The conserved quantity is the normalized full four dimensional phase space occupied by the beam. A method to determine the presence and evaluate the strength of the coupling in emittance measurements made in the laboratory is developed. A method to calculate the four dimensional volume the beam occupies in phase space using quantities available in the laboratory environment is also developed. Results of measurements made of the electron beam at the GTF that demonstrate these concepts are presented and discussed.
Las cinco grandes dimensiones de la personalidad
Jan ter Laak
1996-01-01
Este artículo revisa las distintas posiciones teóricas sobre las cinco grandes dimensiones de la personalidad, mostrando las semejanzas y diferencias entre las posturas teóricas. Esta contribución presenta lo siguiente: (a) la génesis del contenido y la estructura de las cinco dimensiones; (b) la fortaleza de las cinco dimensiones; (e) la relación de las cinco grandes dimensiones con otros constructos de personalidad; (d) discute el valor predictivo de las puntuaciones del perfil de las cinco...
Ultrahigh Resolution 3-Dimensional Imaging Project
National Aeronautics and Space Administration — Southwest Sciences proposes to develop innovative instrumentation for the rapid, 3-dimensional imaging of biological tissues with cellular resolution. Our approach...
Limitations on Dimensional Regularization in Renyi Entropy
Bao, Ning
2016-01-01
Dimensional regularization is a common method used to regulate the UV divergence of field theoretic quantities. When it is used in the context of Renyi entropy, however, it is important to consider whether such a procedure eliminates the statistical interpretation thereof as a measure of entanglement of states living on a Hilbert space. We therefore examine the dimensionally regularized Renyi entropy of a 4d unitary CFT and show that it admits no underlying Hilbert space in the state-counting sense. This gives a concrete proof that dimensionally regularized Renyi entropy cannot always be obtained as a limit of the Renyi entropy of some finite-dimensional quantum system.
Dimensional reduction of nonlinear time delay systems
M. S. Fofana
2005-01-01
infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions of the Duffing and van der Pol equations. For both nonlinear delay equations, transcendental characteristic equations of linearized stability are examined through Hopf bifurcation. The infinite-dimensional nonlinear solutions of the delay equations are decomposed into stable and centre subspaces, whose respective dimensions are determined by the linearized stability of the transcendental equations. Linear semigroups, infinitesimal generators, and their adjoint forms with bilinear pairings are the additional candidates for the infinite-dimensional reduction.
On 2-dimensional topological field theories
Dumitrescu, Florin
2010-01-01
In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that 2-dimensional topological field theories (over a point) are described by finite-dimensional commutative Frobenius algebras. In another direction, this result extends the description of 1-dimensional topological field theories over a space $X$ as vector bundles with connections over $X$, cf. \\cite{DST}.
Dimensional Hierarchy of Fermionic Interacting Topological Phases
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-01
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d -dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Zn.
Dimensional analysis and group theory in astrophysics
Kurth, Rudolf
2013-01-01
Dimensional Analysis and Group Theory in Astrophysics describes how dimensional analysis, refined by mathematical regularity hypotheses, can be applied to purely qualitative physical assumptions. The book focuses on the continuous spectral of the stars and the mass-luminosity relationship. The text discusses the technique of dimensional analysis, covering both relativistic phenomena and the stellar systems. The book also explains the fundamental conclusion of dimensional analysis, wherein the unknown functions shall be given certain specified forms. The Wien and Stefan-Boltzmann Laws can be si
Dimensional Hierarchy of Fermionic Interacting Topological Phases.
Queiroz, Raquel; Khalaf, Eslam; Stern, Ady
2016-11-11
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character of a d-dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end. Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the noninteracting Z classification to Z_{n}.
Two -Dimensional Wavelength Selective Diffraction by High-Order Three-Dimensional Composite Grating
Kohji; Furuhashi; Hideaki; Okayama; Hirochika; Nakajima
2003-01-01
We propose a wavelength selective diffraction using reflectors placed on three-dimensional grid cross points. Different wavelengths are separated into spots distributed in two-dimensional plane. Compact device with high port counts is attainable.
Reynolds, M. D.
1990-01-01
Student pairs were provided cards depicting two cycles of lunar phases; Pairs who used three-dimensional models to explain phases were more likely to have a scientifically accurate explanation than those who used two-dimensional models.
Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting
Chen, Leiming; Lee, Chiu Fan; Toner, John
2016-07-01
Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χx,y that characterize these correlations.
Hawking Radiation of Vector Particles via Tunneling From 4-Dimensional And 5-Dimensional Black Holes
Feng, Zhongwen; Zu, Xiaotao
2016-01-01
Using Proca equation and WKB approximation, we investigate Hawking radiation of vector particles via tunneling from 4-dimensional Kerr-de Sitter black hole and 5-dimensional Schwarzschild-Tangherlini black hole. The results show that the tunneling rates and Hawking temperatures are depended on the properties of spacetime (event horizon, mass and angular momentum). Besides, our results are the same as scalars and fermions tunneling from 4-dimensional Kerr-de Sitter black hole and 5-dimensional Schwarzschild-Tangherlini black hole.
Observation of Zero-Dimensional States in a One-Dimensional Electron Interferometer
Wees, B.J. van; Kouwenhoven, L.P.; Harmans, C.J.P.M.; Williamson, J.G.; Timmering, C.E.; Broekaart, M.E.I.; Foxon, C.T.; Harris, J.J.
1989-01-01
We have studied the electron transport in a one-dimensional electron interferometer. It consists of a disk-shaped two-dimensional electron gas, to which quantum point contacts are attached. Discrete zero-dimensional states are formed due to constructive interference of electron waves traveling along
Three Dimensional Illustrating--Three-Dimensional Vision and Deception of Sensibility
Szállassy, Noémi; Gánóczy, Anita; Kriska, György
2009-01-01
The wide-spread digital photography and computer use gave the opportunity for everyone to make three-dimensional pictures and to make them public. The new opportunities with three-dimensional techniques give chance for the birth of new artistic photographs. We present in detail the biological roots of three-dimensional visualization, the phenomena…
Local Duality for 2-Dimensional Local Ring
Belgacem Draouil
2008-11-01
We prove a local duality for some schemes associated to a 2-dimensional complete local ring whose residue field is an -dimensional local field in the sense of Kato–Parshin. Our results generalize the Saito works in the case =0 and are applied to study the Bloch–Ogus complex for such rings in various cases.
Continuous Dimensionality Characterization of Image Structures
Felsberg, Michael; Kalkan, Sinan; Krüger, Norbert
2009-01-01
Intrinsic dimensionality is a concept introduced by statistics and later used in image processing to measure the dimensionality of a data set. In this paper, we introduce a continuous representation of the intrinsic dimension of an image patch in terms of its local spectrum or, equivalently, its...
3-Dimensional Right Ventricular Volume Assessment
Jainandunsing, Jayant S.; Matyal, Robina; Shahul, Sajid S.; Wang, Angela; Woltersom, Bozena; Mahmood, Feroze
Purpose: The purpose of this review was to evaluate new computer software available for 3-dimensional right ventricular (RV) volume estimation. Description: Based on 2-dimensional echocardiography, various algorithms have been used for RV volume estimation. These are complex, time-consuming
Piezoelectricity in Two-Dimensional Materials
Wu, Tao
2015-02-25
Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.
Strongly interacting two-dimensional Dirac fermions
Lim, L.K.; Lazarides, A.; Hemmerich, Andreas; de Morais Smith, C.
2009-01-01
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature
Two-dimensional magma-repository interactions
Bokhove, O.
2001-01-01
Two-dimensional simulations of magma-repository interactions reveal that the three phases --a shock tube, shock reflection and amplification, and shock attenuation and decay phase-- in a one-dimensional flow tube model have a precursor. This newly identified phase ``zero'' consists of the impact of
Dimension and dimensional reduction in quantum gravity
Carlip, S.
2017-10-01
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning of ‘dimension’ and concluding with some speculative ideas of what dimensional reduction might mean for physics.
Generalised Unitarity for Dimensionally Regulated Amplitudes
Bobadilla, W J Torres; Mastrolia, P; Mirabella, E
2015-01-01
We present a novel set of Feynman rules and generalised unitarity cut-conditions for computing one-loop amplitudes via d-dimensional integrand reduction algorithm. Our algorithm is suited for analytic as well as numerical result, because all ingredients turn out to have a four-dimensional representation. We will apply this formalism to NLO QCD corrections.
Elastocapillary fabrication of three-dimensional microstructures
Honschoten, van J.W.; Berenschot, J.W.; Ondarcuhu, T.; Sanders, R.G.P.; Sundaram, J.; Elwenspoek, M.; Tas, N.R.
2010-01-01
We describe the fabrication of three-dimensional microstructures by means of capillary forces. Using an origami-like technique, planar silicon nitride structures of various geometries are folded to produce three-dimensional objects of 50–100 m. Capillarity is a particularly effective mechanism since
Radon Transform for Finite Dimensional Hilbert Space
Revzen, M
2012-01-01
Finite dimensional, d, Hilbert space operators are underpinned with ?nite geometry. The analysis emphasizes a central role for mutual unbiased bases (MUB) states projectors. Interrelation among the Hilbert space operators revealed via their (?nite) dual a?ne plane geometry (DAPG) underpin- ning is studied and utilized in formulating a ?nite dimensional Radon transformation. The ?nite geometry required for our study is outlines.
One Dimensional Locally Connected S-spaces
Kunen, Joan E Hart Kenneth
2007-01-01
We construct, assuming Jensen's principle diamond, a one-dimensional locally connected hereditarily separable continuum without convergent sequences. The construction is an inverse limit in omega_1 steps, and is patterned after the original Fedorchuk construction of a compact S-space. To make it one-dimensional, each space in the inverse limit is a copy of the Menger sponge.
Multi-Dimensional Aggregation for Temporal Data
Böhlen, M. H.; Gamper, J.; Jensen, Christian Søndergaard
2006-01-01
Business Intelligence solutions, encompassing technologies such as multi-dimensional data modeling and aggregate query processing, are being applied increasingly to non-traditional data. This paper extends multi-dimensional aggregation to apply to data with associated interval values that capture...
Three dimensional measurement of rhinoplasty results.
Heerbeek, N. van; Ingels, K.J.A.O.; Loon, B. van; Plooij, J.M.; Berge, S.J.
2009-01-01
BACKGROUND: Pre- and postoperative imaging is important and essential for evaluation of the results of rhinoplasty surgery. Two-dimensional photographs are used routinely for this purpose, but have several disadvantages as opposed to three-dimensional imaging techniques, such as
PARTICULAR AUXILIARY FEATURES OF DIMENSIONAL THEORY
Vardanyan Gumedin Surenovich
2012-10-01
Full Text Available New approach to selection of the principal measurement units system, different from the one used in the conventional dimensional theory, is proposed in the article. The new approach expands the capacities of dimensional analysis in the resolution of problems of deformable solid mechanics.
Three-Dimensional Gravity and String Ghosts
Carlip, S.; Kogan, I. I.
1991-01-01
It is known that much of the structure of string theory can be derived from three-dimensional topological field theory and gravity. We show here that, at least for simple topologies, the string diffeomorphism ghosts can also be explained in terms of three-dimensional physics.
Topology optimization of two-dimensional waveguides
Jensen, Jakob Søndergaard; Sigmund, Ole
2003-01-01
In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....
Two Dimensional Plasmonic Cavities on Moire Surfaces
Balci, Sinan; Kocabas, Askin; Karabiyik, Mustafa; Kocabas, Coskun; Aydinli, Atilla
2010-03-01
We investigate surface plasmon polariton (SPP) cavitiy modes on two dimensional Moire surfaces in the visible spectrum. Two dimensional hexagonal Moire surface can be recorded on a photoresist layer using Interference lithography (IL). Two sequential exposures at slightly different angles in IL generate one dimensional Moire surfaces. Further sequential exposure for the same sample at slightly different angles after turning the sample 60 degrees around its own axis generates two dimensional hexagonal Moire cavity. Spectroscopic reflection measurements have shown plasmonic band gaps and cavity states at all the azimuthal angles (omnidirectional cavity and band gap formation) investigated. The plasmonic band gap edge and the cavity states energies show six fold symmetry on the two dimensional Moire surface as measured in reflection measurements.
Probabilistic Universality in two-dimensional Dynamics
Lyubich, Mikhail
2011-01-01
In this paper we continue to explore infinitely renormalizable H\\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with the one-dimensional Cantor attractor is at most 1/2-H\\"older. Another formulation of this phenomenon is that the scaling structure of the H\\'enon Cantor attractor differs from its one-dimensional counterpart. However, in this paper we prove that the weight assigned by the canonical invariant measure to these bad spots tends to zero on microscopic scales. This phenomenon is called {\\it Probabilistic Universality}. It implies, in particular, that the Hausdorff dimension of the canonical measure is universal. In this way, universality and rigidity phenomena of one-dimensional dynamics assume a probabilistic nature in the two-dimensional world.
Multi-dimensional model order selection
Roemer Florian
2011-01-01
Full Text Available Abstract Multi-dimensional model order selection (MOS techniques achieve an improved accuracy, reliability, and robustness, since they consider all dimensions jointly during the estimation of parameters. Additionally, from fundamental identifiability results of multi-dimensional decompositions, it is known that the number of main components can be larger when compared to matrix-based decompositions. In this article, we show how to use tensor calculus to extend matrix-based MOS schemes and we also present our proposed multi-dimensional model order selection scheme based on the closed-form PARAFAC algorithm, which is only applicable to multi-dimensional data. In general, as shown by means of simulations, the Probability of correct Detection (PoD of our proposed multi-dimensional MOS schemes is much better than the PoD of matrix-based schemes.
Four-dimensional electron microscopy.
Zewail, Ahmed H
2010-04-09
The discovery of the electron over a century ago and the realization of its dual character have given birth to one of the two most powerful imaging instruments: the electron microscope. The electron microscope's ability to resolve three-dimensional (3D) structures on the atomic scale is continuing to affect different fields, including materials science and biology. In this Review, we highlight recent developments and inventions made by introducing the fourth dimension of time in electron microscopy. Today, ultrafast electron microscopy (4D UEM) enables a resolution that is 10 orders of magnitude better than that of conventional microscopes, which are limited by the video-camera rate of recording. After presenting the central concept involved, that of single-electron stroboscopic imaging, we discuss prototypical applications, which include the visualization of complex structures when unfolding on different length and time scales. The developed UEM variant techniques are several, and here we illucidate convergent-beam and near-field imaging, as well as tomography and scanning-pulse microscopy. We conclude with current explorations in imaging of nanomaterials and biostructures and an outlook on possible future directions in space-time, 4D electron microscopy.
Kornreich, Philipp; Farell, Bart
2013-01-01
An imager that can measure the distance from each pixel to the point on the object that is in focus at the pixel is described. This is accomplished by short photo-conducting lightguides at each pixel. In the eye the rods and cones are the fiber-like lightguides. The device uses ambient light that is only coherent in spherical shell-shaped light packets of thickness of one coherence length. Modern semiconductor technology permits the construction of lightguides shorter than a coherence length of ambient light. Each of the frequency components of the broad band light arriving at a pixel has a phase proportional to the distance from an object point to its image pixel. Light frequency components in the packet arriving at a pixel through a convex lens add constructively only if the light comes from the object point in focus at this pixel. The light in packets from all other object points cancels. Thus the pixel receives light from one object point only. The lightguide has contacts along its length. The lightguide charge carriers are generated by the light patterns. These light patterns, and thus the photocurrent, shift in response to the phase of the input signal. Thus, the photocurrent is a function of the distance from the pixel to its object point. Applications include autonomous vehicle navigation and robotic vision. Another application is a crude teleportation system consisting of a camera and a three-dimensional printer at a remote location.
Akasaka, Y.
1986-12-01
VLSI will be reaching to the limit of minimization in the 1990s, and after that, further increase of packing density or functions might depend on the vertical integration technology. Three-dimensional (3-D) integration is expected to provide several advantages, such as 1) parallel processing, 2) high-speed operation, 3) high packing density, and 4) multifunctional operation. Basic technologies of 3-D IC are to fabricate SOI layers and to stack them monolithically. Crystallinity of the recrystallized layer in SOI has increasingly become better, and very recently crystal-axis controlled, defect-free single-crystal areas has been obtained in chip size level by laser recystallization technology. Some basic functional models showing the concept or image of a future 3-D IC were fabricated in two or three stacked active layers. Some other proposals of subsystems in the application of 3-D structure, and the technical issues for realizing practical 3-D IC, i.e., the technology for fabricating high-quality SOI crystal on complicated surface topology, crosstalk of the signals between the stacked layers, total power consumption and cooling of the chip, are also discussed in this paper.
Three-dimensional colloidal lithography.
Nagai, Hironori; Poteet, Austen; Zhang, Xu A; Chang, Chih-Hao
2017-03-24
Light interactions with colloidal particles can generate a variety of complex three-dimensional (3D) intensity patterns, which can be utilized for nanolithography. The study of particle-light interactions can add more types of intensity patterns by manipulating key factors. Here we investigate a novel 3D nanolithography technique using colloidal particles under two-beam coherent illuminations. The fabricated 3D nanostructures are hollow, nested within periodic structures, and possess multiple chamber geometry. The effects of incident angles and particle size on the fabricated nanostructures were examined. The relative phase shift between particle position and interference pattern is identified as another significant parameter influencing the resultant nanostructures. A numerical model has been developed to show the evolution of nanostructure geometry with phase shifts, and experimental studies confirm the simulation results. Through the introduction of single colloidal particles, the fabrication capability of Lloyd's mirror interference can now be extended to fabrication of 3D nanostructure with complex shell geometry. The fabricated hollow nanostructures with grating background could find potential applications in the area of photonics, drug delivery, and nanofluidics.
The dimensionality of professional commitment
Jeffrey J. Bagraim
2003-10-01
Full Text Available This paper examines the dimensionality of professional commitment amongst a sample of 240 South African actuaries. Data were obtained, via a mailed questionnaire, from members of the South African Actuarial Society employed in the financial services industry. Statistical analysis conducted on the data showed that the 3-component model first proposed by Meyer, Allen and Smith (1993 is appropriate for understanding professional commitment amongst South African professionals. The analysis also showed that South African actuaries are highly committed to their profession. Opsomming Hierdie artikel ondersoek die dimensionaliteit van professionele toewyding by ‘n steekproef van 240 Suid-Afrikaanse aktuarisse. Die data is verkry deur ‘n posvraelys aan lede van die Suid-Afrikaanse Aktuariële Vereniging wat in die finansiële dienstesektor werksaam was. Statistiese ontledings wat uitgevoer is op die data dui aan dat die driekomponentmodel, aanvanklik voorgestel deur Meyer, Allen en Smith (1993, geskik is om professionele toewyding by Suid-Afrikaanse beroepslui te verstaan. Die ontleding dui verder aan dat Suid-Afrikaanse aktuarisse hoogs toegewyd is aan hulle professie.
Three dimensional magnetic abacus memory
Zhang, Shilei; Zhang, Jingyan; Baker, Alexander; Wang, Shouguo; Yu, Guanghua; Hesjedal, Thorsten
2015-03-01
Stacking nonvolatile memory cells into a three-dimensional matrix represents a powerful solution for the future of magnetic memory. However, it is technologically challenging to access the individual data in the storage medium if large numbers of bits are stacked on top of each other. Here we introduce a new type of multilevel, nonvolatile magnetic memory concept, the magnetic abacus. Instead of storing information in individual magnetic layers, thereby having to read out each magnetic layer separately, the magnetic abacus adopts a new encoding scheme which envisages a classical abacus with the beads operated by electron spins. It is inspired by the idea of second quantization, dealing with the memory state of the entire stack simultaneously. Direct read operations are implemented by measuring the artificially engineered `quantized' Hall voltage, representing a count of the spin-up and spin-down layers in the stack. This concept of `second quantization of memory' realizes the 3D memory architecture with superior reading and operation efficiency, thus is a promising approach for future nonvolatile magnetic random access memory.
Three-dimensional colloidal lithography
Nagai, Hironori; Poteet, Austen; Zhang, Xu A.; Chang, Chih-Hao
2017-03-01
Light interactions with colloidal particles can generate a variety of complex three-dimensional (3D) intensity patterns, which can be utilized for nanolithography. The study of particle–light interactions can add more types of intensity patterns by manipulating key factors. Here we investigate a novel 3D nanolithography technique using colloidal particles under two-beam coherent illuminations. The fabricated 3D nanostructures are hollow, nested within periodic structures, and possess multiple chamber geometry. The effects of incident angles and particle size on the fabricated nanostructures were examined. The relative phase shift between particle position and interference pattern is identified as another significant parameter influencing the resultant nanostructures. A numerical model has been developed to show the evolution of nanostructure geometry with phase shifts, and experimental studies confirm the simulation results. Through the introduction of single colloidal particles, the fabrication capability of Lloyd’s mirror interference can now be extended to fabrication of 3D nanostructure with complex shell geometry. The fabricated hollow nanostructures with grating background could find potential applications in the area of photonics, drug delivery, and nanofluidics.
Fidelity of states in infinite dimensional quantum systems
Hou, Jinchuan
2011-01-01
In this paper we discuss the fidelity of states in infinite dimensional systems, give an elementary proof of the infinite dimensional version of Uhlmann's theorem, and then, apply it to generalize several properties of the fidelity from finite dimensional case to infinite dimensional case. Some of them are somewhat different from those for finite dimensional case.
Computational Dimensionalities of Global Supercomputing
Richard S. Segall
2013-12-01
Full Text Available This Invited Paper pertains to subject of my Plenary Keynote Speech at the 17th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2013 held in Orlando, Florida on July 9-12, 2013. The title of my Plenary Keynote Speech was: "Dimensionalities of Computation: from Global Supercomputing to Data, Text and Web Mining" but this Invited Paper will focus only on the "Computational Dimensionalities of Global Supercomputing" and is based upon a summary of the contents of several individual articles that have been previously written with myself as lead author and published in [75], [76], [77], [78], [79], [80] and [11]. The topics of these of the Plenary Speech included Overview of Current Research in Global Supercomputing [75], Open-Source Software Tools for Data Mining Analysis of Genomic and Spatial Images using High Performance Computing [76], Data Mining Supercomputing with SAS™ JMP® Genomics ([77], [79], [80], and Visualization by Supercomputing Data Mining [81]. ______________________ [11.] Committee on the Future of Supercomputing, National Research Council (2003, The Future of Supercomputing: An Interim Report, ISBN-13: 978-0-309-09016- 2, http://www.nap.edu/catalog/10784.html [75.] Segall, Richard S.; Zhang, Qingyu and Cook, Jeffrey S.(2013, "Overview of Current Research in Global Supercomputing", Proceedings of Forty- Fourth Meeting of Southwest Decision Sciences Institute (SWDSI, Albuquerque, NM, March 12-16, 2013. [76.] Segall, Richard S. and Zhang, Qingyu (2010, "Open-Source Software Tools for Data Mining Analysis of Genomic and Spatial Images using High Performance Computing", Proceedings of 5th INFORMS Workshop on Data Mining and Health Informatics, Austin, TX, November 6, 2010. [77.] Segall, Richard S., Zhang, Qingyu and Pierce, Ryan M.(2010, "Data Mining Supercomputing with SAS™ JMP®; Genomics: Research-in-Progress, Proceedings of 2010 Conference on Applied Research in Information Technology, sponsored by
Four-Dimensional Graded Consciousness.
Jonkisz, Jakub; Wierzchoń, Michał; Binder, Marek
2017-01-01
Both the multidimensional phenomenon and the polysemous notion of consciousness continue to prove resistant to consistent measurement and unambiguous definition. This is hardly surprising, given that there is no agreement even as regards the most fundamental issues they involve. One of the basic disagreements present in the continuing debate about consciousness pertains to its gradational nature. The general aim of this article is to show how consciousness might be graded and multidimensional at the same time. We therefore focus on the question of what it is, exactly, that is or could be graded in cases of consciousness, and how we can measure it. Ultimately, four different gradable aspects of consciousness will be described: quality, abstractness, complexity and usefulness, which belong to four different dimensions, these being understood, respectively, as phenomenal, semantic, physiological, and functional. Consequently, consciousness may be said to vary with respect to phenomenal quality, semantic abstraction, physiological complexity, and functional usefulness. It is hoped that such a four-dimensional approach will help to clarify and justify claims about the hierarchical nature of consciousness. The approach also proves explanatorily advantageous, as it enables us not only to draw attention to certain new and important differences in respect of subjective measures of awareness and to justify how a given creature may be ranked higher in one dimension of consciousness and lower in terms of another, but also allows for innovative explanations of a variety of well-known phenomena (amongst these, the interpretations of blindsight and locked-in syndrome will be briefly outlined here). Moreover, a 4D framework makes possible many predictions and hypotheses that may be experimentally tested (We point out a few such possibilities pertaining to interdimensional dependencies).
Optical properties of low-dimensional materials
Ogawa, T
1998-01-01
This book surveys recent theoretical and experimental studies of optical properties of low-dimensional materials. As an extended version of Optical Properties of Low-Dimensional Materials (Volume 1, published in 1995 by World Scientific), Volume 2 covers a wide range of interesting low-dimensional materials including both inorganic and organic systems, such as disordered polymers, deformable molecular crystals, dilute magnetic semiconductors, SiGe/Si short-period superlattices, GaAs quantum wires, semiconductor microcavities, and photonic crystals. There are excellent review articles by promis
Alternative dimensional models of personality disorder
Widiger, Thomas A; Simonsen, Erik
2005-01-01
The recognition of the many limitations of the categorical model of personality disorder classification has led to the development of quite a number of alternative proposals for a dimensional classification. The purpose of this article is to suggest that future research work toward the integration...... of these alternative proposals within a common hierarchical structure. An illustration of a potential integration is provided using the constructs assessed within existing dimensional models. Suggestions for future research that will help lead toward a common, integrative dimensional model of personality disorder...
What is dimensional reduction really telling us?
Coumbe, Daniel
2015-01-01
Numerous approaches to quantum gravity report a reduction in the number of spacetime dimensions at the Planck scale. However, accepting the reality of dimensional reduction also means accepting its consequences, including a variable speed of light. We provide numerical evidence for a variable speed of light in the causal dynamical triangulation (CDT) approach to quantum gravity, showing that it closely matches the superluminality implied by dimensional reduction. We argue that reconciling the appearance of dimensional reduction with a constant speed of light may require modifying our understanding of time, an idea originally proposed in Ref. 1.
Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
A Multi-layer Hybrid Framework for Dimensional Emotion Classification
Nicolaou, Mihalis A.; Gunes, Hatice; Pantic, Maja
2011-01-01
This paper investigates dimensional emotion prediction and classification from naturalistic facial expressions. Similarly to many pattern recognition problems, dimensional emotion classification requires generating multi-dimensional outputs. To date, classification for valence and arousal dimensions
Three-dimensional patterning methods and related devices
Putnam, Morgan C.; Kelzenberg, Michael D.; Atwater, Harry A.; Boettcher, Shannon W.; Lewis, Nathan S.; Spurgeon, Joshua M.; Turner-Evans, Daniel B.; Warren, Emily L.
2016-12-27
Three-dimensional patterning methods of a three-dimensional microstructure, such as a semiconductor wire array, are described, in conjunction with etching and/or deposition steps to pattern the three-dimensional microstructure.
High-Dimensional Integrable Models with Conformal Invariance
LINJi; QIANXian-Ming
2003-01-01
Using the (2+1)-dimensional Schwartz dcrivative, the usual (2+1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n+1)-dimensional conformal invariance equation. The extension possesses Painlcvc property. Some (3+1)-dimensional examples are given and some single three-dimensional camber soliton and two spatial-plane solitons solutions of a (3+1)-dimensional equation are obtained.
Artifacts in three-dimensional transesophageal echocardiography.
Faletra, Francesco Fulvio; Ramamurthi, Alamelu; Dequarti, Maria Cristina; Leo, Laura Anna; Moccetti, Tiziano; Pandian, Natesa
2014-05-01
Three-dimensional (3D) transesophageal echocardiography (TEE) is subject to the same types of artifacts encountered on two-dimensional TEE. However, when displayed in a 3D format, some of the artifacts appear more "realistic," whereas others are unique to image acquisition and postprocessing. Three-dimensional TEE is increasingly used in the setting of percutaneous catheter-based interventions and ablation procedures, and 3D artifacts caused by the metallic components of catheters and devices are particularly frequent. Knowledge of these artifacts is of paramount relevance to avoid misinterpretation of 3D images. Although artifacts and pitfalls on two-dimensional echocardiography are well described and classified, a systematic description of artifacts in 3D transesophageal echocardiographic images and how they affect 3D imaging is still absent. The aim of this review is to describe the most relevant artifacts on 3D TEE, with particular emphasis on those occurring during percutaneous interventions for structural heart disease and ablation procedures.
Two-dimensional function photonic crystals
Liu, Xiao-Jing; Liang, Yu; Ma, Ji; Zhang, Si-Qi; Li, Hong; Wu, Xiang-Yao; Wu, Yi-Heng
2017-01-01
In this paper, we have studied two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , that can become true easily by electro-optical effect and optical kerr effect. We calculated the band gap structures of TE and TM waves, and found the TE (TM) wave band gaps of function photonic crystals are wider (narrower) than the conventional photonic crystals. For the two-dimensional function photonic crystals, when the dielectric constant functions change, the band gaps numbers, width and position should be changed, and the band gap structures of two-dimensional function photonic crystals can be adjusted flexibly, the needed band gap structures can be designed by the two-dimensional function photonic crystals, and it can be of help to design optical devices.
High dimensional neurocomputing growth, appraisal and applications
Tripathi, Bipin Kumar
2015-01-01
The book presents a coherent understanding of computational intelligence from the perspective of what is known as "intelligent computing" with high-dimensional parameters. It critically discusses the central issue of high-dimensional neurocomputing, such as quantitative representation of signals, extending the dimensionality of neuron, supervised and unsupervised learning and design of higher order neurons. The strong point of the book is its clarity and ability of the underlying theory to unify our understanding of high-dimensional computing where conventional methods fail. The plenty of application oriented problems are presented for evaluating, monitoring and maintaining the stability of adaptive learning machine. Author has taken care to cover the breadth and depth of the subject, both in the qualitative as well as quantitative way. The book is intended to enlighten the scientific community, ranging from advanced undergraduates to engineers, scientists and seasoned researchers in computational intelligenc...
Dimensional phase transitions in small Yukawa clusters
Sheridan, T E
2009-01-01
We investigate the one- to two-dimensional zigzag transition in clusters consisting of a small number of particles interacting through a Yukawa (Debye) potential and confined in a two-dimensional biharmonic potential well. Dusty (complex) plasma clusters with $n \\le 19$ monodisperse particles are characterized experimentally for two different confining wells. The well anisotropy is accurately measured, and the Debye shielding parameter is determined from the longitudinal breathing frequency. Debye shielding is shown to be important. A model for this system is used to predict equilibrium particle configurations. The experiment and model exhibit excellent agreement. The critical value of $n$ for the zigzag transition is found to be less than that predicted for an unshielded Coulomb interaction. The zigzag transition is shown to behave as a continuous phase transition from a one-dimensional to a two-dimensional state, where the state variables are the number of particles, the well anisotropy and the Debye shield...
Detection and Prognostics on Low Dimensional Systems
National Aeronautics and Space Administration — This paper describes the application of known and novel prognostic algorithms on systems that can be described by low dimensional, potentially nonlinear dynamics....
Bonnor solution in five-dimensional gravity
Becerril, R.; Matos, T. (Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Apartado Postal 14-740, 07000 Mexico, Distrito Federal, Mexico (MX))
1990-03-15
From Bonnor's solution of Einstein-Maxwell theory, a new solution to five-dimensional Kaluza-Klein equations which refers to a massive source carrying a magnetic and an electric dipole is constructed.
Three-dimensional tori and Arnold tongues
Sekikawa, Munehisa, E-mail: sekikawa@cc.utsunomiya-u.ac.jp [Department of Mechanical and Intelligent Engineering, Utsunomiya University, Utsunomiya-shi 321-8585 (Japan); Inaba, Naohiko [Organization for the Strategic Coordination of Research and Intellectual Property, Meiji University, Kawasaki-shi 214-8571 (Japan); Kamiyama, Kyohei [Department of Electronics and Bioinformatics, Meiji University, Kawasaki-shi 214-8571 (Japan); Aihara, Kazuyuki [Institute of Industrial Science, the University of Tokyo, Meguro-ku 153-8505 (Japan)
2014-03-15
This study analyzes an Arnold resonance web, which includes complicated quasi-periodic bifurcations, by conducting a Lyapunov analysis for a coupled delayed logistic map. The map can exhibit a two-dimensional invariant torus (IT), which corresponds to a three-dimensional torus in vector fields. Numerous one-dimensional invariant closed curves (ICCs), which correspond to two-dimensional tori in vector fields, exist in a very complicated but reasonable manner inside an IT-generating region. Periodic solutions emerge at the intersections of two different thin ICC-generating regions, which we call ICC-Arnold tongues, because all three independent-frequency components of the IT become rational at the intersections. Additionally, we observe a significant bifurcation structure where conventional Arnold tongues transit to ICC-Arnold tongues through a Neimark-Sacker bifurcation in the neighborhood of a quasi-periodic Hopf bifurcation (or a quasi-periodic Neimark-Sacker bifurcation) boundary.
Two-Dimensional Planetary Surface Lander
Hemmati, H.; Sengupta, A.; Castillo, J.; McElrath, T.; Roberts, T.; Willis, P.
2014-06-01
A systems engineering study was conducted to leverage a new two-dimensional (2D) lander concept with a low per unit cost to enable scientific study at multiple locations with a single entry system as the delivery vehicle.
Multi-Dimensional Separations of Polymers
Schoenmakers, P.; Aarnoutse, P.
2014-01-01
Synthetic polymers and comprehensive two-dimensional liq. chromatog. (LC×LC) are a synergistic combination. LC×LC provides unique insights in mutually dependent mol. distributions. Synthetic polymers offer clear demonstrations of the value of LC×LC.
A student's guide to dimensional analysis
Lemons, Don S
2017-01-01
This introduction to dimensional analysis covers the methods, history and formalisation of the field, and provides physics and engineering applications. Covering topics from mechanics, hydro- and electrodynamics to thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis. Introducing basic physics and fluid engineering topics through the mathematical methods of dimensional analysis, this book is perfect for students in physics, engineering and mathematics. Explaining potentially unfamiliar concepts such as viscosity and diffusivity, the text includes worked examples and end-of-chapter problems with answers provided in an accompanying appendix, which help make it ideal for self-study. Long-standing methodological problems arising in popular presentations of dimensional analysis are also identified and solved, making the book a useful text for advanced students and professionals.
Realisation of 3-dimensional data sets.
Brown, D.; Galsgaard, K.; Ireland, J.; Verwichte, E.; Walsh, R.
The visualisation of three-dimensional objects on two dimensions is a very common problem, but is a tricky one to solve. Every discipline has its way of solving it. The artist uses light-shade interaction, perspective, special colour coding. The architect produces projections of the object. The cartographer uses both colour-coding and shading to represent height elevations. There have been many attempts in the last century by the entertainment industry to produce a three-dimensional illusion, in the fifties it was fashionable to have 3d movies which utilize the anaglyph method. Nowadays one can buy "Magic Eye" postcards which show a hidden three dimensional picture if you stare at it half cross-eyed. This poster attempts to demonstrate how some of these techniques can be applied to three-dimensional data sets that can occur in solar physics.
Device fabrication: Three-dimensional printed electronics
Lewis, Jennifer A.; Ahn, Bok Y.
2015-02-01
Can three-dimensional printing enable the mass customization of electronic devices? A study that exploits this method to create light-emitting diodes based on 'quantum dots' provides a step towards this goal.
Finite-dimensional collisionless kinetic theory
Burby, J W
2016-01-01
A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.
Dimensional reduction over fuzzy coset spaces
Aschieri, P. E-mail: aschieri@theorie.physik.uni-muenchen.de; Madore, J.; Manousselis, P.; Zoupanos, G
2004-04-01
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields. (author)
From Dimensional to Cut-Off Regularization
Dillig, M
2006-01-01
We extent the standard approach of dimensional regularization of Feynman diagrams: we replace the transition to lower dimensions by a 'natural' cut-off regulator. Introducing an external regulator of mass Lambda^(2e), we regain in the limit e -> 0 and e > 0 the results of dimensional and cut-off regularization, respectively. We demonstrate the versatility and adequacy of the different regularization schemes for practical examples (such as non covariant regularization, the axial anomaly or regularization in effective field theories).
Three-dimensional imaging modalities in endodontics
Mao, Teresa; NEELAKANTAN, Prasanna
2014-01-01
Recent research in endodontics has highlighted the need for three-dimensional imaging in the clinical arena as well as in research. Three-dimensional imaging using computed tomography (CT) has been used in endodontics over the past decade. Three types of CT scans have been studied in endodontics, namely cone-beam CT, spiral CT, and peripheral quantitative CT. Contemporary endodontics places an emphasis on the use of cone-beam CT for an accurate diagnosis of parameters that cannot be visualize...
Exactly solvable one-dimensional inhomogeneous models
Derrida, B.; France, M.M.; Peyriere, J.
1986-11-01
The authors present a simple way of constructing one-dimensional inhomogeneous models (random or quasiperiodic) which can be solved exactly. They treat the example of an Ising chain in a varying magnetic field, but their procedure can easily be extended to other one-dimensional inhomogeneous models. For all the models they can construct, the free energy and its derivatives with respect to temperature can be computed exactly at one particular temperature.
Three-dimensional imaging modalities in endodontics
Mao, Teresa; Neelakantan, Prasanna
2014-01-01
Recent research in endodontics has highlighted the need for three-dimensional imaging in the clinical arena as well as in research. Three-dimensional imaging using computed tomography (CT) has been used in endodontics over the past decade. Three types of CT scans have been studied in endodontics, namely cone-beam CT, spiral CT, and peripheral quantitative CT. Contemporary endodontics places an emphasis on the use of cone-beam CT for an accurate diagnosis of parameters that cannot be visualize...
Finite dimensional quotients of commutative operator algebras
Meyer, Ralf
1997-01-01
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital operator algebras. This allows to define invariant distances on the spectrum of commutative operator algebras analogous to the Caratheodory distance for complex manifolds. Moreover, unitizations of two-dimensional operator algebras with zero multiplication pro...
(2+1)-dimensional supersymmetric integrable equations
Yan, Zhao-Wen; Tala; Chen, Fang; Liu, Tao-Ran; Han, Jing-Min
2017-09-01
By means of two different approaches, we construct the (2+1)-dimensional supersymmetric integrable equations based on the super Lie algebra osp(3/2). We relax the constraint condition of homogenous space of super Lie algebra osp(3/2) in the first approach. In another one, the technique of extending the dimension of the systems is used. Furthermore for the (2 + 1)-dimensional supersymmetric integrable equations, we also derive their Bäcklund transformations.
Interpolation by two-dimensional cubic convolution
Shi, Jiazheng; Reichenbach, Stephen E.
2003-08-01
This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.
Bayesian Analysis of High Dimensional Classification
Mukhopadhyay, Subhadeep; Liang, Faming
2009-12-01
Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. In these cases , there is a lot of interest in searching for sparse model in High Dimensional regression(/classification) setup. we first discuss two common challenges for analyzing high dimensional data. The first one is the curse of dimensionality. The complexity of many existing algorithms scale exponentially with the dimensionality of the space and by virtue of that algorithms soon become computationally intractable and therefore inapplicable in many real applications. secondly, multicollinearities among the predictors which severely slowdown the algorithm. In order to make Bayesian analysis operational in high dimension we propose a novel 'Hierarchical stochastic approximation monte carlo algorithm' (HSAMC), which overcomes the curse of dimensionality, multicollinearity of predictors in high dimension and also it possesses the self-adjusting mechanism to avoid the local minima separated by high energy barriers. Models and methods are illustrated by simulation inspired from from the feild of genomics. Numerical results indicate that HSAMC can work as a general model selection sampler in high dimensional complex model space.
Semi-relativistic hydrodynamics of three-dimensional and low-dimensional quantum plasma
Andreev, Pavel; Kuz'menkov, Leonid
2014-01-01
Contributions of the current-current and Darwin interactions and weak-relativistic addition to kinetic energy in the quantum hydrodynamic equations are considered. Features of hydrodynamic equations for two-dimensional layer of plasma (two-dimensional electron gas for instance) are described. It is shown that the force fields caused by the Darwin interaction and weak-relativistic addition to kinetic energy are partially reduced. Dispersion of three- and two-dimensional semi-relativistic Langmuir waves is calculated.
Tannenbaum, Eric P; Burns, Geoffrey T; Oak, Nikhil R; Lawton, Jeffrey N
2017-03-01
Metacarpal fractures are commonly treated by a variety of means including casting or open reduction internal fixation when unacceptable alignment is present following attempted closed reduction. Dorsal plating with either single-row 2-dimensional or double-row 3-dimensional plates has been proposed. This study's purpose was to determine if there are any differences in fixation construct stability under cyclic loading and subsequent load to failure between the lower profile 3-dimensional and the larger 2-dimensional plates in a metacarpal fracture gap sawbone model. Thirty metacarpal cortico-cancellous synthetic bones were cut with a 1.75-mm gap between the 2 fragments simulating mid-diaphyseal fracture comminution. Half of the metacarpals were plated with 2.0-mm locking 2-dimensional plates and half with 1.5-mm locking 3-dimensional plates. The plated metacarpals were mounted into a materials testing apparatus and cyclically loaded under cantilever bending for 2,000 cycles at 70 N, then 2,000 cycles at 120 N, and finally monotonically loaded to failure. Throughout testing, fracture gap sizes were measured, failure modes were recorded, and construct strength and stiffness values were calculated. All 3-dimensional constructs survived both cyclic loading conditions. Ten (67%) 2-dimensional constructs survived both loading conditions, whereas 5 (33%) failed the 120-N loading at 1377 ± 363 cycles. When loaded to failure, the 3-dimensional constructs failed at 265 N ± 21 N, whereas the 2-dimensional constructs surviving cyclic loading failed at 190 N ± 17 N. The shorter, thinner 3-dimensional metacarpal plates demonstrated increased resistance to failure in a cyclic loading model and increased load to failure compared with the relatively longer, thicker 2-dimensional metacarpal plates. The lower-profile 3-dimensional metacarpal plate fixation demonstrated greater stability for early postoperative resistance than the thicker 2-dimensional fixation, whereas the smaller
Multichannel transfer function with dimensionality reduction
Kim, Han Suk
2010-01-17
The design of transfer functions for volume rendering is a difficult task. This is particularly true for multi-channel data sets, where multiple data values exist for each voxel. In this paper, we propose a new method for transfer function design. Our new method provides a framework to combine multiple approaches and pushes the boundary of gradient-based transfer functions to multiple channels, while still keeping the dimensionality of transfer functions to a manageable level, i.e., a maximum of three dimensions, which can be displayed visually in a straightforward way. Our approach utilizes channel intensity, gradient, curvature and texture properties of each voxel. The high-dimensional data of the domain is reduced by applying recently developed nonlinear dimensionality reduction algorithms. In this paper, we used Isomap as well as a traditional algorithm, Principle Component Analysis (PCA). Our results show that these dimensionality reduction algorithms significantly improve the transfer function design process without compromising visualization accuracy. In this publication we report on the impact of the dimensionality reduction algorithms on transfer function design for confocal microscopy data.
High-Dimensional Integrable Models with Conformal Invariance
LIN Ji; QIAN Xian-Ming
2003-01-01
Using the (2+1)-dimensional Schwartz derivative, the usual (2+1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n+1)-dimensional conformal invariance equation. The extension possessestwo spatial-plane solitons solutions of a (3+1)-dimensional equation are obtained.
On two-dimensionalization of three-dimensional turbulence in shell models
Chakraborty, Sagar; Jensen, Mogens Høgh; Sarkar, A.
2010-01-01
Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell...
Eilbeck, J. C; Lomdahl, P.S.; Olsen, O.H.
1985-01-01
A two-dimensional model of Josephson junction of overlap type is presented. The energy input is provided through induced magnetic fields modeled by a set of boundary conditions. In the limit of a very narrow junction, this model reduces to the one-dimensional model. Further, an equation derived f...
Finite Dimensional Compensators for Infinite Dimensional Systems with Unbounded Control Action.
1984-05-01
from infinite dimensional linear systems theory that A + GC . V(A) + X generates an exponentially stable semigroup on X (see (5) or [161). It is also...Matheatica Aplicada e Computacional, 2 (1983). 15] R.F. CURTAIN/A.J. PRITCHARD Infinite Dimensional Linear Systems Theory LNCIS 8, Springer-Verlag
Damstra, Janalt; Fourie, Zacharias; Ren, Yijin
2011-01-01
The aim of this study was to compare two- and three-dimensional cephalometric values by using a three-dimensional analysis based on the midsagittal plane. Spherical metal markers were fixed on to the anatomical landmarks of 10 human skulls, which were examined radiographically with conventional late
Dimensionality Reduction on Multi-Dimensional Transfer Functions for Multi-Channel Volume Data Sets
Kim, Han Suk; Schulze, Jürgen P.; Cone, Angela C.; Sosinsky, Gina E.; Martone, Maryann E.
2011-01-01
The design of transfer functions for volume rendering is a non-trivial task. This is particularly true for multi-channel data sets, where multiple data values exist for each voxel, which requires multi-dimensional transfer functions. In this paper, we propose a new method for multi-dimensional transfer function design. Our new method provides a framework to combine multiple computational approaches and pushes the boundary of gradient-based multi-dimensional transfer functions to multiple channels, while keeping the dimensionality of transfer functions at a manageable level, i.e., a maximum of three dimensions, which can be displayed visually in a straightforward way. Our approach utilizes channel intensity, gradient, curvature and texture properties of each voxel. Applying recently developed nonlinear dimensionality reduction algorithms reduces the high-dimensional data of the domain. In this paper, we use Isomap and Locally Linear Embedding as well as a traditional algorithm, Principle Component Analysis. Our results show that these dimensionality reduction algorithms significantly improve the transfer function design process without compromising visualization accuracy. We demonstrate the effectiveness of our new dimensionality reduction algorithms with two volumetric confocal microscopy data sets. PMID:21841914
Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models
Lee, J. M.; Kittel, P.; Timmerhaus, K. D.; Radebaugh, R.
2004-01-01
One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when used in conjunction with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse effects, lumped parameter corrections, which are obtained though experiment, must be used. Or two-dimensional solutions of the differential fluid equations must be obtained. A linear two-dimensional solution to the fluid equations has been obtained. The solution provides lumped parameter corrections for one-dimensional models. The model accounts for heat transfer and shear flow between the gas and the tube. The complex Nusselt number and complex shear wall are useful in describing these corrections, with phase relations and amplitudes scaled with the Prandtl and Valensi numbers. The calculated ratio, a, between a two-dimensional solution of the oscillating temperature and velocity and a one-dimensional solution for the same shows a scales linearly with Va for Va less than 30. In this region alpha less than 0.5, that is, the enthalpy flow calculated with a two-dimensional model is 50% of a calculation using a one-dimensional model. For Va greater than 250, alpha = 0.8, showing that diffusion is still important even when it is confined to a thing layer near the tube wall.
Three dimensional illustrating - three-dimensional vision and deception of sensibility
Anita Gánóczy
2009-03-01
Full Text Available The wide-spread digital photography and computer use gave the opportunity for everyone to make three-dimensional pictures and to make them public. The new opportunities with three-dimensional techniques give chance for the birth of new artistic photographs. We present in detail the biological roots of three-dimensional visualization, the phenomena of movement parallax, which can be used efficiently in making three-dimensional graphics, the Zöllner- and Corridor-illusion. There are present in this paper the visual elements, which contribute to define a plane two-dimensional image in three-dimension: coherent lines, the covering, the measurement changes, the relative altitude state, the abatement of detail profusion, the shadings and the perspective effects of colors.
FROM ZERO-DIMENSIONAL TO 2-DIMENSIONAL CARBON NANOMATERIALS - part I: TYPES OF CNs
Cătălin IANCU
2012-05-01
Full Text Available In recent years, many theoretical and experimental studies have been carried out to develop one of the most interesting aspects of the science and nanotechnology which is called carbon-related nanomaterials. In this review paper are presented some of the most important developments in the synthesis, properties, and applications of low-dimensional carbon nanomaterials. The synthesis techniques are used to produce specific kinds of low-dimensional carbon nanomaterials such as zero-dimensional CNs (including fullerene, carbon-encapsulated metal nanoparticles, nanodiamond, and onion-like carbons, one-dimensional carbon nanomaterials (including carbon nanofibers and carbon nanotubes, and two-dimensional carbon nanomaterials (including graphene and carbon nanowalls.
TWO-DIMENSIONAL TOPOLOGY OF COSMOLOGICAL REIONIZATION
Wang, Yougang; Xu, Yidong; Chen, Xuelei [Key Laboratory of Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 China (China); Park, Changbom [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); Kim, Juhan, E-mail: wangyg@bao.ac.cn, E-mail: cbp@kias.re.kr [Center for Advanced Computation, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)
2015-11-20
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two-dimensional genus curve for the early, middle, and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometre Array.
Clustering high dimensional data using RIA
Aziz, Nazrina [School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia)
2015-05-15
Clustering may simply represent a convenient method for organizing a large data set so that it can easily be understood and information can efficiently be retrieved. However, identifying cluster in high dimensionality data sets is a difficult task because of the curse of dimensionality. Another challenge in clustering is some traditional functions cannot capture the pattern dissimilarity among objects. In this article, we used an alternative dissimilarity measurement called Robust Influence Angle (RIA) in the partitioning method. RIA is developed using eigenstructure of the covariance matrix and robust principal component score. We notice that, it can obtain cluster easily and hence avoid the curse of dimensionality. It is also manage to cluster large data sets with mixed numeric and categorical value.
Universal entanglement for higher dimensional cones
Bueno, Pablo
2015-01-01
The entanglement entropy of a generic $d$-dimensional conformal field theory receives a regulator independent contribution when the entangling region contains a (hyper)conical singularity of opening angle $\\Omega$, codified in a function $a^{(d)}(\\Omega)$. In {\\tt arXiv:1505.04804}, we proposed that for three-dimensional conformal field theories, the coefficient $\\sigma$ characterizing the smooth surface limit of such contribution ($\\Omega\\rightarrow \\pi$) equals the stress tensor two-point function charge $C_{ T}$, up to a universal constant. In this paper, we prove this relation for general three-dimensional holographic theories, and extend the result to general dimensions. In particular, we show that a generalized coefficient $\\sigma^{ (d)}$ can be defined for (hyper)conical entangling regions in the almost smooth surface limit, and that this coefficient is universally related to $C_{ T}$ for general holographic theories, providing a general formula for the ratio $\\sigma^{ (d)}/C_{ T}$ in arbitrary dimensi...
Higher dimensional Numerical Relativity: code comparison
Witek, Helvi; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Shibata, Masaru; Sperhake, Ulrich; Zilhao, Miguel
2014-01-01
The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical evolutions of higher dimensional black hole spacetimes are tremendously complex, involving different diagnostic tools and "dimensional reduction methods". In this work we compare two different successful codes to evolve Einstein's equations in higher dimensions, and show that the results of such different procedures agree to numerical precision, when applied to the collision from rest of two equal-mass black holes. We calculate the total radiated energy to be E/M=9x10^{-4} in five dimensions and E/M=8.1x10^{-4} in six dimensions.
Effective Image Database Search via Dimensionality Reduction
Dahl, Anders Bjorholm; Aanæs, Henrik
2008-01-01
Image search using the bag-of-words image representation is investigated further in this paper. This approach has shown promising results for large scale image collections making it relevant for Internet applications. The steps involved in the bag-of-words approach are feature extraction......, vocabulary building, and searching with a query image. It is important to keep the computational cost low through all steps. In this paper we focus on the efficiency of the technique. To do that we substantially reduce the dimensionality of the features by the use of PCA and addition of color. Building....... In the query step, features from the query image are assigned to the visual vocabulary. The dimensionality reduction enables us to do exact feature labeling using kD-tree, instead of approximate approaches normally used. Despite the dimensionality reduction to between 6 and 15 dimensions we obtain improved...
Two dimensional topology of cosmological reionization
Wang, Yougang; Xu, Yidong; Chen, Xuelei; Kim, Juhan
2015-01-01
We study the two-dimensional topology of the 21-cm differential brightness temperature for two hydrodynamic radiative transfer simulations and two semi-numerical models. In each model, we calculate the two dimensional genus curve for the early, middle and late epochs of reionization. It is found that the genus curve depends strongly on the ionized fraction of hydrogen in each model. The genus curves are significantly different for different reionization scenarios even when the ionized faction is the same. We find that the two-dimensional topology analysis method is a useful tool to constrain the reionization models. Our method can be applied to the future observations such as those of the Square Kilometer Array.
Ligand-Stabilized Reduced-Dimensionality Perovskites
Quan, Li Na
2016-02-03
Metal halide perovskites have rapidly advanced thin film photovoltaic performance; as a result, the materials’ observed instabilities urgently require a solution. Using density functional theory (DFT), we show that a low energy of formation, exacerbated in the presence of humidity, explains the propensity of perovskites to decompose back into their precursors. We find, also using DFT, that intercalation of phenylethylammonium between perovskite layers introduces quantitatively appreciable van der Waals interactions; and these drive an increased formation energy and should therefore improve material stability. Here we report the reduced-dimensionality (quasi-2D) perovskite films that exhibit improved stability while retaining the high performance of conventional three-dimensional perovskites. Continuous tuning of the dimensionality, as assessed using photophysical studies, is achieved by the choice of stoichiometry in materials synthesis. We achieved the first certified hysteresis-free solar power conversion in a planar perovskite solar cell, obtaining a 15.3% certified PCE, and observe greatly improved performance longevity.
7th High Dimensional Probability Meeting
Mason, David; Reynaud-Bouret, Patricia; Rosinski, Jan
2016-01-01
This volume collects selected papers from the 7th High Dimensional Probability meeting held at the Institut d'Études Scientifiques de Cargèse (IESC) in Corsica, France. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, and random graphs. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenome...
Three-dimensional imaging modalities in endodontics
Mao, Teresa; Neelakantan, Prasanna [Dept. of Conservative Dentistry and Endodontics, Saveetha Dental College and Hospitals, Saveetha University, Chennai (India)
2014-09-15
Recent research in endodontics has highlighted the need for three-dimensional imaging in the clinical arena as well as in research. Three-dimensional imaging using computed tomography (CT) has been used in endodontics over the past decade. Three types of CT scans have been studied in endodontics, namely cone-beam CT, spiral CT, and peripheral quantitative CT. Contemporary endodontics places an emphasis on the use of cone-beam CT for an accurate diagnosis of parameters that cannot be visualized on a two-dimensional image. This review discusses the role of CT in endodontics, pertaining to its importance in the diagnosis of root canal anatomy, detection of peri-radicular lesions, diagnosis of trauma and resorption, presurgical assessment, and evaluation of the treatment outcome.
3-Dimensional Topographic Models for the Classroom
Keller, J. W.; Roark, J. H.; Sakimoto, S. E. H.; Stockman, S.; Frey, H. V.
2003-01-01
We have recently undertaken a program to develop educational tools using 3-dimensional solid models of digital elevation data acquired by the Mars Orbital Laser Altimeter (MOLA) for Mars as well as a variety of sources for elevation data of the Earth. This work is made possible by the use of rapid prototyping technology to construct solid 3-Dimensional models of science data. We recently acquired rapid prototyping machine that builds 3-dimensional models in extruded plastic. While the machine was acquired to assist in the design and development of scientific instruments and hardware, it is also fully capable of producing models of spacecraft remote sensing data. We have demonstrated this by using Mars Orbiter Laser Altimeter (MOLA) topographic data and Earth based topographic data to produce extruded plastic topographic models which are visually appealing and instantly engage those who handle them.
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
Three-dimensional imaging modalities in endodontics.
Mao, Teresa; Neelakantan, Prasanna
2014-09-01
Recent research in endodontics has highlighted the need for three-dimensional imaging in the clinical arena as well as in research. Three-dimensional imaging using computed tomography (CT) has been used in endodontics over the past decade. Three types of CT scans have been studied in endodontics, namely cone-beam CT, spiral CT, and peripheral quantitative CT. Contemporary endodontics places an emphasis on the use of cone-beam CT for an accurate diagnosis of parameters that cannot be visualized on a two-dimensional image. This review discusses the role of CT in endodontics, pertaining to its importance in the diagnosis of root canal anatomy, detection of peri-radicular lesions, diagnosis of trauma and resorption, presurgical assessment, and evaluation of the treatment outcome.
A dilogarithmic 3-dimensional Ising tetrahedron
Broadhurst, D J
1999-01-01
In 3 dimensions, the Ising model is in the same universality class as unknown analytical nature. In contrast, all single-scale 4-dimensional tetrahedra were reduced, in hep-th/9803091, to special values of exponentially convergent polylogarithms. Combining dispersion relations with the integer-relation finder PSLQ, we find that $C^{Tet}/2^{5/2} = Cl_2(4\\alpha) - Cl_2(2\\alpha)$, with $Cl_2(\\theta):=\\sum_{n>0}\\sin(n\\theta)/n^2$ and 1,000-digit precision and readily yields 50,000 digits of $C^{Tet}$, after transformation to an exponentially convergent sum, akin to those studied in math.CA/9803067. It appears that this 3-dimensional result entails a polylogarithmic ladder beginning with the classical formula for $\\pi/\\sqrt2$, in the manner that 4-dimensional results build on that for $\\pi/\\sqrt3$.
Multi-Dimensional Systematic Block Codes
YUEDianwu; CHENTao
2004-01-01
This paper is concerned with a family of Mmulti-dimensional systematic block (MDSB) codes,which can be decoded iteratively. Simulation results of MDSB codes based on Single-parity-check (SPC) and Hamming codes are presented for an additive white Gaussian noise channel. It is shown that performance improves and the code rate decreases with the increasing dimension-ality. Convergence characteristics of iterative decoding are described in detail. Simulation results show that these systematic codes perform better than 2-dimensional counterparts, but have a disadvantage of error floor although they can provide near Shannon capacity's limit performance.MDSB codes offer a good performance versus complexity tradeoff if they use mixture of SPC and Hamming codes as their component codes.
Two-Dimensional NMR Lineshape Analysis
Waudby, Christopher A.; Ramos, Andres; Cabrita, Lisa D.; Christodoulou, John
2016-04-01
NMR titration experiments are a rich source of structural, mechanistic, thermodynamic and kinetic information on biomolecular interactions, which can be extracted through the quantitative analysis of resonance lineshapes. However, applications of such analyses are frequently limited by peak overlap inherent to complex biomolecular systems. Moreover, systematic errors may arise due to the analysis of two-dimensional data using theoretical frameworks developed for one-dimensional experiments. Here we introduce a more accurate and convenient method for the analysis of such data, based on the direct quantum mechanical simulation and fitting of entire two-dimensional experiments, which we implement in a new software tool, TITAN (TITration ANalysis). We expect the approach, which we demonstrate for a variety of protein-protein and protein-ligand interactions, to be particularly useful in providing information on multi-step or multi-component interactions.
Extra-dimensional confinement of quantum particles
Hedin, Eric R
2016-01-01
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and 5th spatial component. A higher-dimensional simple harmonic oscillator confining potential localizes particles into 3-d space, characterizing the brane tension which confines Standard Model particles to the sub-manifold. Quantum effects allow a non-zero probability for a particle's evanescent existence in the higher dimensions, and suggest an experimental test for the validity of this model via particles being temporarily excited into the first excited state of the extra-dimensional potential well, in which their probability of existing in 3-d space transiently drops to zero. Several consistency checks of the outcomes of this extra-dimensional model are included in this paper. Among the outcomes of this model are: a match with the quantum phenomenon of zitterbewegung; the pr...
Ligand-Stabilized Reduced-Dimensionality Perovskites.
Quan, Li Na; Yuan, Mingjian; Comin, Riccardo; Voznyy, Oleksandr; Beauregard, Eric M; Hoogland, Sjoerd; Buin, Andrei; Kirmani, Ahmad R; Zhao, Kui; Amassian, Aram; Kim, Dong Ha; Sargent, Edward H
2016-03-02
Metal halide perovskites have rapidly advanced thin-film photovoltaic performance; as a result, the materials' observed instabilities urgently require a solution. Using density functional theory (DFT), we show that a low energy of formation, exacerbated in the presence of humidity, explains the propensity of perovskites to decompose back into their precursors. We find, also using DFT, that intercalation of phenylethylammonium between perovskite layers introduces quantitatively appreciable van der Waals interactions. These drive an increased formation energy and should therefore improve material stability. Here we report reduced-dimensionality (quasi-2D) perovskite films that exhibit improved stability while retaining the high performance of conventional three-dimensional perovskites. Continuous tuning of the dimensionality, as assessed using photophysical studies, is achieved by the choice of stoichiometry in materials synthesis. We achieve the first certified hysteresis-free solar power conversion in a planar perovskite solar cell, obtaining a 15.3% certified PCE, and observe greatly improved performance longevity.
Localized shear generates three-dimensional transport
Smith, Lachlan D.; Rudman, Murray; Lester, Daniel R.; Metcalfe, Guy
2017-04-01
Understanding the mechanisms that control three-dimensional (3D) fluid transport is central to many processes, including mixing, chemical reaction, and biological activity. Here a novel mechanism for 3D transport is uncovered where fluid particles are kicked between streamlines near a localized shear, which occurs in many flows and materials. This results in 3D transport similar to Resonance Induced Dispersion (RID); however, this new mechanism is more rapid and mutually incompatible with RID. We explore its governing impact with both an abstract 2-action flow and a model fluid flow. We show that transitions from one-dimensional (1D) to two-dimensional (2D) and 2D to 3D transport occur based on the relative magnitudes of streamline jumps in two transverse directions.
Multi-Dimensional Recurrent Neural Networks
Graves, Alex; Schmidhuber, Juergen
2007-01-01
Recurrent neural networks (RNNs) have proved effective at one dimensional sequence learning tasks, such as speech and online handwriting recognition. Some of the properties that make RNNs suitable for such tasks, for example robustness to input warping, and the ability to access contextual information, are also desirable in multidimensional domains. However, there has so far been no direct way of applying RNNs to data with more than one spatio-temporal dimension. This paper introduces multi-dimensional recurrent neural networks (MDRNNs), thereby extending the potential applicability of RNNs to vision, video processing, medical imaging and many other areas, while avoiding the scaling problems that have plagued other multi-dimensional models. Experimental results are provided for two image segmentation tasks.
Accelerating cosmologies and a phase transition in M-theory
Wohlfarth, Mattias N.R
2003-06-19
M-theory compactifies on a seven-dimensional time-dependent hyperbolic or flat space to a four-dimensional FLRW cosmology undergoing a period of accelerated expansion in Einstein conformal frame. The strong energy condition is violated by the scalar fields produced in the compactification, as is necessary to evade the no-go theorem for time-independent compactifications. The four-form field strength of eleven-dimensional supergravity smoothly switches on during the period of accelerated expansion in hyperbolic compactifications, whereas in flat compactifications, the three-form potential smoothly changes its sign. For small acceleration times, this behaviour is like a phase transition of the three-form potential, during which the cosmological scale factor approximately doubles.
Accelerating Cosmologies and a Phase Transition in M-Theory
Wohlfarth, M N R
2003-01-01
M-theory compactifies on a seven-dimensional time-dependent hyperbolic or flat space to a four-dimensional FLRW cosmology undergoing a period of accelerated expansion in Einstein conformal frame. The strong energy condition is violated by the scalar fields produced in the compactification, as is necessary to evade the no-go theorem for time-independent compactifications. The four-form field strength of eleven-dimensional supergravity smoothly switches on during the period of accelerated expansion in hyperbolic compactifications, whereas in flat compactifications, the three-form potential smoothly changes its sign. For small acceleration times, this behaviour is like a phase transition of the three-form potential, during which the cosmological scale factor approximately doubles.
Dimensiones de la responsabilidad social del marketing
María Matilde Schwalb Helguero
2013-01-01
Full Text Available La creciente desconfianza ciudadana y las demandas del movimiento de defensa del consumidor presionan al marketing para que amplíe su función más allá del diseño de un buen marketing mix y para que las empresas se comprometan con la responsabilidad social (RS. Sin embargo, no se sabe cuáles son las dimensiones que comprende esta función ampliada del marketing. Por eso, este artículo tiene por objetivo identificar y validar las dimensiones que conforman el nuevo constructo Responsabilidad Social del Marketing (RSM. Con este fin se efectuó un análisis de contenido de instrumentos normativos y de diagnóstico de la RS y se sometió la propuesta de dimensiones e ítems de la RSM a la consideración de un panel de 40 expertos. Como resultado se identificaron seis dimensiones y se seleccionaron preliminarmente 141 ítems. El contenido de estas dimensiones sugiere que laRSMdebe invadir todos los niveles de la organización. La identificación y el contenido de estas dimensiones constituyen un aporte valioso para la comunidad académica del marketing, las empresas, los consumidores y los responsables de diseñar las políticas públicas. Con este estudio, se han cumplido los primeros pasos para el desarrollo de una escala fiable y válida que permita medir, en posteriores trabajos confirmatorios, la actitud del consumidor hacia la RSM.
Two-dimensional x-ray diffraction
He, Bob B
2009-01-01
Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea
Stationary one-dimensional dispersive shock waves
Kartashov, Yaroslav V
2011-01-01
We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defect in defocusing media with linear gain and two-photon absorption. We found that in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from defect or generating beam, the competition between gain and two-photon absorption in dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed certain critical value.
Dimensionality of high temperature superconductivity in oxides
Chu, C. W.
1989-01-01
Many models have been proposed to account for the high temperature superconductivity observed in oxide systems. Almost all of these models proposed are based on the uncoupled low dimensional carrier Cu-O layers of the oxides. Results of several experiments are presented and discussed. They suggest that the high temperature superconductivity observed cannot be strictly two- or one-dimensional, and that the environment between the Cu-O layers and the interlayer coupling play an important role in the occurrence of such high temperature superconductivity. A comment on the very short coherence length reported is also made.