Pro-torus actions on Poincaré duality spaces
Indian Academy of Sciences (India)
duality spaces, Borel's dimension formula and topological splitting principle to local weights, hold if 'torus' is replaced by 'pro-torus'. Keywords. Pro-torus; Poincaré duality space; local weight. 1. Introduction. In the theory of linear representations of compact connected Lie groups, the crucial first step is restriction to the ...
From Koszul duality to Poincaré duality
Indian Academy of Sciences (India)
2012-06-09
Jun 9, 2012 ... Our aim here is to describe elements of the formulation of the Koszul duality and ... Throughout this paper K denotes a (commutative) field and all vector ... the form A = T(E)/I where E is a finite-dimensional vector space and I is a finitely gen- .... for any n ∈ N. The Koszul complex of A is then defined to be the ...
Reduction of the Poincare gauge field equations by means of a duality rotation
International Nuclear Information System (INIS)
Mielke, E.W.
1981-10-01
A rather general procedure is developed in order to reduce the two field equations of the Poincare gauge theory of gravity by a modified ansatz for the curvature tensor involving double duality. In the case of quasi-linear Lagrangians of the Yang-Mills type it is shown that non-trivial torsion solutions with duality properties necessarily ''live'' on an Einstein space as metrical background. (author)
International Nuclear Information System (INIS)
Lukierski, J.; Ruegg, H.; Tolstoy, V.N.
1994-08-01
After a description of three distinguished bases proposed for k-Poincare algebra, the representations of the k-deformed Poincare algebra as differential operators acting on the functions of commuting moments are considered. Further, the duality between the k-Poincare algebra U n (P 4 ) and the quantum Poincare group P k is discussed. The recent developments of the k-deformed formalism are presented in conclusion. 51 refs
International Nuclear Information System (INIS)
Pusztai, B.G.
2011-01-01
In a symplectic reduction framework we construct action-angle systems of canonical coordinates for both the hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen integrable models associated with the C n root system. The presented dual reduction picture permits us to establish the action-angle duality between these many-particle systems.
Holography with broken Poincaré symmetry
Korovins, J.
2014-01-01
This thesis deals with the extensions of the holographic dualities to the situations where part of the Poincaré group has been broken. Such theories are particularly relevant for applications of gauge/gravity dualities to condensed matter systems, which usually exhibit non-relativistic symmetry.
Twisted classical Poincare algebras
International Nuclear Information System (INIS)
Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.
1993-11-01
We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)
On the duality condition for quantum fields
International Nuclear Information System (INIS)
Bisognano, J.J.; Wichmann, E.H.
1976-01-01
A general quantum field theory is considered in which the fields are assumed to be operator-valued tempered distributions. The system of fields may include any number of boson fields and fermion fields. A theorem which relates certain complex Lorentz transformations to the TCP transformation is stated and proved. With reference to this theorem, duality conditions are considered, and it is shown that such conditions hold under various physically reasonable assumptions about the fields. Extensions of the algebras of field operators are discussed with reference to the duality conditions. Local internal symmetries are discussed, and it is shown that these commute with the Poincare group and with the TCP transformation
Extended Poincare supersymmetry
International Nuclear Information System (INIS)
Strathdee, J.
1986-05-01
Supersymmetric extensions of the Poincare algebra in D-dimensional space-time are reviewed and a catalogue of their representations is developed. This catalogue includes all supermultiplets whose states carry helicity <2 in the massless cases and <=1 in the massive cases. (author)
Some remarks on defects and T-duality
DEFF Research Database (Denmark)
Sarkissian, Gor; Schweigert, Christoph
2009-01-01
The equations of motion for a conformal field theory in the presence of defect lines can be derived from an action that includes contributions from bibranes. For T-dual toroidal compactifications, they imply a direct relation between Poincaré line bundles and the action of T-duality on boundary...
Poincare gauge in electrodynamics
International Nuclear Information System (INIS)
Brittin, W.E.; Smythe, W.R.; Wyss, W.
1982-01-01
The gauge presented here, which we call the Poincare gauge, is a generalization of the well-known expressions phi = -rxE 0 and A = 1/2 B 0 x r for the scalar and vector potentials which describe static, uniform electric and magnetic fields. This gauge provides a direct method for calculating a vector potential for any given static or dynamic magnetic field. After we establish the validity and generality of this gauge, we use it to produce a simple and unambiguous method of computing the flux linking an arbitrary knotted and twisted closed circuit. The magnetic flux linking the curve bounding a Moebius band is computed as a simple example. Arguments are then presented that physics students should have the opportunity of learning early in their curriculum modern geometric approaches to physics. (The language of exterior calculus may be as important to future physics as vector calculus was to the past.) Finally, an appendix illustrates how the Poincare gauge (and others) may be derived from Poincare's lemma relating exact and closed exterior differential forms
International Nuclear Information System (INIS)
Zakharov, V.I.
2009-01-01
A mini-review concerning the duality between higher orders in perturbative expansions and the quadratic power corrections to the parton model. The note contains no new results and is prompted by a continuing controversy in the literature. Sometimes one considers the two ways of describing QCD observables - in terms of a long perturbative series and in terms of the leading quadratic power correction - as contradicting to each other. While they are in fact dual to each other
Duality Quantum Information and Duality Quantum Communication
International Nuclear Information System (INIS)
Li, C. Y.; Wang, W. Y.; Wang, C.; Song, S. Y.; Long, G. L.
2011-01-01
Quantum mechanical systems exhibit particle wave duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi-slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d-slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so-called duality quantum computing mode. The quantum particle-wave duality can be used in providing secure communication. In this paper, we will review duality quantum computing and duality quantum key distribution.
On pseudoparticle solutions in the Poincare gauge theory of gravity
International Nuclear Information System (INIS)
Mielke, E.W.
1983-12-01
The dynamical structure of the Poincare gauge field theory coupled to matter fields and some of its implications for a quantum theory of gravity are investigated. Essentially, the method of Belavin et al. for generating instanton solutions in Yang-Mills theory is transferred to the gravitational gauge model. The results are as follows: For configurations obeying a modified double duality Ansatz for the curvature the metrical background is determined by Einstein-type field equations coupled almost canonically to the stress-energy content of external fields. Exact electrovac solutions with non-trivial torsion are derived from the duality Ansatz. In a Euclidean space-time the corresponding pseudoparticle solutions are expected to play a dominant role in the quantization of gravity via Feynman's method of path integrals. (author)
International Nuclear Information System (INIS)
Ogievetsky, O.; Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA
1992-01-01
The q-differential calculus for the q-Minkowski space is developed. The algebra of the q-derivatives with the q-Lorentz generators is found giving the q-deformation of the Poincare algebra. The reality structure of the q-Poincare algebra is given. The reality structure of the q-differentials is also found. The real Laplaacian is constructed. Finally the comultiplication, counit and antipode for the q-Poincare algebra are obtained making it a Hopf algebra. (orig.)
A natural Poincare gauge model
International Nuclear Information System (INIS)
Aldrovandi, R.; Pereira, J.G.
1985-01-01
A natural candidate model for a gauge theory for the Poincare group is discussed. It satisfies the usual electric-magnetic symmetry of gauge models and is a contraction of a gauge model for the De Sitter group. Its field equations are just the Yang-Mills equations for the Poincare group. It is shown that these equations do not follow from a Lagrangean. (Author) [pt
Dittrich, K.; Jaspers, F.P.H.; Valk, van der W.; Wynstra, J.Y.F.
2006-01-01
This paper introduces the topic of dealing with dualities, which is the theme of this special issue. We first give a short review of the notion of paradox and duality in management research. After this, we discuss the relevance of dualities for the IMP approach of analyzing industrial networks.
Unification of string dualities
International Nuclear Information System (INIS)
Sen, A.
1997-01-01
We argue that all conjectured dualities involving various string, M- and F-theory compactifications can be 'derived' from the conjectured duality between type I and SO(32) heterotic string theory, T-dualities and the definition of M-and F-theories. (orig.)
Planar Poincare chart - A planar graphic representation of the state of light polarization
Tedjojuwono, Ken K.; Hunter, William W., Jr.; Ocheltree, Stewart L.
1989-01-01
The planar Poincare chart, which represents the complete planar equivalence of the Poincare sphere, is proposed. The four sets of basic lines are drawn on two separate charts for the generalization and convenience of reading the scale. The chart indicates the rotation of the principal axes of linear birefringent material. The relationships between parameters of the two charts are given as 2xi-2phi (orientation angle of the major axis-ellipticity angle) pair and 2alpha-delta (angle of amplitude ratio-phase difference angle) pair. The results are useful for designing and analyzing polarization properties of optical components with birefringent properties.
Duality in vector optimization
Bot, Radu Ioan
2009-01-01
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the s
Poincare invariant algebra from instant to light-front quantization
International Nuclear Information System (INIS)
Ji, Chueng-Ryong; Mitchell, Chad
2001-01-01
We present the Poincare algebra interpolating between instant and light-front time quantizations. The angular momentum operators satisfying SU(2) algebra are constructed in an arbitrary interpolation angle and shown to be identical to the ordinary angular momentum and Leutwyler-Stern angular momentum in the instant and light-front quantization limits, respectively. The exchange of the dynamical role between the transverse angular mometum and the boost operators is manifest in our newly constructed algebra
Plane wave limits and T-duality
International Nuclear Information System (INIS)
Guven, R.
2000-04-01
The Penrose limit is generalized to show that, any leading order solution of the low-energy field equations in any one of the five string theories has a plane wave solution as a limit. This limiting procedure takes into account all the massless fields that may arise and commutes with the T-duality so that any dual solution has again a plane wave limit. The scaling rules used in the limit are unique and stem from the scaling property of the D = 11 supergravity action. Although the leading order dual solutions need not be exact or supersymmetric, their plane wave limits always preserve some portion of the Poincare supersymmetry and solve the relevant field equations in all powers of the string tension parameter. Further properties of the limiting procedure are discussed. (author)
Duality and supersymmetric monopoles
International Nuclear Information System (INIS)
Gauntlett, J.P.
1998-01-01
Exact duality in supersymmetric gauge theories leads to highly non-trivial predictions about the moduli spaces of BPS monopole solutions. These notes attempt to be a pedagogical review of the current status of these investigations. (orig.)
Duality ensures modular covariance
International Nuclear Information System (INIS)
Li Miao; Yu Ming
1989-11-01
We show that the modular transformations for one point functions on the torus, S(n), satisfy the polynomial equations derived by Moore and Seiberg, provided the duality property of the model is ensured. The formula for S(n) is derived by us previously and should be valid for any conformal field theory. As a consequence, the full consistency conditions for modular invariance at higher genus are completely guaranteed by duality of the theory on the sphere. (orig.)
Remarks on unitary representations of Poincare group
International Nuclear Information System (INIS)
Burzynski, A.
1979-01-01
In this paper the elementary review of methods and notions using in the theory of unitary representations of Poincare group is included. The Poincare group is a basic group for relativistic quantum mechanics. Our aim is to introduce the reader into some problems of quantum physics, which are difficult approachable for beginners. (author)
Henri Poincaré a scientific biography
Gray, Jeremy
2013-01-01
The first in-depth and comprehensive look at his many accomplishments, Jeremy Gray explores all the fields that Poincar touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today. Math historian Jeremy Gray shows that Poincar's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincar conjecture. And Poincar's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincar the public intellectual did not shy away from scientific controversy, and he defended mathematics against ...
Poincare covariance and κ-Minkowski spacetime
International Nuclear Information System (INIS)
Dabrowski, Ludwik; Piacitelli, Gherardo
2011-01-01
A fully Poincare covariant model is constructed as an extension of the κ-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincare group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincare covariance is realised a la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of 'Poincare covariance'. -- Highlights: → We construct a 4d model of noncommuting coordinates (quantum spacetime). → The coordinates are fully covariant under the undeformed Poincare group. → Covariance a la Wigner holds in presence of two dimensionful parameters. → Hence we are not forced to deform covariance (e.g. as quantum groups). → The underlying κ-Minkowski model is unphysical; covariantisation does not cure this.
Mass and spin of double dual solutions in Poincare gauge theory
International Nuclear Information System (INIS)
Mielke, E.W.; Wallner, R.P.
1988-01-01
Mass and spin are derived for a class of exact solutions of the Poincare gauge (PG) theory of gravity, provided the curvature fulfills a modified double-duality ansatz. It is executed a (3+1)-decomposition and clarified and semplified the structure of the energy-momentum and spin complexes. In case the quadratic PG Lagrangian contains the curvature-square pieces in the Yang-Mills fashion, the (3+1)-decomposition provides rather detailed information on admissible solutions. The PG energy-momentum complex turns out to be intimately related to the von Freud complex of general relativity
Dualities in five dimensions and charged string solutions
International Nuclear Information System (INIS)
Kar, S.; Maharana, J.
1996-01-01
We consider an eleven dimensional supergravity compactified on K3 x T 2 and show that the resulting five dimensional theory has identical massless states as that of a heterotic string compactified on a specific five torus T 5 . The strong-weak coupling duality of the five dimensional theory is argued to represent a ten dimensional Type IIA string compactified on K3 x S 1 , supporting the conjecture of string-string duality in six dimensions. In this perspective, we present a magnetically charged solution of the low energy heterotic string effective action in five dimensions with a charge defined on a three sphere S 3 due to the two form potential. We use the Poincare duality to replace the antisymmetric two form with a gauge field in the effective action and obtain a string solution with charge on a two sphere S 2 instead of that on a three sphere S 3 in the five dimensional spacetime. We note that the string-particle duality is accompanied by a change of topology from S 3 to S 2 and vice versa. (orig.)
Duality and 'particle' democracy
Castellani, Elena
2017-08-01
Weak/strong duality is usually accompanied by what seems a puzzling ontological feature: the fact that under this kind of duality what is viewed as 'elementary' in one description gets mapped to what is viewed as 'composite' in the dual description. This paper investigates the meaning of this apparent 'particle democracy', as it has been called, by adopting an historical approach. The aim is to clarify the nature of the correspondence between 'dual particles' in the light of a historical analysis of the developments of the idea of weak/strong duality, starting with Dirac's electric-magnetic duality and its successive generalizations in the context of (Abelian and non-Abelian) field theory, to arrive at its first extension to string theory. This analysis is then used as evidential basis for discussing the 'elementary/composite' divide and, after taking another historical detour by analyzing an instructive analogy case (DHS duality and related nuclear democracy), drawing some conclusions on the particle-democracy issue.
International Nuclear Information System (INIS)
Henneaux, Marc; Teitelboim, Claudio
2005-01-01
We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two superpotentials, one for the spatial components of the spin-2 field and the other for their canonically conjugate momenta. These superpotentials are two-index, symmetric tensors. They can be taken to be the basic dynamical fields and appear locally in the action. They are simply rotated into each other under duality. In terms of the superpotentials, the canonical generator of duality rotations is found to have a Chern-Simons-like structure, as in the Maxwell case
Supersymmetry and gravitational duality
International Nuclear Information System (INIS)
Argurio, Riccardo; Dehouck, Francois; Houart, Laurent
2009-01-01
We study how the supersymmetry algebra copes with gravitational duality. As a playground, we consider a charged Taub-Newman-Unti-Tamburino(NUT) solution of D=4, N=2 supergravity. We find explicitly its Killing spinors, and the projection they obey provides evidence that the dual magnetic momenta necessarily have to appear in the supersymmetry algebra. The existence of such a modification is further supported using an approach based on the Nester form. In the process, we find new expressions for the dual magnetic momenta, including the NUT charge. The same expressions are then rederived using gravitational duality.
International Nuclear Information System (INIS)
Brown, T.W.
2010-11-01
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)
Entanglement entropy and duality
Energy Technology Data Exchange (ETDEWEB)
Radičević, Ðorđe [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305-4060 (United States)
2016-11-22
Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.
Energy Technology Data Exchange (ETDEWEB)
Brown, T.W.
2010-11-15
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)
The scientific legacy of Poincaré
Charpentier, Éric; Lesne, Annick; Bowman, Joshua
2010-01-01
Henri Poincaré (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions. He revolutionized celestial mechanics, discovering deterministic chaos. In physics, he is one of the fathers of special relativity, and his work in the philosophy of sciences is illuminating. For this book, about twenty world experts were asked to present one part of Poincaré's extraordinary work. Each chapter treats one theme, presenting Poincaré's approach, and achievements, along with examples of recent applications and some current prospects. Their contributions emphasize the power and modernity of the work of Poincaré, an inexhaustible source of inspiration for researchers, as illustrated by the...
Forgotten and neglected theories of Poincare
International Nuclear Information System (INIS)
Arnold, V.I.
2006-04-01
This paper describes a number of published and unpublished works of Henri Poincare that await continuation by the next generations of mathematicians: works on celestial mechanics, on topology, on the theory of chaos and dynamical systems, and on homology, intersections and links. Also discussed are the history of the theory of relativity and the theory of functions and the connection between the Poincare conjecture and the theory of knot invariants. (author)
Forgotten and neglected theories of Poincare
International Nuclear Information System (INIS)
Arnol'd, Vladimir I
2006-01-01
This paper describes a number of published and unpublished works of Henri Poincare that await continuation by the next generations of mathematicians: works on celestial mechanics, on topology, on the theory of chaos and dynamical systems, and on homology, intersections and links. Also discussed are the history of the theory of relativity and the theory of generalized functions (distributions) and the connection between the Poincare conjecture and the theory of knot invariants.
A heuristic algorithm for computing the Poincar\\'e series of the invariants of binary forms
Djoković, Dragomir Ž.
2006-01-01
We propose a heuristic algorithm for fast computation of the Poincar\\'{e} series $P_n(t)$ of the invariants of binary forms of degree $n$, viewed as rational functions. The algorithm is based on certain polynomial identities which remain to be proved rigorously. By using it, we have computed the $P_n(t)$ for $n\\le30$.
Magnetic bottles on the Poincar\\'e half-plane: spectral asymptotics
Morame, Abderemane; Truc, Francoise
2007-01-01
We consider a magnetic laplacian P(A) on the Poincar\\'e half-plane, when the magnetic field dA is infinite at infinity such that P(A) has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.
S-duality in N = 4 supersymmetric gauge theories with arbitrary gauge group
International Nuclear Information System (INIS)
Dorey, Nicholas; Fraser, Christophe; Hollowood, Timothy J.; Kneipp, Marco A.C.
1996-12-01
The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in the Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle θ. This extended S-duality conjecture includes the case when the unbroken gauge group in non-Abelian and a definite prediction for the spectrum of dyons results. (author)
From 3 d duality to 2 d duality
Aharony, Ofer; Razamat, Shlomo S.; Willett, Brian
2017-11-01
In this paper we discuss 3 d N = 2 supersymmetric gauge theories and their IR dualities when they are compactified on a circle of radius r, and when we take the 2 d limit in which r → 0. The 2 d limit depends on how the mass parameters are scaled as r → 0, and often vacua become infinitely distant in the 2 d limit, leading to a direct sum of different 2 d theories. For generic mass parameters, when we take the same limit on both sides of a duality, we obtain 2 d dualities (between gauge theories and/or Landau-Ginzburg theories) that pass all the usual tests. However, when there are non-compact branches the discussion is subtle because the metric on the moduli space, which is not controlled by supersymmetry, plays an important role in the low-energy dynamics after compactification. Generally speaking, for IR dualities of gauge theories, we conjecture that dualities involving non-compact Higgs branches survive. On the other hand when there is a non-compact Coulomb branch on at least one side of the duality, the duality fails already when the 3 d theories are compactified on a circle. Using the valid reductions we reproduce many known 2 d IR dualities, giving further evidence for their validity, and we also find new 2 d dualities.
International Nuclear Information System (INIS)
Alvarez-Gaume, L.; Gomez, C.; Sierra, G.
1990-01-01
We show that the duality properties of Rational Conformal Field Theories follow from the defining relations and the representation theory of quantum groups. The fusion and braiding matrices are q-analogues of the 6j-symbols and the modular transformation matrices are obtained from the properties of the co-multiplication. We study in detail the Wess-Zumino-Witten models and the rational gaussian models as examples, but carry out the arguments in general. We point out the connections with the Chern-Simons approach. We give general arguments of why the general solution to the polynomial equations of Moore and Seiberg describing the duality properties of Rational Conformal Field Theories defines a Quantum Group acting on the space of conformal blocks. A direct connection between Rational Theories and knot invariants is also presented along the lines of Jones' original work. (orig.)
Pretko, Michael; Radzihovsky, Leo
2018-05-01
Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.
Energy Technology Data Exchange (ETDEWEB)
Strassler, M J [University of Pennsylvania, Philadelphia, PA (United States)
2002-05-15
Confinement in four-dimensional gauge theories is considered from several points of view. General features are discussed, and the mechanism of confinement is investigated. Dualities between field theories, and duality between field theory and string theory, are both put to use. In these lectures I have given an overview of some of the key ideas underlying confinement as a property of field theory, and now, of string theory as well. This is a tiny fraction of what field theory (and now string theory) is capable of, and we are still uncovering new features on a monthly basis. In fact, most field theories do not have confinement, for reasons entirely different from those of QCD. Many become nontrivial conformal field theories at low energy. Others become composite, weakly-coupled gauge theories. Dualities of many stripes are found everywhere. Ordinary dimensional analysis in string theory is totally wrong in the regime where it looks like weakly-coupled field theory, and ordinary dimensional analysis in field theory is totally wrong in the regime where it looks like weakly-coupled supergravity.
Poincaré recurrences of DNA sequences
Frahm, K. M.; Shepelyansky, D. L.
2012-01-01
We analyze the statistical properties of Poincaré recurrences of Homo sapiens, mammalian, and other DNA sequences taken from the Ensembl Genome data base with up to 15 billion base pairs. We show that the probability of Poincaré recurrences decays in an algebraic way with the Poincaré exponent β≈4 even if the oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent ν≈0.6 that leads to an anomalous superdiffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than one million base pairs. We argue that the approach based on Poncaré recurrences determines new proximity features between different species and sheds a new light on their evolution history.
Off-shell Poincaré supergravity
Energy Technology Data Exchange (ETDEWEB)
Freedman, Daniel Z. [SITP and Department of Physics, Stanford University,Stanford, California 94305 (United States); Center for Theoretical Physics and Department of Mathematics,Massachusetts Institute of Technology,Cambridge, Massachusetts 02139 (United States); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Proeyen, Antoine Van [KU Leuven, Institute for Theoretical Physics,Celestijnenlaan 200D, B-3001 Leuven (Belgium)
2017-02-21
We present the action and transformation rules of Poincaré supergravity coupled to chiral multiplets (z{sup α},χ{sup α},h{sup α}) with off-shell auxiliary fields. Starting from the geometric formulation of the superconformal theory with auxiliary fields, we derive the Poincaré counterpart by gauge-fixing the Weyl and chiral symmetry and S-supersymmetry. We show how this transition is facilitated by retaining explicit target-space covariance. Our results form a convenient starting point to study models with constrained superfields, including general matter-coupled de Sitter supergravity.
Free fields on the Poincare group
Energy Technology Data Exchange (ETDEWEB)
Toller, M; Vanzo, L [Dipartimento di Matematica e Fisica della Libera Universita di Trento, Italy
1978-07-01
Using a general formalism the tensor and spinor free fields as fields defined on the Poincare group manifold is treated. From an action principle it is deduced, besides the usual Klein-Gordon or Dirac equations, also the equations which describe the transformation properties of the fields under proper Lorentz transformations.
Direct gauging of the Poincare group
International Nuclear Information System (INIS)
Edelen, D.G.B.
1985-01-01
The problem of gauging matter fields with a Poincare invariant action functional that admits an r parameter, semisimple group G(r) of internal symmetries is considered. A minimal replacement operator for the total group P 10 xG(r) is obtained, together with the requisite compensating 1-forms for both the Poincare and the G(r) sectors. A basis for P 10 xG(r)-invariant Lagrangian densities for the free fields is obtained. Restriction to Lagrangian densities that are at most quadratic in the associated curvature and torsion fields eliminates active coupling between the P 10 free field Lagrangian and the G(r) free field Lagrangian, although there is passive coupling that arises through the requirement of tensorial covariance under general coordinate transformations generated by the local action of the translation group. A superposition principle, modulo passive coupling, thus holds for quadratic free field Lagrangian for the total group: Lsub(TOT)=Lsub(p)+Lsub(G(r)). Field equations for the matter fields and the compensating fields of the G(r) sector are obtained. Both share the passive coupling to P 10 that is required in order to achieve ''tensorial'' covariance, but only the matter fields couple directly to the Poincare fields and only to the Lorentz sector. For ''weak'' Poincare fields, the field equations for the matter fields and the compensating fields of the internal symmetries go over into the standard field equations of gauge theory for an internal symmetry group. (author)
Sacramento, P. D.; Vieira, V. R.
2018-04-01
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.
International Nuclear Information System (INIS)
Townsend, P.
1995-01-01
The author suggest that the discovery of ''hidden'' symmetries in the subatomic world will, in due time succeed in uniting the strong and weak nuclear forces and the electromagnetic force (already successfully united in the Standard Model) with the fourth universal force, gravity, to produce a ''unified theory of everything''. Concepts such as groups, in the context of quantum field theory, supersymmetry and superstrings are explained to back this contention. Recent work on the nature of electromagnetic duality, may, it is argued, increase our comprehension to a level where ''theories of everything'' may emerge. (UK)
Duality after supersymmetry breaking
International Nuclear Information System (INIS)
Shadmi, Yael; Cheng, Hsin-Chia
1998-05-01
Starting with two supersymmetric dual theories, we imagine adding a chiral perturbation that breaks supersymmetry dynamically. At low energy we then get two theories with soft supersymmetry-breaking terms that are generated dynamically. With a canonical Kaehler potential, some of the scalars of the ''magnetic'' theory typically have negative mass-squared, and the vector-like symmetry is broken. Since for large supersymmetry breaking the ''electric'' theory becomes ordinary QCD, the two theories are then incompatible. For small supersymmetry breaking, if duality still holds, the magnetic theory analysis implies specific patterns of chiral symmetry breaking in supersymmetric QCD with small soft masses
Multivalued synchronization by Poincaré coupling
Ontañón-García, L. J.; Campos-Cantón, E.; Femat, R.; Campos-Cantón, I.; Bonilla-Marín, M.
2013-10-01
This work presents multivalued chaotic synchronization via coupling based on the Poincaré plane. The coupling is carried out by an underdamped signal, triggered every crossing event of the trajectory of the master system through a previously defined Poincaré plane. A master-slave system is explored, and the synchronization between the systems is detected via the auxiliary system approach and the maximum conditional Lyapunov exponent. Due to the response to specific conditions two phenomena may be obtained: univalued and multivalued synchronization. Since the Lyapunov exponent is not enough to detect these two phenomena, the distance between the pieces of trajectories of the slave and auxiliary systems with different initial conditions is also used as a tool for the detection of multivalued synchronization. Computer simulations using the benchmark chaotic systems of Lorenz and Rössler are used to exemplify the approach proposed.
Asymptotic Poincare lemma and its applications
International Nuclear Information System (INIS)
Ziolkowski, R.W.; Deschamps, G.A.
1984-01-01
An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures
International Nuclear Information System (INIS)
Volkov, D.V.; Zheltukhin, A.A.; Pashnev, A.I.
1975-01-01
As it has shown, the study of vacuum transitions in dual models makes it possible to establish certain relations between duality, on the one hand, and the quark structure of resonances and the internal symmetries, on the other. In the case of Veneziano model the corresponding quark structure of resonances is determined by the infinity number of quarks of increasing mass. The intercents of the main trajectory and all adopted trajectories are additive with respect to squares of mass-forming quarks. The latter circumstance results in a number of important consequences: the presence of quadratic mass formulas for resonance states; the exact SU(infinity)-symmetry for the three-resonance coupling constants; the validity of Adler's self-consistency principle for external particles composed of different quarks and anti-quarks, etc
Conformal amplitude hierarchy and the Poincaré disk
Shimada, Hirohiko
2018-02-01
The amplitude for the singlet channels in the 4-point function of the fundamental field in the conformal field theory of the 2d O(n) model is studied as a function of n. For a generic value of n, the 4-point function has infinitely many amplitudes, whose landscape can be very spiky as the higher amplitude changes its sign many times at the simple poles, which generalize the unique pole of the energy operator amplitude at n = 0. In the stadard parameterization of n by angle in unit of π, we find that the zeros and poles happen at the rational angles, forming a hierarchical tree structure inherent in the Poincaré disk. Some relation between the amplitude and the Farey path, a piecewise geodesic that visits these zeros and poles, is suggested. In this hierarchy, the symmetry of the congruence subgroup Γ(2) of SL(2, ℤ) naturally arises from the two clearly distinct even/odd classes of the rational angles, in which one respectively gets the truncated operator algebras and the logarithmic 4-point functions.
Topological field theories and duality
International Nuclear Information System (INIS)
Stephany, J.; Universidad Simon Bolivar, Caracas
1996-05-01
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifold are discussed in a simple example, and their relation with the properties of Topological Field Theories is established. (author). 16 refs
The Power of Poincar\\'e: Elucidating the Hidden Symmetries in Focal Conic Domains
Alexander, Gareth P.; Chen, Bryan Gin-ge; Matsumoto, Elisabetta A.; Kamien, Randall D.
2010-01-01
Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincar\\'e symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal...
Travelling Randomly on the Poincar\\'e Half-Plane with a Pythagorean Compass
Cammarota, Valentina; Orsingher, Enzo
2011-01-01
A random motion on the Poincar\\'e half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the case where returns to the starting point are admitted. The main results concern the mean hyperbolic distance (and also the conditional mean distance) in all versions of the motion envisaged. Also an analogous motion on orthogonal circles of the sphere is examined and the evolution of the mean distance from th...
Dualities and emergent gravity: Gauge/gravity duality
de Haro, Sebastian
2017-08-01
In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', from the physics literature, cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence (via coarse-graining). I apply this framework to gauge/gravity dualities, considering in detail three examples: AdS/CFT, Verlinde's scheme, and black holes. My main point about gauge/gravity dualities is that the theories involved, qua theories of gravity, must be background-independent. I distinguish two senses of background-independence: (i) minimalistic and (ii) extended. I argue that the former is sufficiently strong to allow for a consistent theory of quantum gravity; and that AdS/CFT is background-independent on this account; while Verlinde's scheme best fits the extended sense of background-independence. I argue that this extended sense should be applied with some caution: on pain of throwing the baby (general relativity) out with the bath-water (extended background-independence). Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction. It suggests some directions for possible generalisations of gauge/gravity dualities. The interpretation of dualities is discussed; and the so-called 'internal' vs. 'external' viewpoints are articulated in terms of: (i) epistemic and metaphysical commitments; (ii) parts vs. wholes. I then analyse the emergence of gravity in gauge/gravity dualities in terms of the two available conceptualisations of emergence; and I show how emergence in AdS/CFT and in Verlinde's scenario differ from each other. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on
String dualities and superpotential
International Nuclear Information System (INIS)
Ha, Tae-Won
2010-09-01
The main objective of this thesis is the computation of the superpotential induced by D5- branes in the type IIB string theory and by five-branes in the heterotic string theory. Both superpotentials have the same functional form which is the chain integral of the holomorphic three-form. Using relative (co)homology we can unify the flux and brane superpotential. The chain integral can be seen as an example of the Abel-Jacobi map. We discuss many structures such as mixed Hodge structure which allows for the computation of Picard-Fuchs differential equations crucial for explicit computations. We blow up the Calabi-Yau threefold along the submanifold wrapped by the brane to obtain geometrically more appropriate configuration. The resulting geometry is non-Calabi-Yau and we have a canonically given divisor. This blown-up geometry makes it possible to restrict our attention to complex structure deformations. However, the direct computation is yet very difficult, thus the main tool for computation will be the lift of the brane configuration to a F-theory compactification. In F-theory, since complex structure, brane and, if present, bundlemoduli are all contained in the complex structure moduli space of the elliptic Calabi-Yau fourfold, the computation can be dramatically simplified. The heterotic/F-theory duality is extended to include the blow-up geometry and thereby used to give the blow-up geometry amore physical meaning. (orig.)
International Nuclear Information System (INIS)
Johnson, C.V.
1998-01-01
The nature of M-theory on K3 x I, where I is a line interval, is considered, with a view towards formulating a ''matrix theory'' representation of that situation. Various limits of this compactification of M-theory yield a number of well known N=1 six-dimensional compactifications of the heterotic and type I string theories. Geometrical relations between these limits give rise to string/string dualities between some of these compactifications. At a special point in the moduli space of compactifications, this motivates a partial definition of the matrix theory representation of the M-theory on K3 x I as the large N limit of a certain type IA orientifold model probed by a conglomerate of N D-branes. Such a definition in terms of D-branes and orientifold planes is suggestive, but necessarily incomplete, due to the low amount of supersymmetry. It is proposed - following hints from the orientifold model - that the complete matrix theory representation of the K3 x I compactified M-theory is given by the large N limit of compactification - on a suitable ''dual'' surface - of the ''little heterotic string'' N=1 six-dimensional quantum theories. (orig.)
String dualities and superpotential
Energy Technology Data Exchange (ETDEWEB)
Ha, Tae-Won
2010-09-15
The main objective of this thesis is the computation of the superpotential induced by D5- branes in the type IIB string theory and by five-branes in the heterotic string theory. Both superpotentials have the same functional form which is the chain integral of the holomorphic three-form. Using relative (co)homology we can unify the flux and brane superpotential. The chain integral can be seen as an example of the Abel-Jacobi map. We discuss many structures such as mixed Hodge structure which allows for the computation of Picard-Fuchs differential equations crucial for explicit computations. We blow up the Calabi-Yau threefold along the submanifold wrapped by the brane to obtain geometrically more appropriate configuration. The resulting geometry is non-Calabi-Yau and we have a canonically given divisor. This blown-up geometry makes it possible to restrict our attention to complex structure deformations. However, the direct computation is yet very difficult, thus the main tool for computation will be the lift of the brane configuration to a F-theory compactification. In F-theory, since complex structure, brane and, if present, bundlemoduli are all contained in the complex structure moduli space of the elliptic Calabi-Yau fourfold, the computation can be dramatically simplified. The heterotic/F-theory duality is extended to include the blow-up geometry and thereby used to give the blow-up geometry amore physical meaning. (orig.)
(Non-)Abelian Kramers-Wannier duality and topological field theory
Severa, Pavol
2002-01-01
We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for higher-dimensional cases. In this form they lead to simple TFTs with boundary coloured in two colours. The statistical models live on the boundary of these TFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-Lie T-duality) suggest a non-abelian generalization in the 2dcase, with abelian groups replaced by quantum groups. Amazingly, the TFT formulation solves the problem without computation: quantum groups appear in pictures, independently of the classical motivation. Connection with Chern-Simons theory appears at the symplectic level, and also in the pictures of the Drinfeld double: Reshetikhin-Turaev invariants of links in 3-manifolds, computed from the double, are included in these TFTs. All this suggests nice phenomena in higher dimensions.
Spontaneously broken supersymmetry and Poincare invariance
International Nuclear Information System (INIS)
Tata, X.R.; Sudarshan, E.C.G.; Schechter, J.M.
1982-12-01
It is argued that the spontaneous breakdown of global supersymmetry is consistent with unbroken Poincare invariance if and only if the supersymmetry algebra A = 0 is understood to mean the invariance of the dynamical variables phi under the transformations generated by the algebra, i.e. [A, phi] = 0 rather than as an operator equation. It is further argued that this weakening of the algebra does not alter any of the conclusions about supersymmetric quantum field theories that have been obtained using the original (stronger) form of the algebra
Spontaneously broken supersymmetry and Poincare invariance
International Nuclear Information System (INIS)
Tata, X.R.; Sudarshan, E.C.G.; Schechter, J.M.
1983-01-01
It is argued that the spontaneous breakdown of global supersymmetry is consistent with unbroken Poincare invariance if and only if the supersymmetry algebra 'A=0' is understood to mean the invariance of the dynamical variables phi under the transformations generated by the algebra, i.e. [A, phi]=0 rather than as an operator equation. It is further argued that this 'weakening' of the algrebra does not alter any of the conclusions about supersymmetry quantum field theories that have been obtained using the original (stronger) form of the algebra. (orig.)
International Nuclear Information System (INIS)
Paulot, Louis
2003-01-01
In their search for a unified theory of fundamental interactions, with quantum gravity, physicists introduced superstring theories. In addition to the fundamental strings, they contain extended objects of diverse dimensions, exchanged by U-duality groups. There is also a conjectured mother theory, called 'M-theory', which would give eleven-dimensional supergravity in the low energy limit. In this work, we show that one can construct from del Pezzo surfaces generalized Kac-Moody super-algebras which extend U-duality groups. These super-algebras give the bosonic fields content of M-theory dimensional reductions. We recover the fields equations of motion as a self-duality condition, related to a symmetry of the Picard lattice of the corresponding del Pezzo surface. This allows to explain the symmetry of the 'magic triangle' of Cremmer, Julia, Lue and Pope. (author) [fr
Duality rotations for interacting fields
International Nuclear Information System (INIS)
Gaillard, M.K.; Zumino, Bruno
1981-05-01
We study the properties of interacting field theories which are invariant under duality rotations which transform a vector field strength into its dual. We consider non-abelian duality groups and find that the largest group for n interacting field strengths is the non-compact Sp(2n,R), which has U(n) as its maximal compact subgroup. We show that invariance of the equations of motion requires that the Lagrangian change in a particular way under duality. We use this property to demonstrate the existence of conserved currents, the invariance of the energy momentum tensor, and also in the general construction of the Lagrangian. Finally we comment on the existence of zero mass spin one bound states in N=8 supergravity, which possesses a non-compact E 7 dual invariance
Killings, duality and characteristic polynomials
Álvarez, Enrique; Borlaf, Javier; León, José H.
1998-03-01
In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved. © 1998
Lectures on strings and dualities
International Nuclear Information System (INIS)
Vafa, C.
1997-01-01
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in string theory accessible to those with no previous background in string theory who wish to join the research effort in this area. Topics covered include a brief review of string theory, its compactifications, solitons and D-branes, black hole entropy and wed of string dualities. (author)
Henri Poincaré: Death centenary (1854-1912)
Heinzmann, Gerhard; Villani, Cédric
2014-08-01
The year 2012 marked the centenary of the death of Henri Poincaré (Nancy, 1854-Paris, 1912), and through the agency of the Henri-Poincaré Institute in Paris, the Henri-Poincaré Archives in Nancy and The London Mathematical Society, brought with it several exhibitions and meetings commemorating one of the greatest minds in contemporary times. Often referred to as the last polymath, Poincaré embraced multiple branches of mathematics, theoretical physics and celestial mechanics, and made significant contributions to philosophy of science (Heinzmann & Stump, Henri Poincaré, 2013). He wrote 25 textbooks and monographs, 500-plus articles, and was deeply involved in the organization and administration of science at both the national and international levels.1
Poincare ball embeddings of the optical geometry
International Nuclear Information System (INIS)
Abramowicz, M A; Bengtsson, I; Karas, V; Rosquist, K
2002-01-01
It is shown that the optical geometry of the Reissner-Nordstroem exterior metric can be embedded in a hyperbolic space all the way down to its outer horizon. The adopted embedding procedure removes a breakdown of flat-space embeddings which occurs outside the horizon, at and below the Buchdahl-Bondi limit (R/M=9/4 in the Schwarzschild case). In particular, the horizon can be captured in the optical geometry embedding diagram. Moreover, by using the compact Poincare ball representation of the hyperbolic space, the embedding diagram can cover the whole extent of radius from spatial infinity down to the horizon. Attention is drawn to the advantages of such embeddings in an appropriately curved space: this approach gives compact embeddings and it clearly distinguishes the case of an extremal black hole from a non-extremal one in terms of the topology of the embedded horizon
Duplantier, Bertrand; Raimond, Jean-Michel; Rivasseau, Vincent
2016-01-01
This fourteenth volume in the Poincaré Seminar Series is devoted to Niels Bohr, his foundational contributions to understanding atomic structure and quantum theory and their continuing importance today. This book contains the following chapters: - Tomas Bohr, Keeping Things Open; - Olivier Darrigol, Bohr's Trilogy of 1913; -John Heilbron, The Mind that Created the Bohr Atom; - Serge Haroche & Jean-Michel Raimond, Bohr's Legacy in Cavity QED; - Alain Aspect, From Einstein, Bohr, Schrödinger to Bell and Feynman: a New Quantum Revolution?; - Antoine Browaeys, Interacting Cold Rydberg Atoms: A Toy Many-Body System; - Michel Bitbol & Stefano Osnaghi, Bohr´s Complementarity and Kant´s Epistemology. Dating from their origin in lectures to a broad scientific audience these seven chapters are of high educational value. This volume is of general interest to physicists, mathematicians and historians.
Biological Physics : Poincaré seminar
Bio-physique : séminaire Poincaré
2011-01-01
This new volume in the Poincaré Seminar Series, describing recent developments at the interface between physics and biology, is directed towards a broad audience of physicists, biologists, and mathematicians. Both the theoretical and experimental aspects are covered, and particular care is devoted to the pedagogical nature of the presentations. The first survey article, by Jean-Francois Joanny and Jacques Prost, describes the theoretical advances made in the study of "active gels", with applications to liquid crystals and cell motility. Jasper van der Gucht and Cécile Sykes then report on recent advances made with biomimetic model systems in the understanding of cytokinesis. The next article, by Jonathon Howard, presents several molecular models for motor proteins, which are compared with experimental results for kinesin. David Lacoste and Kirone Mallick then show theoretically that similar ratchet models of motor proteins naturally satisfy a fundamental time-reversal symmetry, the Gallavotti-Cohen fluctuat...
Gravitation as Gauge theory of Poincare Group
International Nuclear Information System (INIS)
Stedile, E.
1982-08-01
The geometrical approach to gauge theories, based on fiber-bundles, is shown in detail. Several gauge formalisms for gravitation are examined. In particular, it is shown how to build gauge theories for non-semisimple groups. A gravitational theory for the Poincare group, with all the essential characteristics of a Yang-Mills theory is proposed. Inonu-Wigner contractions of gauge theories are introduced, which provide a Lagrangian formalism, equivalent to a Lagrangian de Sitter theory supplemented by weak constraints. Yang and Einstein theories for gravitation become particular cases of a Yang-Mills theory. The classical limit of the proposed formalism leads to the Poisson equation, for the static case. (Author) [pt
Poincaré chaos and unpredictable functions
Akhmet, Marat; Fen, Mehmet Onur
2017-07-01
The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.
A duality web in condensed matter systems
Ma, Chen-Te
2018-03-01
We study various dualities in condensed matter systems. The dualities in three dimensions can be derived from a conjecture of a duality between a Dirac fermion theory and an interacting scalar field theory at a Wilson-Fisher fixed point and zero temperature in three dimensions. We show that the dualities are not affected by non-trivial holonomy, use a mean-field method to study the dualities, and discuss the dualities at a finite temperature. Finally, we combine a bulk theory, which is an Abelian p-form theory with a theta term in 2 p + 2 dimensions, and a boundary theory, which is a 2 p + 1 dimensional theory, to discuss constraints and difficulties of a 2 p + 1 dimensional duality web.
Poincare indices for analyzing meditative heart rate signals
Directory of Open Access Journals (Sweden)
Atefeh Goshvarpour
2015-06-01
Full Text Available Background: Poincare plots are commonly used to study the nonlinear behavior of physiologic signals. The aim of this study is to evaluate the Poincare plot indices of human heart rate signals during meditation. Methods: For this purpose, heart rate time series of eight Chi meditators available in Physionet database were used. Poincare plots with lags of 1 and 6 were constructed, and the ratio of the minor axis to major axis (SD1/SD2 and the area of Poincare plots were calculated for each lag. Results: The results show that the SD1/SD2 ratio increased significantly during meditation compared to that before meditation, especially the index measured from Poincare plots reconstructed with a lag of 6 (p < 0.05. In addition, in both lags, the area of Poincare plots decreased significantly during meditation compared to before meditation (p < 0.05. Conclusion: The comparative dynamic measures of the Poincare plot indices during and before meditation give more insight of the heart rate signals in a specific psychophysiological state.
Duality in diffraction dissociations
International Nuclear Information System (INIS)
Santoro, Alberto.
1977-01-01
Diffractive dissociations (aN→a*πN) are naturally explained and a model that accounts for the three-variable correlation (mass-transfer-Jackson angle correlation) is presented. This model takes into account the three possible exchanges: t (pion), u(a*) and s(a) channel exchanger. The physical consequences of the model are: a strong mass-slope correlation due to the zeros of the amplitude, a factorization of diffractive dissociations (factorization of the Pomeron), the possibility of extending this model to double diffractive dissociation and diffraction by nuclei. This model was applied to the NN→NπN reaction. Using the usual parameters of the Deck model, a comparison is made with experiments for all available distributions. the strong slope of the peak at 1400 MeV is naturally explained [fr
Poincaré, philosopher of science problems and perspectives
DiSalle, Robert
2014-01-01
This volume presents a selection of papers from the Poincaré Project of the Center for the Philosophy of Science, University of Lisbon, bringing together an international group of scholars with new assessments of Henri Poincaré's philosophy of science—both its historical impact on the foundations of science and mathematics, and its relevance to contemporary philosophical inquiry. The work of Poincaré (1854-1912) extends over many fields within mathematics and mathematical physics. But his scientific work was inseparable from his groundbreaking philosophical reflections, and the scientific ferment in which he participated was inseparable from the philosophical controversies in which he played a pre-eminent part. The subsequent history of the mathematical sciences was profoundly influenced by Poincaré’s philosophical analyses of the relations between and among mathematics, logic, and physics, and, more generally, the relations between formal structures and the world of experience. The papers in this col...
Hilbert space, Poincare dodecahedron and golden mean transfiniteness
International Nuclear Information System (INIS)
El Naschie, M.S.
2007-01-01
A rather direct connection between Hilbert space and E-infinity theory is established via an irrational-transfinite golden mean topological probability. Subsequently the ramifications for Kleinian modular spaces and the cosmological Poincare Dodecahedron proposals are considered
Fractional Poincaré inequalities for general measures
Mouhot, Clément
2011-01-01
We prove a fractional version of Poincaré inequalities in the context of Rn endowed with a fairly general measure. Namely we prove a control of an L2 norm by a non-local quantity, which plays the role of the gradient in the standard Poincaré inequality. The assumption on the measure is the fact that it satisfies the classical Poincaré inequality, so that our result is an improvement of the latter inequality. Moreover we also quantify the tightness at infinity provided by the control on the fractional derivative in terms of a weight growing at infinity. The proof goes through the introduction of the generator of the Ornstein-Uhlenbeck semigroup and some careful estimates of its powers. To our knowledge this is the first proof of fractional Poincaré inequality for measures more general than Lévy measures. © 2010 Elsevier Masson SAS.
Kleshchev, Alexander
2017-01-01
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.
International Nuclear Information System (INIS)
Hislop, P.D.
1988-01-01
The Tomita modular operators and the duality property for the local von Neumann algebras in quantum field models describing free massless particles with arbitrary helicity are studied. It is proved that the representation of the Poincare group in each model extends to a unitary representation of SU(2, 2), a covering group of the conformal group. An irreducible set of ''standard'' linear fields is shown to be covariant with respect to this representation. The von Neumann algebras associated with wedge, double-cone, and lightcone regions generated by these fields are proved to be unitarily equivalent. The modular operators for these algebras are obtained in explicit form using the conformal covariance and the results of Bisognano and Wichmann on the modular structure of the wedge algebras. The modular automorphism groups are implemented by one-parameter groups of conformal transformations. The modular conjugation operators are used to prove the duality property for the double-cone algebras and the timelike duality property for the lightcone algebras. copyright 1988 Academic Press, Inc
Serre duality, Abel's theorem, and Jacobi inversion for supercurves over a thick superpoint
Rothstein, Mitchell J.; Rabin, Jeffrey M.
2015-04-01
The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1 | q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincaré duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic groups and class fields, combined with an invariance result for the topology on the dual of the space of répartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.
Euler-Poincare reduction for discrete field theories
International Nuclear Information System (INIS)
Vankerschaver, Joris
2007-01-01
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed
Hidden twelve-dimensional super Poincare symmetry in eleven dimensions
International Nuclear Information System (INIS)
Bars, Itzhak; Deliduman, Cemsinan; Pasqua, Andrea; Zumino, Bruno
2004-01-01
First, we review a result in our previous paper, of how a ten-dimensional superparticle, taken off-shell, has a hidden eleven-dimensional super Poincare symmetry. Then, we show that the physical sector is defined by three first-class constraints which preserve the full eleven-dimensional symmetry. Applying the same concepts to the eleven-dimensional superparticle, taken off-shell, we discover a hidden twelve-dimensional super Poincare symmetry that governs the theory
On massless representations of the Q-deformed Poincare algebra
International Nuclear Information System (INIS)
Ogievetsky, O.; Pillin, M.; Schmidke, W.B.; Wess, J.
1993-01-01
This talk is devoted to the construction of massless representations of the q-deformed Poincare algebra. In section 2 we give Hilbert space representations of the SL q (2, C)-covariant quantum space. We then show in the next section how the generators of the q-Poincare algebra can be expressed in terms of operators which live in the light cone. The q-deformed massless one-particle states are considered in section 4. (orig.)
Thermal duality and gravitational collapse
International Nuclear Information System (INIS)
Hewitt, Michael
2015-01-01
Thermal duality is a relationship between the behaviour of heterotic string models of the E(8)×E(8) or SO(32) types at inversely related temperatures, a variant of T duality in the Euclidean regime. This duality would have consequences for the nature of the Hagedorn transition in these string models. We propose that the vacuum admits a family of deformations in situations where there are closed surfaces of constant area but high radial acceleration (a string regularized version of a Penrose trapped surface), such as would be formed in situations of extreme gravitational collapse. This would allow a radical resolution of the firewall paradox by allowing quantum effects to significantly modify the spacetime geometry around a collapsed object. A string bremsstrahlung process would convert the kinetic energy of infalling matter in extreme gravitational collapse to form a region of the deformed vacuum, which would be equivalent to forming a high temperature string phase. A heuristic criterion for the conversion process is presented, relating Newtonian gravity to the string tension, suggesting an upper limit to the strength of the gravitational interaction. This conversion process might have observable consequences for charged particles falling into a rotating collapsed object by producing high energy particles via a variant of the Penrose process. (paper)
Holographic duality: Stealing dimensions from metals
Zaanen, Jan
2013-10-01
Although electrically charged black holes seem remote from superconductors and strange metals in the laboratory, they might be intimately related by the holographic dualities discovered in string theory.
Non-hermitian symmetric N = 2 coset models, Poincare polynomials, and string compactification
International Nuclear Information System (INIS)
Fuchs, J.; Schweigert, C.
1994-01-01
The field identification problem, including fixed point resolution, is solved for the non-hermitian symmetric N = 2 superconformal coset theories. Thereby these models are finally identified as well-defined modular invariant conformal field theories. As an application, the theories are used as subtheories in N = 2 tensor products with c = 9, which in turn are taken as the inner sector of heterotic superstring compactifications. All string theories of this type are classified, and the chiral ring as well as the number of massless generations and anti-generations are computed with the help of the extended Poincare polynomial. Several equivalences between a priori different non-hermitian coset theories show up; in particular there is a level-rank duality for an infinite series of coset theories based on C-type Lie algebras. Further, some general results for generic N = 2 coset theories are proven: a simple formula for the number of identification currents is found, and it is shown that the set of Ramond ground states of any N = 2 coset model is invariant under charge conjugation. (orig.)
Morita duality for monoids / Peeter Normak
Normak, Peeter
1990-01-01
In this paper Morita duality for monoids is introduced. Necessary and sufficient conditions for two monoids S and T to be Morita dual are given. Moreover, it is shown that if S and T are Morita dual monoids, then S and U are Moriaddition, every finite monoid having Morita duality is selfdual and even reflexive.
Duality for heavy-quark systems
International Nuclear Information System (INIS)
Durand, B.; Durand, L.
1981-01-01
We give a proof of the duality relation approx. = for nonrelativistic potential models, using Feynman propagators. There are important and calculable corrections to the duality relation, both for smooth long-range potentials and for singular short-range potentials. We illustrate the corrections for the exactly solvable harmonic-oscillator, linear, and Hulthen potentials
Duality in non-linear programming
Jeyalakshmi, K.
2018-04-01
In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
Prime Factorization in the Duality Computer
International Nuclear Information System (INIS)
Wang Wanying; Wang Chuan; Long Guilu; Shang Bin
2007-01-01
We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in classical computing. All these algorithms may be polynomial in the input size.
Supersymmetry: Compactification, flavor, and dualities
Heidenreich, Benjamin Jones
N = 1 gauge theory dualities relating different world-volume gauge theories of D3 branes probing an orientifold singularity. We argue that these dualities originate from the S-duality of type IIB string theory, much like electromagnetic dualities of N = 4 gauge theories.
Poincaré and the three body problem
Barrow-Green, June
1997-01-01
The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincaré, on a problem in celestial mechanics: the three body problem. This ancient problem-to describe the paths of three bodies in mutual gravitational interaction-is one of those which is simple to pose but impossible to solve precisely. Poincaré's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincaré and the Three Body Problem opens with a discussion of the development of the th...
Ring wormholes via duality rotations
Directory of Open Access Journals (Sweden)
Gary W. Gibbons
2016-09-01
Full Text Available We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy–Voorhees–Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than −c4/4G. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a hole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations.
A generalized 2-D Poincaré inequality
Directory of Open Access Journals (Sweden)
Crisciani Fulvio
2000-01-01
Full Text Available Two 1-D Poincaré-like inequalities are proved under the mild assumption that the integrand function is zero at just one point. These results are used to derive a 2-D generalized Poincare inequality in which the integrand function is zero on a suitable arc contained in the domain (instead of the whole boundary. As an application, it is shown that a set of boundary conditions for the quasi geostrophic equation of order four are compatible with general physical constraints dictated by the dissipation of kinetic energy.
Three-body forces mandated by Poincare invariance
International Nuclear Information System (INIS)
Coester, F.
1986-01-01
Poincare invariant models for the three-nucleon system are examined which have the same heuristic relation to field theories as the nonrelativistic nuclear models. The generators of the infinitesimal dynamical transformations can be obtained as functions of the kinematic generators, the invariant mass operator of the interacting system, and additional operators. These additional operators are the components of the Newton-Wigner position operator in the instant form, and the transverse components of the spin in the front form. The relativistic dynamics of Poincare transformations is examined, and then these concepts are applied to two-nucleon systems. The transition to a fully interacting three-nucleon system is made
Euler-Poincare Reduction of Externall Forced Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Euler-Poincare Reduction of a Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2005-01-01
|If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system afected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems......-known Euler-Poincare reduction to a rigid body motion with forcing....
Euler-Poincaré Reduction of a Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Lorentz and Poincaré invariance 100 years of relativity
Hsu Jong Ping
2001-01-01
This collection of papers provides a broad view of the development of Lorentz and Poincaré invariance and spacetime symmetry throughout the past 100 years. The issues explored in these papers include: (1) formulations of relativity theories in which the speed of light is not a universal constant but which are consistent with the four-dimensional symmetry of the Lorentz and Poincaré groups and with experimental results, (2) analyses and discussions by Reichenbach concerning the concepts of simultaneity and physical time from a philosophical point of view, and (3) results achieved by the union o
General Duality for Perpetual American Options
Alfonsi, Aurélien; Jourdain, Benjamin
2006-01-01
In this paper, we investigate the generalization of the Call-Put duality equality obtained in Alfonsi and Jourdain (preprint, 2006, available at ) for perpetual American options when the Call-Put payoff (y - x)+ is replaced by ϕ(x,y). It turns out that the duality still holds under monotonicity and concavity assumptions on ϕ. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the derivation of the Call-Put duality equality for Europ...
Aspects of space-time dualities
Giveon, Amit
1996-01-01
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling matrices. We interpret (some of) such dualities as the geometrical symmetries of compactified theories in higher dimensions. In particular, we consider compactifications of a (self-dual) 2-form in 6-D, and compactifications of a self-dual 4-form in 10-D. Relations with a self-dual superstring in 6-D and with the type IIB superstring are discussed.
Freudenthal duality and generalized special geometry
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio, E-mail: sergio.ferrara@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Marrani, Alessio, E-mail: Alessio.Marrani@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); Yeranyan, Armen, E-mail: ayeran@lnf.infn.it [INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics, Yerevan State University, Alex Manoogian St. 1, Yerevan, 0025 (Armenia)
2011-07-27
Freudenthal duality, introduced in Borsten et al. (2009) and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential. Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.
Persson, Daniel; Volpato, Roberto
2018-04-01
We define a very general class of CHL-models associated with any string theory S (bosonic or supersymmetric) compactified on an internal CFT C× Td . We take the orbifold by a pair (g, δ) , where g is a (possibly non-geometric) symmetry of C and δ is a translation along T n . We analyze the T-dualities of these models and show that in general they contain Atkin–Lehner type symmetries. This generalizes our previous work on N=4 CHL-models based on heterotic string theory on T 6 or type II on K3× T2 , as well as the ‘monstrous’ CHL-models based on a compactification of heterotic string theory on the Frenkel–Lepowsky–Meurman CFT V\
Törnqvist, N A
1972-01-01
As shown by Deck, the double-peripheral model for three-particle final states gives a substantial low-mass enhancement over phase space in two-body subchannels. With the advent of duality it was conjectured that the Deck effect and a true resonance are just different manifestations of the same phenomena. Thus the presence of a Deck enhancement could be interpreted as evidence for the existence of the A/sub 1/ resonance. The conjecture has been subject to criticism of two different kinds. These two points are clarified by constructing a counter example to the conjecture of Chew and Pignotti, using the five-point amplitude (B/sub 5/) of the generalized Veneziano model. (8 refs).
Duality for discrete integrable systems
International Nuclear Information System (INIS)
Quispel, G R W; Capel, H W; Roberts, J A G
2005-01-01
A new class of discrete dynamical systems is introduced via a duality relation for discrete dynamical systems with a number of explicitly known integrals. The dual equation can be defined via the difference of an arbitrary linear combination of integrals and its upshifted version. We give an example of an integrable mapping with two parameters and four integrals leading to a (four-dimensional) dual mapping with four parameters and two integrals. We also consider a more general class of higher-dimensional mappings arising via a travelling-wave reduction from the (integrable) MKdV partial-difference equation. By differencing the trace of the monodromy matrix we obtain a class of novel dual mappings which is shown to be integrable as level-set-dependent versions of the original ones
Direct mediation, duality and unification
International Nuclear Information System (INIS)
Abel, Steven; Khoze, Valentin V.
2008-01-01
It is well-known that in scenarios with direct gauge mediation of supersymmetry breaking the messenger fields significantly affect the running of Standard Model couplings and introduce Landau poles which are difficult to avoid. Among other things, this appears to remove any possibility of a meaningful unification prediction and is often viewed as a strong argument against direct mediation. We propose two ways that Seiberg duality can circumvent this problem. In the first, which we call 'deflected-unification', the SUSY-breaking hidden sector is a magnetic theory which undergoes a Seiberg duality to an electric phase. Importantly, the electric version has fewer fundamental degrees of freedom coupled to the MSSM compared to the magnetic formulation. This changes the β-functions of the MSSM gauge couplings so as to push their Landau poles above the unification scale. We show that this scenario is realised for recently suggested models of gauge mediation based on a metastable SCQD-type hidden sector directly coupled to MSSM. The second possibility for avoiding Landau poles, which we call 'dual-unification', begins with the observation that, if the mediating fields fall into complete SU(5) multiplets, then the MSSM+messengers exhibits a fake unification at unphysical values of the gauge couplings. We show that, in known examples of electric/magnetic duals, such a fake unification in the magnetic theory reflects a real unification in the electric theory. We therefore propose that the Standard Model could itself be a magnetic dual of some unknown electric theory in which the true unification takes place. This scenario maintains the unification prediction (and unification scale) even in the presence of Landau poles in the magnetic theory below the GUT scale. We further note that this dual realization of grand unification can explain why Nature appears to unify, but the proton does not decay.
Aspects of Poincare's program for dynamical systems and mathematical physics
Verhulst, Ferdinand
2012-01-01
This article is mainly historical, except for the discussion of integrability and characteristic exponents in Sect. 2. After summarising the achievements of Henri Poincaré, we discuss his theory of critical exponents. The theory is applied to the case of three degreesof- freedom Hamiltonian systems
Harmonic Function of Poincare Cone Condition In Solving Dirichlet ...
African Journals Online (AJOL)
Harmonic Function of Poincare Cone Condition In Solving Dirichlet Problem. ... Journal of the Nigerian Association of Mathematical Physics ... theorem, the dirichlet problem and maximum principle where we conclude that the application of sums , differences and scalar multiples of harmonic functions are again harmonic.
A superparticle on the 'super' Poincare upper half plane
International Nuclear Information System (INIS)
Uehara, S.; Yasui, Yukinora
1988-01-01
A non-relativistic superparticle moving freely on the 'super' Poincare upper half plane is investigated. The lagrangian is invariant under the super Moebius transformations SPL (2, R), so that it can be projected into the lagrangian on the super Riemann surface. The quantum hamiltonian becomes the 'super' Laplace-Beltrami operator in the curved superspace. (orig.)
Superparticle on the 'super' Poincare upper half plane
Energy Technology Data Exchange (ETDEWEB)
Uehara, S; Yasui, Yukinora
1988-03-17
A non-relativistic superparticle moving freely on the 'super' Poincare upper half plane is investigated. The lagrangian is invariant under the super Moebius transformations SPL (2, R), so that it can be projected into the lagrangian on the super Riemann surface. The quantum hamiltonian becomes the 'super' Laplace-Beltrami operator in the curved superspace.
Extension of Poincare's program for integrability, chaos and bifurcations
Verhulst, Ferdinand|info:eu-repo/dai/nl/068380437
2012-01-01
We will review the achievements of Henri Poincar e in the theory of dy- namical systems and will add a number of extensions and generalizations of his results. It is pointed out that the attention given to two degrees-of-freedom Hamiltonian sys- tems is rather deceptive as near stable equilibrium
On the quantization of the Poincare gange model
International Nuclear Information System (INIS)
Aldrovandi, R.; Pereira, J.G.
1986-01-01
A gauge model based on the Yang-Mills equations for the Poincare group cannot be consistently quantized, at least in a perturbative approach. The problem is related to the absence of a Lagrangian. Adding the counterterms required by consistency and renormalizability turns the model into a gauge theory for a de Sitter group. (Author) [pt
Quark-Hadron Duality in Electron Scattering
Energy Technology Data Exchange (ETDEWEB)
Wally Melnitchouk; Rolf Ent; Cynthia Keppel
2004-08-01
The duality between partonic and hadronic descriptions of physical phenomena is one of the most remarkable features of strong interaction physics. A classic example of this is in electron-nucleon scattering, in which low-energy cross sections, when averaged over appropriate energy intervals, are found to exhibit the scaling behavior expected from perturbative QCD. We present a comprehensive review of data on structure functions in the resonance region, from which the global and local aspects of duality are quantified, including its flavor, spin and nuclear medium dependence. To interpret the experimental findings, we discuss various theoretical approaches which have been developed to understand the microscopic origins of quark-hadron duality in QCD. Examples from other reactions are used to place duality in a broader context, and future experimental and theoretical challenges are identified.
Color-kinematic duality for form factors
International Nuclear Information System (INIS)
Boels, Rutger H.; Kniehl, Bernd A.; Tarasov, Oleg V.; Yang, Gang
2012-12-01
Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory observables formed by form factors. After a discussion of the general setup the existence of the duality is verified in two and three loop examples in four dimensional maximally supersymmetric Yang-Mills theory which involve the stress energy tensor multiplet. In these cases the duality reproduces known results in a particularly transparent and uniform way. As a non-trivial application we obtain a very simple form of the integrand of the four-loop two-point (Sudakov) form factor which passes a large set of unitarity cut checks.
Color-kinematic duality for form factors
Energy Technology Data Exchange (ETDEWEB)
Boels, Rutger H.; Kniehl, Bernd A.; Tarasov, Oleg V.; Yang, Gang [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2012-12-15
Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory observables formed by form factors. After a discussion of the general setup the existence of the duality is verified in two and three loop examples in four dimensional maximally supersymmetric Yang-Mills theory which involve the stress energy tensor multiplet. In these cases the duality reproduces known results in a particularly transparent and uniform way. As a non-trivial application we obtain a very simple form of the integrand of the four-loop two-point (Sudakov) form factor which passes a large set of unitarity cut checks.
Fourier duality as a quantization principle
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs
Introduction to dualities in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kneipp, Marco A.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: kneipp@cbpf.br
2000-12-01
These notes present a pedagogical introduction to magnetic monopoles, supersymmetry and dualities in gauge theories. They are based on lectures given at the X Jorge Andre Swieca Summer School on Particles and Fields. (author)
Can (electric-magnetic) duality be gauged?
International Nuclear Information System (INIS)
Bunster, Claudio; Henneaux, Marc
2011-01-01
There exists a formulation of the Maxwell theory in terms of two vector potentials, one electric and one magnetic. The action is then manifestly invariant under electric-magnetic duality transformations, which are rotations in the two-dimensional internal space of the two potentials, and local. We ask the question: Can duality be gauged? The only known and battle-tested method of accomplishing the gauging is the Noether procedure. In its decanted form, it amounts to turning on the coupling by deforming the Abelian gauge group of the free theory, out of whose curvatures the action is built, into a non-Abelian group which becomes the gauge group of the resulting theory. In this article, we show that the method cannot be successfully implemented for electric-magnetic duality. We thus conclude that, unless a radically new idea is introduced, electric-magnetic duality cannot be gauged. The implication of this result for supergravity is briefly discussed.
A nonabelian particle–vortex duality
Directory of Open Access Journals (Sweden)
Jeff Murugan
2016-02-01
Full Text Available We define a nonabelian particle–vortex duality as a 3-dimensional analogue of the usual 2-dimensional worldsheet nonabelian T-duality. The transformation is defined in the presence of a global SU(2 symmetry and, although derived from a string theoretic setting, we formulate it generally. We then apply it to so-called “semilocal strings” in an SU(2G×U(1L gauge theory, originally discovered in the context of cosmic string physics.
SLE local martingales, reversibility and duality
Energy Technology Data Exchange (ETDEWEB)
Kytoelae, Kalle; Kemppainen, Antti [Department of Mathematics and Statistics, PO Box 68, FIN-00014 University of Helsinki (Finland)
2006-11-17
We study Schramm-Loewner evolutions (SLEs) reversibility and duality using the Virasoro structure of the space of local martingales. For both problems we formulate a setup where the questions boil down to comparing two processes at a stopping time. We state algebraic results showing that local martingales for the processes have enough in common. When one has in addition integrability, the method gives reversibility and duality for any polynomial expected value. (letter to the editor)
SLE local martingales, reversibility and duality
International Nuclear Information System (INIS)
Kytoelae, Kalle; Kemppainen, Antti
2006-01-01
We study Schramm-Loewner evolutions (SLEs) reversibility and duality using the Virasoro structure of the space of local martingales. For both problems we formulate a setup where the questions boil down to comparing two processes at a stopping time. We state algebraic results showing that local martingales for the processes have enough in common. When one has in addition integrability, the method gives reversibility and duality for any polynomial expected value. (letter to the editor)
Deconfined Quantum Critical Points: Symmetries and Dualities
Directory of Open Access Journals (Sweden)
Chong Wang
2017-09-01
Full Text Available The deconfined quantum critical point (QCP, separating the Néel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of (2+1D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher criticality. In this work, we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low-energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to N_{f}=2 fermionic quantum electrodynamics, which has its own self-duality and hence may have an O(4×Z_{2}^{T} symmetry. We propose several dualities for the deconfined QCP with SU(2 spin symmetry which together make natural the emergence of a previously suggested SO(5 symmetry rotating the Néel and valence bond solid orders. These emergent symmetries are implemented anomalously. The associated infrared theories can also be viewed as surface descriptions of (3+1D topological paramagnets, giving further insight into the dualities. We describe a number of numerical tests of these dualities. We also discuss the possibility of “pseudocritical” behavior for deconfined critical points, and the meaning of the dualities and emergent symmetries in such a scenario.
Nonlinear self-duality and supergravity
International Nuclear Information System (INIS)
Kuzenko, Sergei M.; McCarthy, Shane A.
2003-01-01
The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N=1 supergravity, for both the old minimal and the new minimal versions of N=1 supergravity. We derive the self-duality equation, which has to be satisfied by the action functional of any U(1) duality invariant model of a massless vector multiplet, and construct a family of self-dual nonlinear models. This family includes a curved superspace extension of the N=1 super Born-Infeld action. The supercurrent and supertrace in such models are proved to be duality invariant. The most interesting and unexpected result is that the requirement of nonlinear self-duality yields nontrivial couplings of the vector multiplet to Kaehler sigma models. We explicitly derive the couplings to general Kaehler sigma models in the case when the matter chiral multiplets are inert under the duality rotations, and more specifically to the dilaton-axion chiral multiplet when the group of duality rotations is enhanced to SL(2,R). (author)
Nonlinear self-duality in even dimensions
International Nuclear Information System (INIS)
Aschieri, Paolo; Brace, Daniel; Morariu, Bogdan; Zumino, Bruno
2000-01-01
We show that the Born-Infeld theory with n complex abelian gauge fields written in an auxiliary field formulation has a U(n, n) duality group. We conjecture the form of the Lagrangian obtained by eliminating the auxiliary fields and then introduce a new reality structure leading to a Born-Infeld theory with n real gauge fields and an Sp(2n, IR) duality symmetry. The real and complex constructions are extended to arbitrary even dimensions. The maximal noncompact duality group is U(n, n) for complex fields. For real fields the duality group is Sp(2n, IR) if half of the dimension of space-time is even and O(n, n) if it is odd. We also discuss duality under the maximal compact subgroup, which is the self-duality group of the theory obtained by fixing the expectation value of a scalar field. Supersymmetric versions of self-dual theories in four dimensions are also discussed
Discrete gravity as a local theory of the Poincare group in the first-order formalism
Energy Technology Data Exchange (ETDEWEB)
Gionti, Gabriele [Vatican Observatory Research Group, Steward Observatory, 933 North Cherry Avenue, University of Arizona, Tucson, AZ 85721 (United States); Specola Vaticana, V-00120 Citta Del Vaticano (Vatican City State, Holy See,)
2005-10-21
A discrete theory of gravity, locally invariant under the Poincare group, is considered as in a companion paper. We define a first-order theory, in the sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex. We follow the same spirit as the continuum theory of general relativity in the Cartan formalism. The field equations are carefully derived taking in account the constraints of the theory. They look very similar to first-order Einstein continuum equations in the Cartan formalism. It is shown that in the limit of small deficit angles these equations have Regge calculus, locally, as the only solution. A quantum measure is easily defined which does not suffer the ambiguities of Regge calculus, and a coupling with fermionic matter is easily introduced.
Discrete gravity as a local theory of the Poincare group in the first-order formalism
International Nuclear Information System (INIS)
Gionti, Gabriele
2005-01-01
A discrete theory of gravity, locally invariant under the Poincare group, is considered as in a companion paper. We define a first-order theory, in the sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex. We follow the same spirit as the continuum theory of general relativity in the Cartan formalism. The field equations are carefully derived taking in account the constraints of the theory. They look very similar to first-order Einstein continuum equations in the Cartan formalism. It is shown that in the limit of small deficit angles these equations have Regge calculus, locally, as the only solution. A quantum measure is easily defined which does not suffer the ambiguities of Regge calculus, and a coupling with fermionic matter is easily introduced
Poincaré Embeddings for Learning Hierarchical Representations
CERN. Geneva
2018-01-01
Abstracts: Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically do not account for this property. In this talk, I will discuss a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability. &...
Orbifold construction of the modes of the Poincare dodecahedral space
International Nuclear Information System (INIS)
Lachieze-Rey, Marc; Weeks, Jeffrey
2008-01-01
We provide a new construction of the modes of the Poincare dodecahedral space S 3 /I*. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S 3 /I*, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves
Orbifold construction of the modes of the Poincare dodecahedral space
Energy Technology Data Exchange (ETDEWEB)
Lachieze-Rey, Marc [Astroparticule et Cosmologie (APC), CNRS-UMR 7164 (France); Weeks, Jeffrey [15 Farmer Street, Canton, New York (United States)
2008-07-25
We provide a new construction of the modes of the Poincare dodecahedral space S{sup 3}/I*. The construction uses the Hopf map, Maxwell's multipole vectors and orbifolds. In particular, the *235-orbifold serves as a parameter space for the modes of S{sup 3}/I*, shedding new light on the geometrical significance of the dimension of each space of k-modes, as well as on the modes themselves.
A demonstration of particle duality of light
Jiang, Haili; Liu, Zhihai; Sun, Qiuhua; Zhao, Yancheng
2017-08-01
The need of understanding and teaching about wave-particle duality if light with gets more and more apparent in the background of the attention of modern physics. As early as the beginning of twentieth Century, Einstein dared to "deny" the development of a very perfect light electromagnetic theory, so that the quantum of light can be developed. In 1924, De Broglie put forward wave-particle duality if light to other micro particles and the concept of matter wave, pointed out that all micro particle has wave-particle duality. This is a very abstract concept for students, most college physics teaching all lack of demonstration about particle duality of light. The present article aims to contribute to demonstrate the wave-particle duality of light at the same time using a simple way based on fiber optical tweezers. It is hoped that useful lesson can be absorbed so that students can deepen the understanding of the particle and wave properties of light. To complement the demonstration experiment for this attribute light has momentum.
General Quantum Interference Principle and Duality Computer
International Nuclear Information System (INIS)
Long Guilu
2006-01-01
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
Henri Poincaré a biography through the daily papers
Ginoux, Jean-Marc
2014-01-01
On July 17, 2012, the centenary of Henri Poincaré's death was commemorated; his name being associated with so many fields of knowledge that he was considered as the Last Universalist. In Pure and Applied Mathematics, Physics, Astronomy, Engineering and Philosophy, his works have had a great impact all over the world. Poincaré acquired in his lifetime such a reputation that, both nationally and internationally, his life and career were made the object of various articles in the daily papers not only in France, but also in the USA. Some of his philosophical concepts have even caused sharp controversies in the Press (as we will discover in this book).This work presents an original portrait of Henri Poincaré based on various press cuttings from The New York Times, The San Francisco Sunday Call, The Times, The Sun, The Washington Post that chronicled unknown anecdotes of his life (for example, his first name was actually not Henri, but Henry; he obtained his high school diploma in sciences with a zero in mathem...
Organizational identity construction in family businesses a dualities perspective
Boers, Börje
2013-01-01
This dissertation is about organizational identity construction with a dualities perspective. By taking a dualities perspective the focus shifts from assuming that organizational identity actually is in place towards organizational identity construction where identities are socially constructed. A dualities perspective is very suitable for studying family business where family and business are seen as interdependent and interconnected forming a duality. Family business is an identity statemen...
Interactive Spacecraft Trajectory Design Strategies Featuring Poincare Map Topology
Schlei, Wayne R.
Space exploration efforts are shifting towards inexpensive and more agile vehicles. Versatility regarding spacecraft trajectories refers to the agility to correct deviations from an intended path or even the ability to adapt the future path to a new destination--all with limited spaceflight resources (i.e., small DeltaV budgets). Trajectory design methods for such nimble vehicles incorporate equally versatile procedures that allow for rapid and interactive decision making while attempting to reduce Delta V budgets, leading to a versatile trajectory design platform. A versatile design paradigm requires the exploitation of Poincare map topology , or the interconnected web of dynamical structures, existing within the chaotic dynamics of multi-body gravitational models to outline low-Delta V transfer options residing nearby to a current path. This investigation details an autonomous procedure to extract the periodic orbits (topology nodes) and correlated asymptotic flow structures (or the invariant manifolds representing topology links). The autonomous process summarized in this investigation (termed PMATE) overcomes discontinuities on the Poincare section that arise in the applied multi-body model (the planar circular restricted three-body problem) and detects a wide variety of novel periodic orbits. New interactive capabilities deliver a visual analytics foundation for versatile spaceflight design, especially for initial guess generation and manipulation. Such interactive strategies include the selection of states and arcs from Poincare section visualizations and the capabilities to draw and drag trajectories to remove dependency on initial state input. Furthermore, immersive selection is expanded to cull invariant manifold structures, yielding low-DeltaV or even DeltaV-free transfers between periodic orbits. The application of interactive design strategies featuring a dense extraction of Poincare map topology is demonstrated for agile spaceflight with a simple
Residues and duality for projective algebraic varieties
Kunz, Ernst; Dickenstein, Alicia
2008-01-01
This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of K�hler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations. The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership. D. A. Cox explains toric residues and relates them to the earlier text. The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given.
Duality property for a hermitian scalar field
International Nuclear Information System (INIS)
Bisognano, J.J.
1975-01-01
A general hermitian scalar Wightman field is considered. On the Hilbert space of physical states ''natural'' domains for certain complex Lorentz transformations are constructed, and a theorem relating these transformations to the TCP symmetry is stated and proved. Under the additional assumption that the field is ''locally'' essentially self-adjoint, duality is considered for the algebras generated by spectral projections of smeared fields. For a class of unbounded regions duality is proved, and for certain bounded regions ''local'' extensions of the algebras are constructed which satisfy duality. The relationship of the arguments presented to the Tomita--Takesaki theory of modular Hilbert algebras is discussed. A separate analysis for the free field is also given. (auth)
The FZZ-duality conjecture. A proof
Energy Technology Data Exchange (ETDEWEB)
Hikida, Y. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan); Schomerus, V. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2008-05-15
We prove that the cigar conformal field theory is dual to the Sine-Liouville model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov. Since both models possess the same chiral algebra, our task is to show that correlations of all tachyon vertex operators agree. We accomplish this goal through an off-critical version of the geometric Langlands duality for sl(2). More explicitly, we combine the well-known self-duality of Liouville theory with an intriguing correspondence between the cigar and Liouville field theory. The latter is derived through a path integral treatment. After a very detailed discussion of genus zero amplitudes, we extend the duality to arbitrary closed surfaces. (orig.)
Projective Fourier duality and Weyl quantization
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs
An uplifting discussion of T-duality
Harvey, Jeffrey A.; Moore, Gregory W.
2018-05-01
It is well known that string theory has a T-duality symmetry relating circle compactifications of large and small radius. This symmetry plays a foundational role in string theory. We note here that while T-duality is order two acting on the moduli space of compactifications, it is order four in its action on the conformal field theory state space. More generally, involutions in the Weyl group W ( G) which act at points of enhanced G symmetry have canonical lifts to order four elements of G, a phenomenon first investigated by J. Tits in the mathematical literature on Lie groups and generalized here to conformal field theory. This simple fact has a number of interesting consequences. One consequence is a reevaluation of a mod two condition appearing in asymmetric orbifold constructions. We also briefly discuss the implications for the idea that T-duality and its generalizations should be thought of as discrete gauge symmetries in spacetime.
The FZZ-duality conjecture. A proof
International Nuclear Information System (INIS)
Hikida, Y.; Schomerus, V.
2008-05-01
We prove that the cigar conformal field theory is dual to the Sine-Liouville model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov. Since both models possess the same chiral algebra, our task is to show that correlations of all tachyon vertex operators agree. We accomplish this goal through an off-critical version of the geometric Langlands duality for sl(2). More explicitly, we combine the well-known self-duality of Liouville theory with an intriguing correspondence between the cigar and Liouville field theory. The latter is derived through a path integral treatment. After a very detailed discussion of genus zero amplitudes, we extend the duality to arbitrary closed surfaces. (orig.)
Duality and self-duality (energy reflection symmetry) of quasi-exactly solvable periodic potentials
International Nuclear Information System (INIS)
Dunne, Gerald V.; Shifman, M.
2002-01-01
A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation interchanges bands at the bottom (top) of the spectrum of one potential with gaps at the top (bottom) of the spectrum of the other, dual, potential. Thus, the duality transformation provides an exact mapping between the weak coupling (perturbative) and semiclassical (nonperturbative) sectors
Self-duality in generalized Lorentz superspaces
International Nuclear Information System (INIS)
Devchand, C.; Nuyts, J.
1996-12-01
We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspace are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvatures, we define generalized self-duality as the Lorentz covariant vanishing of certain irreducible parts of the curvatures. (author). 4 refs
International Nuclear Information System (INIS)
Pusztai, B.G.
2012-01-01
In this paper, we construct canonical action-angle variables for both the hyperbolic BC n Sutherland and the rational BC n Ruijsenaars-Schneider-van Diejen models with three independent coupling constants. As a byproduct of our symplectic reduction approach, we establish the action-angle duality between these many-particle systems. The presented dual reduction picture builds upon the construction of a Lax matrix for the BC n -type rational Ruijsenaars-Schneider-van Diejen model.
Duality invariant class of exact string backgrounds
Klimcík, C
1994-01-01
We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.
Global-local duality in eternal inflation
International Nuclear Information System (INIS)
Bousso, Raphael; Yang, I-S.
2009-01-01
We prove that the light-cone time cutoff on the multiverse defines the same probabilities as a causal patch with initial conditions in the longest-lived metastable vacuum. This establishes the equivalence of two measures of eternal inflation which naively appear very different (though both are motivated by holography). The duality can be traced to an underlying geometric relation which we identify.
String duality and novel theories without gravity
International Nuclear Information System (INIS)
Kachru, Shamit
1998-01-01
We describe some of the novel 6d quantum field theories which have been discovered in studies of string duality. The role these theories (and their 4d descendants) may play in alleviating the vacuum degeneracy problem in string theory is reviewed. The DLCQ of these field theories is presented as one concrete way of formulating them, independent of string theory
Duality properties of Gorringe Leach equations
Grandati, Yves; Bérard, Alain; Mohrbach, Hervé
2009-02-01
In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold Vassiliev type. The specific associated conserved quantities (Laplace Runge Lenz vector and Fradkin Jauch Hill tensor) are then dual reflections of each other.
Duality for Z(N) gauge theories
International Nuclear Information System (INIS)
Korthals Altes, C.P.
1978-01-01
The duality properties of simple Z(N) gauge theories are discussed. For N 4 these systems are not self dual. Also, the order parameter is discussed. The general Z(N) gauge theory is found to be self dual for all N. (Auth.)
A CMB/Dark Energy Cosmic Duality
DEFF Research Database (Denmark)
Enqvist, Kari; Sloth, Martin Snoager
2004-01-01
We investigate a possible connection between the suppression of the power at low multipoles in the CMB spectrum and the late time acceleration. We show that, assuming a cosmic IR/UV duality between the UV cutoff and a global infrared cutoff given by the size of the future event horizon...
Natsuume, Makoto
2015-01-01
This book describes applications of the AdS/CFT duality to the "real world." The AdS/CFT duality is an idea that originated from string theory and is a powerful tool for analyzing strongly-coupled gauge theories using classical gravitational theories. In recent years, it has been shown that one prediction of AdS/CFT is indeed close to the experimental result of the real quark–gluon plasma. Since then, the AdS/CFT duality has been applied to various fields of physics; examples are QCD, nuclear physics, condensed-matter physics, and nonequilibrium physics. The aim of this book is to provide background materials such as string theory, black holes, nuclear physics, condensed-matter physics, and nonequilibrium physics as well as key applications of the AdS/CFT duality in a single volume. The emphasis throughout the book is on a pedagogical and intuitive approach focusing on the underlying physical concepts. It also includes step-by-step computations for important results, which are useful for beginners. Th...
Refined large N duality for knots
DEFF Research Database (Denmark)
Kameyama, Masaya; Nawata, Satoshi
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
Indian Academy of Sciences (India)
IAS Admin
QCD, grand unified theories, magnetic monopoles and string theory. a flavour of some of these works in this article. ..... gular momentum of the charged particle due to the mag- netic field .... put to good use for testing duality. He showed that if.
Magnetic monopoles, duality and cosmological phase transitions
International Nuclear Information System (INIS)
Escobar, C.O.; Natale, A.A.; Marques, G.C.
1981-06-01
Is is shown that duality for magnetic monopoles, as proposed by Montonen and Olive, does not hold in quatum field theory at finite temperatures. Furthermore, the evolution picture of the Universe looks different when analyzed in the original 'electric' theory or in its dual 'magnetic' counterpart. (Author) [pt
Lie-isotopic generalization of the Poincare symmetry: Classical formulation
International Nuclear Information System (INIS)
Santilli, R.M.
1991-03-01
This paper is devoted to the origin and methodology of the several phenomenological predictions of deviations from Einstein's Special Relativity and related Lorentz symmetry in the behaviour of the lifetime of unstable hadrons at different speeds, that exist in the literature since the early '60's. After reviewing the background phenomenological literature, we outline the Lie-isotopic symmetry of the emerging deformations of the Minkowski metric introduced in a preceding paper, and extend the results to the construction of the full Poincare-isotopic symmetry. The local isomorphism of the Poincare-isotopic symmetry with the conventional symmetry is proved for all possible topology-preserving deformations of the Minkowski metric. In this way we establish that the phenomenological predictions of deviations recalled earlier must be specifically referred to Einstein's Special Relativity, but they cannot be referred to the Lorentz (or to the Poincare) symmetry which remains exact. Particular attention is devoted to the proof of the compatibility of the exact validity of the Special Relativity for the center-of-mass trajectory of a hadron in a particle accelerator, with conceivable deviations from the same relativity in the interior structural problem. For completeness, the analysis is complemented with a few remarks on the gravitational profile. First, we review the pioneering Lie-isotopic generalization of Einstein's Gravitation worked out by Gasperini, which possesses precisely a locally Lorentz-isotopic structure. We then restrict this theory to the interior gravitational problem in order to achieve compatibility with the particle setting. The paper concludes with a review of the need to finally conduct direct experimental measures of the lifetime of unstable hadrons at different speeds, in order to finally resolve whether Einsteins's Special and General Relativities are locally valid in the interior of hadrons, or structurally more general relativities must be worked
Discussion of the duality in three dimensional quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Ma, Chen-Te, E-mail: yefgst@gmail.com
2017-05-10
We discuss the duality in three dimensional quantum field theory at infrared limit. The starting point is to use a conjecture of a duality between the free fermion and the interacting scalar field theories at the Wilson–Fisher fixed point. The conjecture is useful for deriving various dualities in three dimensions to obtain a duality web. The study is also interesting for understanding the dualities, or equivalence of different theories from the perspective of the renormalization group flow. We first discuss the “derivation” without losing the holonomy. Furthermore, we also derive these dualities from the mean-field study, and consider the extension of the conjecture or dualities at finite temperature.
Poincare map for some polynomial systems of differential equations
International Nuclear Information System (INIS)
Varin, V P
2004-01-01
One approach to the classical problem of distinguishing between a centre and a focus for a system of differential equations with polynomial right-hand sides in the plane is discussed. For a broad class of such systems necessary and sufficient conditions for a centre are expressed in terms of equations in variations of higher order. By contrast with the existing methods of investigation, attention is concentrated on the explicit calculation of the asymptotic behaviour of the Poincare map rather than on finding sufficient centre conditions as such; this also enables one to study bifurcations of birth of arbitrarily strongly degenerate cycles.
Wave computation on the Poincaré dodecahedral space
Bachelot-Motet, Agnès
2013-12-01
We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non-trivial topology: the Poincaré dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We adopt a variational approach using a space of finite elements that is invariant under the action of the binary icosahedral group. The computation of the transient waves is validated with their spectral analysis by computing a lot of eigenvalues of the Laplace-Beltrami operator.
The dual algebra of the Poincare group on Fock space
International Nuclear Information System (INIS)
Klink, W.H.; Iowa Univ., Iowa City, IA
1989-01-01
The Lie algebra of operators commuting with the Poincare group on the Fock space appropriate for a massive spinless particle is constructed in terms of raising and lowering operators indexed by a Lorentz invariant function. From the assumption that the phase operator is an element of this Lie algebra, it is shown that the scattering operator can be written as a unitary representation operator of the group associated with the Lie algebra. A simple choice of the phase operator shows that the Lorentz invariant function can be interpreted as a basic scattering amplitude, in the sense that all multiparticle scattering amplitudes can be written in terms of this basic scattering amplitude. (orig.)
Atrial fibrillation detection by heart rate variability in Poincare plot.
Park, Jinho; Lee, Sangwook; Jeon, Moongu
2009-12-11
Atrial fibrillation (AFib) is one of the prominent causes of stroke, and its risk increases with age. We need to detect AFib correctly as early as possible to avoid medical disaster because it is likely to proceed into a more serious form in short time. If we can make a portable AFib monitoring system, it will be helpful to many old people because we cannot predict when a patient will have a spasm of AFib. We analyzed heart beat variability from inter-beat intervals obtained by a wavelet-based detector. We made a Poincare plot using the inter-beat intervals. By analyzing the plot, we extracted three feature measures characterizing AFib and non-AFib: the number of clusters, mean stepping increment of inter-beat intervals, and dispersion of the points around a diagonal line in the plot. We divided distribution of the number of clusters into two and calculated mean value of the lower part by k-means clustering method. We classified data whose number of clusters is more than one and less than this mean value as non-AFib data. In the other case, we tried to discriminate AFib from non-AFib using support vector machine with the other feature measures: the mean stepping increment and dispersion of the points in the Poincare plot. We found that Poincare plot from non-AFib data showed some pattern, while the plot from AFib data showed irregularly irregular shape. In case of non-AFib data, the definite pattern in the plot manifested itself with some limited number of clusters or closely packed one cluster. In case of AFib data, the number of clusters in the plot was one or too many. We evaluated the accuracy using leave-one-out cross-validation. Mean sensitivity and mean specificity were 91.4% and 92.9% respectively. Because pulse beats of ventricles are less likely to be influenced by baseline wandering and noise, we used the inter-beat intervals to diagnose AFib. We visually displayed regularity of the inter-beat intervals by way of Poincare plot. We tried to design an
Poincare' maps of impulsed oscillators and two-dimensional dynamics
International Nuclear Information System (INIS)
Lupini, R.; Lenci, S.; Gardini, L.; Urbino Univ.
1996-01-01
The Poincare' map of one-dimensional linear oscillators subject to periodic, non-linear and time-delayed impulses is shown to reduce to a family of plane maps with possible non-uniqueness of the inverse. By restricting the analysis to a convenient form of the impulse function, a variety of interesting dynamical behaviours in this family are pointed out, including multistability and homoclinic bifurcations. Critical curves of two-dimensional endomorphisms are used to identify the structure of absorbing areas and their bifurcations
Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations
International Nuclear Information System (INIS)
Mestdag, T; Crampin, M
2008-01-01
We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated with Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper, we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory
Effective Einsteinian gravity from Poincare gauge field theory
International Nuclear Information System (INIS)
Baekler, P.; Mielke, E.W.
1985-10-01
The Poincare gauge theory of gravity should apply in the microphysical domain. Here we investigate its implications for macrophysics. Weakly self double dual Riemann-Cartan curvature is assumed throughout. It is shown that the metrical background is then determined by Einstein's field equations with the Belinfante-Rosenfeld symmetrized energy-momentum current amended by spin squared terms. Moreover, the effective cosmological constant can be reconciled with the empirical data by absorbing the corresponding constant curvature part into the dynamical torsion of recently found exact solutions. Macroscopically this extra torsion remains undetectable. (author)
On the universe's cybernetics duality behavior
Feria, Erlan H.
2015-05-01
Universal cybernetics is the study of control and communications in living and non-living systems. In this paper the universal cybernetics duality principle (UCDP), first identified in control theory in 1978 and expressing a cybernetic duality behavior for our universe, is reviewed. The review is given on the heels of major prizes given to physicists for their use of mathematical dualities in solving intractable problems in physics such as those of cosmology's `dark energy', an area that according to a recent New York Times article has become "a cottage industry in physics today". These dualities are not unlike those of our UCDP that are further enhanced with physical dualities. For instance, in 2008 the UCDP guided us to the derivation of the laws of retention in physics as the space-penalty dual of the laws of motion in physics, including the dark energy thought responsible for the observed increase of the volume of our Universe as it ages. The UCDP has also guided us to the discovery of significant results in other fields such as: 1) in matched processors for quantized control with applications in the modeling of central nervous system (CNS) control mechanisms; 2) in radar designs where the discovery of latency theory, the time-penalty dual of information-theory, has led us to high-performance radar solutions that evade the use of `big data' in the form of SAR imagery of the earth; and 3) in unveiling biological lifespan bounds where the life-expectancy of an organism is sensibly predicted through lingerdynamics, the identified time-penalty dual of thermodynamics, which relates its adult lifespan to either: a. the ratio of its body size to its nutritional consumption rate; or b. its specific heat-capacity; or c. the ratio of its nutritional consumption rate energy to its entropic volume energy, a type of dark energy that is consistent with the observed decrease in the mass density of the organism as it ages.
Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System
Amjad, Hussain; Syed Tauseef, Mohyud-Din; Ahmet, Yildirim
2012-03-01
MacMillan's equations are extended to Poincaré's formalism, and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré parameters. The equivalence of the results obtained here with other forms of equations of motion is demonstrated. An illustrative example of the theory is provided as well.
Of gluons and gravitons. Exploring color-kinematics duality
International Nuclear Information System (INIS)
Isermann, Reinke Sven
2013-06-01
In this thesis color-kinematics duality will be investigated. This duality is a statement about the kinematical dependence of a scattering amplitude in Yang-Mills gauge theories obeying group theoretical relations similar to that of the color gauge group. The major consequence of this duality is that gravity amplitudes can be related to a certain double copy of gauge theory amplitudes. The main focus of this thesis is on exploring the foundations of color-kinematics duality and its consequences. It is shown how color-kinematics duality can be made manifest at the one-loop level for rational amplitudes. A Lagrangian-based argument will be given for the validity of the double copy construction for these amplitudes including explicit examples at four points. Secondly, it is studied how color-kinematics duality can be used to improve powercounting in gravity theories. To this end the duality is reformulated in terms of linear maps. It is shown as an example how this can be used to derive the large BCFW shift behavior of a gravity integrand constructed through the duality to any loop order up to subtleties inherent to the duality that is addressed. As it becomes clear the duality implies massive cancellations with respect to the usual powercounting of Feynman graphs indicating that gravity theories are much better behaved than naively expected. As another example the linear map approach will be used to investigate the question of UV-finiteness of N=8 supergravity, and it is seen that the amount of cancellations depends on the exact implementation of the duality at loop level. Lastly, color-kinematics duality is considered from a Feynman-graph perspective reproducing some of the results of the earlier chapters thus giving non-trivial evidence for the duality at the loop level from a different perspective.
Of gluons and gravitons. Exploring color-kinematics duality
Energy Technology Data Exchange (ETDEWEB)
Isermann, Reinke Sven
2013-06-15
In this thesis color-kinematics duality will be investigated. This duality is a statement about the kinematical dependence of a scattering amplitude in Yang-Mills gauge theories obeying group theoretical relations similar to that of the color gauge group. The major consequence of this duality is that gravity amplitudes can be related to a certain double copy of gauge theory amplitudes. The main focus of this thesis is on exploring the foundations of color-kinematics duality and its consequences. It is shown how color-kinematics duality can be made manifest at the one-loop level for rational amplitudes. A Lagrangian-based argument will be given for the validity of the double copy construction for these amplitudes including explicit examples at four points. Secondly, it is studied how color-kinematics duality can be used to improve powercounting in gravity theories. To this end the duality is reformulated in terms of linear maps. It is shown as an example how this can be used to derive the large BCFW shift behavior of a gravity integrand constructed through the duality to any loop order up to subtleties inherent to the duality that is addressed. As it becomes clear the duality implies massive cancellations with respect to the usual powercounting of Feynman graphs indicating that gravity theories are much better behaved than naively expected. As another example the linear map approach will be used to investigate the question of UV-finiteness of N=8 supergravity, and it is seen that the amount of cancellations depends on the exact implementation of the duality at loop level. Lastly, color-kinematics duality is considered from a Feynman-graph perspective reproducing some of the results of the earlier chapters thus giving non-trivial evidence for the duality at the loop level from a different perspective.
Holographic duality in condensed matter physics
Zaanen, Jan; Sun, Ya-Wen; Schalm, Koenraad
2015-01-01
A pioneering treatise presenting how the new mathematical techniques of holographic duality unify seemingly unrelated fields of physics. This innovative development morphs quantum field theory, general relativity and the renormalisation group into a single computational framework and this book is the first to bring together a wide range of research in this rapidly developing field. Set within the context of condensed matter physics and using boxes highlighting the specific techniques required, it examines the holographic description of thermal properties of matter, Fermi liquids and superconductors, and hitherto unknown forms of macroscopically entangled quantum matter in terms of general relativity, stars and black holes. Showing that holographic duality can succeed where classic mathematical approaches fail, this text provides a thorough overview of this major breakthrough at the heart of modern physics. The inclusion of extensive introductory material using non-technical language and online Mathematica not...
Conference on Strings, Duality, and Geometry
Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV
2002-01-01
This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...
Mordell integrals and Giveon-Kutasov duality
Energy Technology Data Exchange (ETDEWEB)
Giasemidis, Georgios [CountingLab LTD & Centre for the Mathematics of Human Behaviour (CMoHB),Department of Mathematics and Statistics, University of Reading, Reading, RG6 6AX (United Kingdom); Tierz, Miguel [Departamento de Matemática, Grupo de Física Matemática, Faculdade de Ciências,Universidade de Lisboa, Campo Grande, Edifício C6, Lisboa, 1749-016 (Portugal); Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas,Universidad Complutense de Madrid, Madrid, 28040 (Spain)
2016-01-12
We solve, for finite N, the matrix model of supersymmetric U(N) Chern-Simons theory coupled to N{sub f} massive hypermultiplets of R-charge (1/2), together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order N{sub f}−1) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the N=3 setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to N{sub f}=12 flavours).
Duality based optical flow algorithms with applications
DEFF Research Database (Denmark)
Rakêt, Lars Lau
We consider the popular TV-L1 optical flow formulation, and the so-called duality based algorithm for minimizing the TV-L1 energy. The original formulation is extended to allow for vector valued images, and minimization results are given. In addition we consider different definitions of total...... variation regularization, and related formulations of the optical flow problem that may be used with a duality based algorithm. We present a highly optimized algorithmic setup to estimate optical flows, and give five novel applications. The first application is registration of medical images, where X......-ray images of different hands, taken using different imaging devices are registered using a TV-L1 optical flow algorithm. We propose to regularize the input images, using sparsity enhancing regularization of the image gradient to improve registration results. The second application is registration of 2D...
Mordell integrals and Giveon-Kutasov duality
Giasemidis, Georgios; Tierz, Miguel
2016-01-01
We solve, for finite N, the matrix model of supersymmetric U( N) Chern-Simons theory coupled to N f massive hypermultiplets of R-charge 1/2 , together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order N f - 1) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the N=3 setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to N f = 12 flavours).
Mordell integrals and Giveon-Kutasov duality
International Nuclear Information System (INIS)
Giasemidis, Georgios; Tierz, Miguel
2016-01-01
We solve, for finite N, the matrix model of supersymmetric U(N) Chern-Simons theory coupled to N_f massive hypermultiplets of R-charge (1/2), together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order N_f−1) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the N=3 setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to N_f=12 flavours).
International Nuclear Information System (INIS)
Borlaf, J.
1997-01-01
We study T-duality for open strings in arbitrary background fields including the abelian electromagnetic one. We focus in the mapping of the boundary conditions in the disk and the crosscap topologies and we discuss in detail the consistency of the gauging procedure for the bosonic and the N = 1 supersymmetric theories. A brief account is made on the dilaton transformation and global issues in higher genus. (orig.)
Managing dualities in organizational change projects
Shaw, David
2016-01-01
When managers want to change their organisation they often set up a project to do it, in the belief that doing so simplifies and focuses the change initiative and brings greater assurance of success. Case studies of three organisational change projects undertaken by Arts Council England during 2006-2007 are used to examine the notion of project management and change management as a duality. It is argued that the structured, systematic approach associated with project management needs to be ba...
Strong Stationary Duality for Diffusion Processes
Fill, James Allen; Lyzinski, Vince
2014-01-01
We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by linking the separation distance in the primal diffusion to the absorption time in the dual diffusion. We also exhibit our strong stationary dual as the natural limiting process of the strong stationary dual sequence of a well ch...
On Berenstein-Douglas-Seiberg duality
International Nuclear Information System (INIS)
Braun, Volker
2003-01-01
I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the requirements. Then I explicitly show that a pair of toric dual quivers is also dual according to their proposal. All these computations go beyond tilting modules, and really work in the derived category. I introduce all necessary mathematics where needed. (author)
Aspects of some dualities in string theory
Kim, Bom Soo
AdS/CFT correspondence in string theory has changed landscape of the theoretical physics. Through this celebrated duality between gravity theory and field theory, one can investigate analytically strongly coupled gauge theories such as Quantum Chromodynamics (QCD) in terms of weakly coupled string theory such as supergravity theory and vice versa. In the first part of this thesis we used this duality to construct a new type of nonlocal field theory, called Puff Field Theory, in terms of D3 branes in type IIB string theory with a geometric twist. In addition to the strong-weak duality of AdS/CFT, there also exists a weak-weak duality, called Twistor String Theory. Twistor technique is successfully used to calculate the SYM scattering amplitude in an elegant fashion. Yet, the progress in the string theory side was hindered by a non-unitary conformal gravity. We extend the Twistor string theory by introducing mass terms, in the second part of the thesis. A chiral mass term is identified as a vacuum expectation value of a conformal supergravity field and is tied with the breaking of the conformal symmetry of gravity. As a prime candidate for a quantum theory of gravity, string theory revealed many promising successes such as counting the number of microstates in supersymmetric Black Holes thermodynamics and resolution of timelike and null singularities, to name a few. Yet, the fundamental string and M-theroy formulations are not yet available. Various string theories without gravity, such as Non-Commutative Open String (NCOS) and Open Membrane (OM) theories, are very nice playground to investigate the fundamental structure of string and M-theory without the complication of gravity. In the last part of the thesis, simpler Non-Relativistic String Theories are constructed and investigated. One important motivation for those theories is related to the connection between Non-Relativistic String Theories and Non-critical String Theories through the bosonization of betagamma
Dynamic Convex Duality in Constrained Utility Maximization
Li, Yusong; Zheng, Harry
2016-01-01
In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint process coming from the dual FBSDEs in a dynamic fashion and vice versa. Moreover, we also...
Canonical Duality Theory for Topology Optimization
Gao, David Yang
2016-01-01
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer nonlinear programming problem (MINLP), i.e. for a given deformation, the first-level optimization is a typical linear constrained 0-1 programming problem, while for a given structure, the second-level optimization is a general nonlinear continuous minimization pro...
Dual projection and self duality in three dimensions
International Nuclear Information System (INIS)
Banerjee, Rabin; Wotzasek, Clovis
2000-01-01
Full text follows: We discuss the notion of duality and self duality in the context of the dual projection operation that creates an internal space of potentials. This technique is applicable to both even and odd dimensions. We derive the appropriate invariant actions, discuss the symmetry groups and their proper generators. In particular, the novel concept of duality symmetry and self duality in Maxwell theory in (2+1) dimensions is analysed in details. The corresponding action is a 3D version of the familiar duality symmetric electromagnetic theory in 4D. Finally, the duality symmetric actions in the different dimensions constructed here manifest both the SO(2) and Z 2 symmetries, contrary to conventional results. (author)
Patching DFT, T-duality and gerbes
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S.; Papadopoulos, G. [Department of Mathematics, King’s College London,Strand, London WC2R 2LS (United Kingdom)
2017-04-12
We clarify the role of the dual coordinates as described from the perspectives of the Buscher T-duality rules and Double Field Theory. We show that the T-duality angular dual coordinates cannot be identified with Double Field Theory dual coordinates in any of the proposals that have been made in the literature for patching the doubled spaces. In particular, we show with explicit examples that the T-duality angular dual coordinates can have non-trivial transition functions over a spacetime and that their identification with the Double Field Theory dual coordinates is in conflict with proposals in which the latter remain inert under the patching of the B-field. We then demonstrate that the Double Field Theory coordinates can be identified with some C-space coordinates and that the T-dual spaces of a spacetime are subspaces of the gerbe in C-space. The construction provides a description of both the local O(d,d) symmetry and the T-dual spaces of spacetime.
Patching DFT, T-duality and gerbes
International Nuclear Information System (INIS)
Howe, P.S.; Papadopoulos, G.
2017-01-01
We clarify the role of the dual coordinates as described from the perspectives of the Buscher T-duality rules and Double Field Theory. We show that the T-duality angular dual coordinates cannot be identified with Double Field Theory dual coordinates in any of the proposals that have been made in the literature for patching the doubled spaces. In particular, we show with explicit examples that the T-duality angular dual coordinates can have non-trivial transition functions over a spacetime and that their identification with the Double Field Theory dual coordinates is in conflict with proposals in which the latter remain inert under the patching of the B-field. We then demonstrate that the Double Field Theory coordinates can be identified with some C-space coordinates and that the T-dual spaces of a spacetime are subspaces of the gerbe in C-space. The construction provides a description of both the local O(d,d) symmetry and the T-dual spaces of spacetime.
Electric magnetic duality in string theory
International Nuclear Information System (INIS)
Sen, A.
1992-07-01
The electric-magnetic duality transformation in four dimensional heterotic string theory discussed by Shapere, Trivedi and Wilczek is shown to be an exact symmetry of the equations of motion of low energy effective field theory even after including the scalar and the vector fields, arising due to compactification, in the effective field theory. Using this duality transformation we construct rotating black hole solutions in the effective field theory carrying both electric and magnetic charges. The spectrum of extremal magnetically charged black holes turn out to be similar to that of electrically charged elementary string excitations lying on the leading Regge trajectory. We also discuss the possibility that the duality symmetry is an exact symmetry of the full string theory under which electrically charged elementary string excitations get exchanged with magnetically charged soliton like solutions. This proposal might be made concrete following the suggestion of Dabholkar et. al. that fundamental strings may be regarded as soliton like classical solutions in the effective field theory. (author). 20 refs
Color-Kinematics Duality for QCD Amplitudes
Johansson, Henrik
2016-01-01
We show that color-kinematics duality is present in tree-level amplitudes of quantum chromodynamics with massive flavored quarks. Starting with the color structure of QCD, we work out a new color decomposition for n-point tree amplitudes in a reduced basis of primitive amplitudes. These primitives, with k quark-antiquark pairs and (n-2k) gluons, are taken in the (n-2)!/k! Melia basis, and are independent under the color-algebra Kleiss-Kuijf relations. This generalizes the color decomposition of Del Duca, Dixon, and Maltoni to an arbitrary number of quarks. The color coefficients in the new decomposition are given by compact expressions valid for arbitrary gauge group and representation. Considering the kinematic structure, we show through explicit calculations that color-kinematics duality holds for amplitudes with general configurations of gluons and massive quarks. The new (massive) amplitude relations that follow from the duality can be mapped to a well-defined subset of the familiar BCJ relations for gluo...
Building up reggeons and the pomeron from duality and unitarity
International Nuclear Information System (INIS)
Sakai, N.
1975-07-01
The subject is treated under the following headings: duality; unitarity; duality and unitarity; 1/N expansion; Reggeon bootstrap; Pomeron equation; triple Pomeron. The results are summarized: (1) combining duality with unitarity, powerful constraints are obtained; (2) many phenomenological successes have been obtained since some practical methods of calculation were devised; and (3) even the complete unitarization is hopeful; 1/N expansion may be useful for this purpose. (author)
POINCARE O LA PROFUNDA NECESIDAD DE LA CONVENCION
Directory of Open Access Journals (Sweden)
Carlos Alberto Cardona Suárez
2005-01-01
Full Text Available En el marco de la celebración de los cien años de la publicación del artículo que dio origen a la teoría especial de la relatividad, se presenta una semblanza de las discusiones suscitadas a raíz de las implicaciones filosóficas que se derivan de la posibilidad de aceptar marcos no euclidianos para nuestro espacio de representación. Se exhibe el argumento de Poincaré en defensa del principio de relatividad de la geometría y se discute la crítica formulada por Hans Reichenbach.
On the representations of Poincare group associated with unstable particles
International Nuclear Information System (INIS)
Exner, RP.
1983-01-01
The problem of relativistically-covariant description of unstable particles is reexamined. We follow the approach which associates a unitary reducible representation of Poincare group with a larger isolated system, and compare it with the one ascribing a non-unitary irreducible representation to the unstable particle alone. It is shown that the problem roots in choice of the subspace Hsub(u) of the state Hilbert space which could be related to the unstable particle. Translational invariance of Hsub(u) is proved to be incompatible with unitarity of the boosts. Further we propose a concrete choice of Hsub(u) and argue that in most cases of the actual experimental arrangements, this subspace is effectively one-dimensional. A correct slow-down for decay of a moving particle is obtained
T-Duality Group for Open String Theory
Kajiura, Hiroshige
2001-01-01
We study T-duality for open strings on tori $\\T^d$. The general boundary conditions for the open strings are constructed, and it is shown that T-duality group, which preserves the mass spectrum of closed strings, preserves also the mass spectrum of the open strings. The open strings are transformed to those with different boundary conditions by T-duality. We also discuss the T-duality for D-brane mass spectrum, and show that the D-branes and the open strings with both ends on them are transfo...
Duality and calculus of convex objects (theory and applications)
International Nuclear Information System (INIS)
Brinkhuis, Ya; Tikhomirov, V M
2007-01-01
A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.
Conventionalism, structuralism and neo-Kantianism in Poincaré's philosophy of science
Ivanova, Milena
2015-11-01
Poincaré is well known for his conventionalism and structuralism. However, the relationship between these two theses and their place in Poincaré's epistemology of science remain puzzling. In this paper I show the scope of Poincaré's conventionalism and its position in Poincaré's hierarchical approach to scientific theories. I argue that for Poincaré scientific knowledge is relational and made possible by synthetic a priori, empirical and conventional elements, which, however, are not chosen arbitrarily. By examining his geometric conventionalism, his hierarchical account of science and defence of continuity in theory change, I argue that Poincaré defends a complex structuralist position based on synthetic a priori and conventional elements, the mind-dependence of which precludes epistemic access to mind-independent structures. The object of mathematical theories is not to reveal to us the real nature of things; that would be an unreasonable claim. Their only object is to coordinate the physical laws with which physical experiments make us acquainted, the enunciation of which, without the aid of mathematics, would be unable to effect. (Poincaré, 2001, 117)
Duality results for co-compact Gabor systems
DEFF Research Database (Denmark)
Jakobsen, Mads Sielemann; Lemvig, Jakob
2015-01-01
In this paper we give an account of recent developments in the duality theory of Gabor frames. We prove the Wexler-Raz biorthogonality relations and the duality principle for co-compact Gabor systems on second countable, locally compact abelian groups G. Our presentation does not rely on the exis...
Residues and duality for singularity categories of isolated Gorenstein singularities
Murfet, Daniel
2009-01-01
We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.
Dualities in M-theory and Born-Infeld Theory
International Nuclear Information System (INIS)
Brace, Daniel M.
2001-01-01
We discuss two examples of duality. The first arises in the context of toroidal compactification of the discrete light cone quantization of M-theory. In the presence of nontrivial moduli coming from the M-theory three form, it has been conjectured that the system is described by supersymmetric Yang-Mills gauge theory on a noncommutative torus. We are able to provide evidence for this conjecture, by showing that the dualities of this M-theory compactification, which correspond to T-duality in Type IIA string theory, are also dualities of the noncommutative supersymmetric Yang-Mills description. One can also consider this as evidence for the accuracy of the Matrix Theory description of M-theory in this background. The second type of duality is the self-duality of theories with U(1) gauge fields. After discussing the general theory of duality invariance for theories with complex gauge fields, we are able to find a generalization of the well known U(1) Born-Infeld theory that contains any number of gauge fields and which is invariant under the maximal duality group. We then find a supersymmetric extension of our results, and also show that our results can be extended to find Born-Infeld type actions in any even dimensional spacetime
Duality in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Duality in supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N f c , in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N f large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs
Pouliot type duality via a-maximization
International Nuclear Information System (INIS)
Kawano, Teruhiko; Ookouchi, Yutaka; Tachikawa, Yuji; Yagi, Futoshi
2006-01-01
We study four-dimensional N=1Spin(10) gauge theory with a single spinor and N Q vectors at the superconformal fixed point via the electric-magnetic duality and a-maximization. When gauge invariant chiral primary operators hit the unitarity bounds, we find that the theory with no superpotential is identical to the one with some superpotential at the infrared fixed point. The auxiliary field method in the electric theory offers a satisfying description of the infrared fixed point, which is consistent with the better picture in the magnetic theory. In particular, it gives a clear description of the emergence of new massless degrees of freedom in the electric theory
Eleven-dimensional supergravity from filtered subdeformations of the Poincaré superalgebra
International Nuclear Information System (INIS)
Figueroa-O’Farrill, José; Santi, Andrea
2016-01-01
We summarise recent results concerning the classification of filtered deformations of graded subalgebras of the Poincaré superalgebra in eleven dimensions, highlighting what could be considered a novel Lie-algebraic derivation of eleven-dimensional supergravity. (paper)
Form factors of Ising spin and disorder fields on the Poincare disc
International Nuclear Information System (INIS)
Doyon, Benjamin
2004-01-01
Using recent results concerning form factors of certain scaling fields in the massive Dirac theory on the Poincare disc, we find expressions for the form factors of Ising spin and disorder fields in the massive Majorana theory on the Poincare disc. In particular, we verify that these recent results agree with the factorization properties of the fields in the Dirac theory representing tensor products of spin and of disorder fields in the Majorana theory
A Hidden Twelve-Dimensional SuperPoincare Symmetry In Eleven Dimensions
Energy Technology Data Exchange (ETDEWEB)
Bars, Itzhak; Deliduman, Cemsinan; Pasqua, Andrea; Zumino, Bruno
2003-12-13
First, we review a result in our previous paper, of how a ten-dimensional superparticle, taken off-shell, has a hidden eleven-dimensional superPoincare symmetry. Then, we show that the physical sector is defined by three first-class constraints which preserve the full eleven-dimensional symmetry. Applying the same concepts to the eleven dimensional superparticle, taken off-shell, we discover a hidden twelve dimensional superPoincare symmetry that governs the theory.
Natural curvature for manifest T-duality
International Nuclear Information System (INIS)
Poláček, Martin; Siegel, Warren
2014-01-01
We reformulate the manifestly T-dual description of the massless sector of the closed bosonic string, directly from the geometry associated with the (left and right) affine Lie algebra of the coset space Poincaré/Lorentz. This construction initially doubles not only the (spacetime) coordinates for translations but also those for Lorentz transformations (and their “dual”). As a result, the Lorentz connection couples directly to the string (as does the vielbein), rather than being introduced ad hoc to the covariant derivative as previously. This not only reproduces the old definition of T-dual torsion, but automatically gives a general, covariant definition of T-dual curvature (but still with some undetermined connections)
Seiberg duality and e+e- experiments
International Nuclear Information System (INIS)
De Gouvea, Andre; Friedland, Alexander; Murayama, Hitoshi
1998-01-01
Seiberg duality in supersymmetric gauge theories is the claim that two different theories describe the same physics in the infrared limit. However, one cannot easily work out physical quantities in strongly coupled theories and hence it has been difficult to compare the physics of the electric and magnetic theories. In order to gain more insight into the equivalence of two theories, we study the ''e + e - '' cross sections into ''hadrons'' for both theories in the superconformal window. We describe a technique which allows us to compute the cross sections exactly in the infrared limit. They are indeed equal in the low-energy limit and the equality is guaranteed because of the anomaly matching condition. The ultraviolet behavior of the total ''e + e - '' cross section is different for the two theories. We comment on proposed nonsupersymmetric dualities. We also analyze the agreement of the ''γγ'' and ''WW'' scattering amplitudes in both theories, and in particular try to understand if their equivalence can be explained by the anomaly matching condition
Scale factor duality for conformal cyclic cosmologies
Energy Technology Data Exchange (ETDEWEB)
Silva, University Camara da; Lima, A.L. Alves; Sotkov, G.M. [Departamento de Física - CCE,Universidade Federal de Espirito Santo, 29075-900, Vitoria ES (Brazil)
2016-11-16
The scale factor duality is a symmetry of dilaton gravity which is known to lead to pre-big-bang cosmologies. A conformal time version of the scale factor duality (SFD) was recently implemented as a UV/IR symmetry between decelerated and accelerated phases of the post-big-bang evolution within Einstein gravity coupled to a scalar field. The problem investigated in the present paper concerns the employment of the conformal time SFD methods to the construction of pre-big-bang and cyclic extensions of these models. We demonstrate that each big-bang model gives rise to two qualitatively different pre-big-bang evolutions: a contraction/expansion SFD model and Penrose’s Conformal Cyclic Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving certain gauged Kähler sigma models minimally coupled to Einstein gravity are studied. We also describe the specific SFD features of the thermodynamics and the conditions for validity of the generalized second law in the case of Gauss-Bonnet (GB) extension of these selected CCC models.
Scale factor duality for conformal cyclic cosmologies
International Nuclear Information System (INIS)
Silva, University Camara da; Lima, A.L. Alves; Sotkov, G.M.
2016-01-01
The scale factor duality is a symmetry of dilaton gravity which is known to lead to pre-big-bang cosmologies. A conformal time version of the scale factor duality (SFD) was recently implemented as a UV/IR symmetry between decelerated and accelerated phases of the post-big-bang evolution within Einstein gravity coupled to a scalar field. The problem investigated in the present paper concerns the employment of the conformal time SFD methods to the construction of pre-big-bang and cyclic extensions of these models. We demonstrate that each big-bang model gives rise to two qualitatively different pre-big-bang evolutions: a contraction/expansion SFD model and Penrose’s Conformal Cyclic Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving certain gauged Kähler sigma models minimally coupled to Einstein gravity are studied. We also describe the specific SFD features of the thermodynamics and the conditions for validity of the generalized second law in the case of Gauss-Bonnet (GB) extension of these selected CCC models.
Field on Poincare group and quantum description of orientable objects
Energy Technology Data Exchange (ETDEWEB)
Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Caixa Postal 66318-CEP, Sao Paulo, S.P. (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engineering, Electronics and Automation, Moscow (Russian Federation)
2009-05-15
We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincare group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group {pi}=G x G. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points x element of G/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix Z element of Spin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties. (orig.)
On the origin of Poincaré gauge gravity
Chkareuli, J. L.
2017-06-01
We argue that the origin of Poincaré gauge gravity (PGG) may be related to spontaneous violation of underlying spacetime symmetries involved and appearance of gauge fields as vector Goldstone bosons. In essence, we start with an arbitrary theory of some vector and fermion fields which possesses only global spacetime symmetries, such as Lorentz and translational invariance, in flat Minkowski space. The two vector field multiplets involved are assumed to belong, respectively, to the adjoint (Aμij) and vector (eμi) representations of the starting global Lorentz symmetry. We propose that these prototype vector fields are covariantly constrained, Aμij Aijμ = ±MA2 and eμi eiμ = ±Me2 , that causes a spontaneous violation of the accompanying global symmetries (MA,e are their presumed violation scales). It then follows that the only possible theory compatible with these length-preserving constraints is turned out to be the gauge invariant PGG, while the corresponding massless (pseudo)Goldstone modes are naturally collected in the emergent gauge fields of tetrads and spin-connections. In a minimal theory case being linear in a curvature we unavoidably come to the Einstein-Cartan theory. The extended theories with propagating spin-connection and tetrad modes are also considered and their possible unification with the Standard Model is briefly discussed.
On systems having Poincaré and Galileo symmetry
International Nuclear Information System (INIS)
Holland, Peter
2014-01-01
Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics
On the structure of Poincare gauge Langrangians for gravity
International Nuclear Information System (INIS)
Wallner, R.P.
1980-01-01
As in translational gauge theories of gravity the pure gauge field Lagrangian Lsub(transl) approximately (translational field strength) 2 approximately (torsion) 2 does not work in its standard form THETA sup(a) Λ *THETAsub(a) because of the lack of any correct Newtonian limit, one has to replace it by a suitable linear combination of other invariants squared in torsion. The appearance of unphysical solutions in full Poincare-gauge theories of gravity due to the standard Lsub(rot) approximately (curvature) 2 -term Ω sub(ab) Λ*Ω sub(ab) now suggests an analogous procedure for Lsub(rot). Here, the various invariants squared in curvature are listed and the number of those coming into question is reduced to two by a formal argument. In addtion, the field equations to all translational and rotational squared invariants are given and a certain combination, which will exclude massive gauge field solutions of the linearized equations, is proposed. For the purpose of rotational and calculational economy, the calculus of exterior forms is used throughout. (Author)
On the origin of Poincaré gauge gravity
Directory of Open Access Journals (Sweden)
J.L. Chkareuli
2017-06-01
Full Text Available We argue that the origin of Poincaré gauge gravity (PGG may be related to spontaneous violation of underlying spacetime symmetries involved and appearance of gauge fields as vector Goldstone bosons. In essence, we start with an arbitrary theory of some vector and fermion fields which possesses only global spacetime symmetries, such as Lorentz and translational invariance, in flat Minkowski space. The two vector field multiplets involved are assumed to belong, respectively, to the adjoint (Aμij and vector (eμi representations of the starting global Lorentz symmetry. We propose that these prototype vector fields are covariantly constrained, AμijAijμ=±MA2 and eμieiμ=±Me2, that causes a spontaneous violation of the accompanying global symmetries (MA,e are their presumed violation scales. It then follows that the only possible theory compatible with these length-preserving constraints is turned out to be the gauge invariant PGG, while the corresponding massless (pseudoGoldstone modes are naturally collected in the emergent gauge fields of tetrads and spin-connections. In a minimal theory case being linear in a curvature we unavoidably come to the Einstein–Cartan theory. The extended theories with propagating spin-connection and tetrad modes are also considered and their possible unification with the Standard Model is briefly discussed.
Fundamental vortices, wall-crossing, and particle-vortex duality
Energy Technology Data Exchange (ETDEWEB)
Hwang, Chiung; Yi, Piljin [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of); Yoshida, Yutaka [Research Institute for Mathematical Sciences, Kyoto University,Kyoto 606-8502 (Japan)
2017-05-18
We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact partition functions. Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a priori clear what should happen to the vortex dynamics. We observe that the 1d quivers for the vortices remain the same, and the net effect of the 3d duality map manifests as 1d Wall-Crossing phenomenon; although the vortex number can shift along such duality maps, the ranks of the 1d quiver theory are unaffected, leading to a notion of fundamental vortices as basic building blocks for topological sectors. For Aharony-type duality, in particular, where one must supply extra chiral fields to couple with monopole operators on the dual side, 1d wall-crossings of an infinite number of vortex quiver theories are neatly and collectively encoded by 3d determinant of such extra chiral fields. As such, 1d wall-crossing of the vortex theory encodes the particle-vortex duality embedded in the 3d Seiberg-like duality. For N=4, the D-brane picture is used to motivate this 3d/1d connection, while, for N=2, this 3d/1d connection is used to fine-tune otherwise ambiguous vortex dynamics. We also prove some identities of 3d supersymmetric partition functions for the Aharony duality using this vortex wall-crossing interpretation.
Transformation of Black-Hole Hair under Duality and Supersymmetry
Alvarez, Enrique; Ortín, Tomas; Alvarez, Enrique; Meessen, Patrick; Ortin, Tomas
1997-01-01
We study the transformation under the String Theory duality group of the observable charges (mass, angular momentum, NUT charge, electric, magnetic and different scalar charges) of four dimensional point-like objects whose asymptotic behavior constitutes a subclass closed under duality. The charges fall into two complex four-dimensional representations of the duality group. T duality (including Buscher's) has an O(1,2) action on them and S duality a U(1) action. The generalized Bogomol'nyi bound is an U(2,2)-invariant built out of one representations while the other representation (which includes the angular momentum) never appears in it. The bound is manifestly duality-invariant. Consistency between T duality and supersymmetry requires that primary scalar hair is included in the Bogomol'nyi bound. Four-dimensional supersymmetric massless black holes are the T duals in time of massive supersymmetric black holes. Non-extreme massless ``black holes'' are the T duals of the non-extreme black holes and have prima...
Anisotropic phenomena in gauge/gravity duality
International Nuclear Information System (INIS)
Zeller, Hansjoerg
2014-01-01
In this thesis we use gauge/gravity duality to model anisotropic effects realised in nature. Firstly we analyse transport properties in holographic systems with a broken rotational invariance. Secondly we discuss geometries dual to IR fixed points with anisotropic scaling behaviour, which are related to quantum critical points in condensed matter systems. Gauge/gravity duality relates a gravity theory in Anti-de Sitter space to a lower dimensional strongly coupled quantum field theory in Minkowski space. Over the past decade this duality provided many insights into systems at strong coupling, e.g. quark-gluon plasma and condensed matter close to quantum critical points. One very important result computed in this framework is the value of the shear viscosity divided by the entropy density in strongly coupled theories. The quantitative result agrees very well with measurements of the ratio in quark-gluon plasma. However, for isotropic two derivative Einstein gravity it is temperature independent. We show that by breaking the rotational symmetry of a system we obtain a temperature dependent shear viscosity over entropy density. This is important to make contact with real world systems, since substances in nature display such dependence. In addition, we derive various transport properties in strongly coupled anisotropic systems using the gauge/gravity dictionary. The most notable results include an electrical conductivity with Drude behaviour in the low frequency region. This resembles conductors with broken translational invariance. However, we did not implement the breaking explicitly. Furthermore, our analysis shows that this setup models effects, resembling the piezoelectric and exoelectric effects, known from liquid crystals. In a second project we discuss a geometry with non-trivial scaling behaviour in order to model an IR fixed point of condensed matter theories. We construct the UV completion of this geometry and analyse its properties by computing the
Anisotropic phenomena in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Zeller, Hansjoerg
2014-05-26
In this thesis we use gauge/gravity duality to model anisotropic effects realised in nature. Firstly we analyse transport properties in holographic systems with a broken rotational invariance. Secondly we discuss geometries dual to IR fixed points with anisotropic scaling behaviour, which are related to quantum critical points in condensed matter systems. Gauge/gravity duality relates a gravity theory in Anti-de Sitter space to a lower dimensional strongly coupled quantum field theory in Minkowski space. Over the past decade this duality provided many insights into systems at strong coupling, e.g. quark-gluon plasma and condensed matter close to quantum critical points. One very important result computed in this framework is the value of the shear viscosity divided by the entropy density in strongly coupled theories. The quantitative result agrees very well with measurements of the ratio in quark-gluon plasma. However, for isotropic two derivative Einstein gravity it is temperature independent. We show that by breaking the rotational symmetry of a system we obtain a temperature dependent shear viscosity over entropy density. This is important to make contact with real world systems, since substances in nature display such dependence. In addition, we derive various transport properties in strongly coupled anisotropic systems using the gauge/gravity dictionary. The most notable results include an electrical conductivity with Drude behaviour in the low frequency region. This resembles conductors with broken translational invariance. However, we did not implement the breaking explicitly. Furthermore, our analysis shows that this setup models effects, resembling the piezoelectric and exoelectric effects, known from liquid crystals. In a second project we discuss a geometry with non-trivial scaling behaviour in order to model an IR fixed point of condensed matter theories. We construct the UV completion of this geometry and analyse its properties by computing the
Khan, Abu M. A. S.
We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is
Review of lattice supersymmetry and gauge-gravity duality
International Nuclear Information System (INIS)
Joseph, Anosh
2015-12-01
We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity duality connects systems of D0-branes and black hole geometries at finite temperature to maximally supersymmetric gauged quantum mechanics at the same temperature. Recent simulations show that non-perturbative gauge theory results give excellent agreement with the quantum gravity predictions, thus proving strong evidence for the validity of the duality conjecture and more insight into quantum black holes and gravity.
On the article by Henri Poincare' open-quotes on the dynamics of the electronclose quotes
International Nuclear Information System (INIS)
Logunov, A.A.
1996-01-01
The first complete translations into English are presented of two articles written by the outstanding French scientist Henri Poincare and submitted by him in 1905 under the common title of open-quotes Sur la dynamique de l'electronclose quotes to different journals. In the present edition of these articles by H. Poincare, modern notation is used, and the articles are accompanied by comments written by A.A. Logunov. The author of the comments explains the profound physical meaning and essential novelty of the particular points and relationships established by Poincare. Such explanations are often interspersed with quotations from earlier articles by Poincare, thus clearly indicating that the main initial points of the new theory were put forward by the French scientist much before 1905, while certain concepts like 'local' time and the arbitrariness of simultaneity were given a clear explanation from the point of view of physical meaning. A.A. Logunov's book, presenting the works of Poincare on the development of relativity theory, has had quite a high success among specialists interested in the history of physics, and since 1984 it has been published in Russian three times. The present English-language edition is identical to the last 1988 Russian edition, and is dedicated to the 90th anniversary of Poincare's articles 'On the Dynamics of the Electron'. In preparing the English text, fragments were used of the translation of the long article by H.Poincare published in the book by Professor C.W. Kilmister from King's College in London/Special Theory of Relativity, Pergamon Press, New York, 1970/
Bubbling surface operators and S-duality
International Nuclear Information System (INIS)
Gomis, Jaume; Matsuura, Shunji
2007-01-01
We construct smooth asymptotically /ADS solutions of Type IIB supergravity corresponding to all the half-BPS surface operators in N = 4 SYM. All the parameters labeling a half-BPS surface operator are identified in the corresponding bubbling geometry. We use the supergravity description of surface operators to study the action of the SL(2,Z) duality group of N 4 SYM on the parameters of the surface operator, and find that it coincides with the recent proposal by Gukov and Witten in the framework of the gauge theory approach to the geometrical Langlands with ramification. We also show that whenever a bubbling geometry becomes singular that the path integral description of the corresponding surface operator also becomes singular
Gauge/string duality in confining theories
International Nuclear Information System (INIS)
Edelstein, J.D.; Portugues, R.
2006-01-01
This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Gauge/string duality in confining theories
Energy Technology Data Exchange (ETDEWEB)
Edelstein, J.D. [Departamento de Fi sica de Particulas, Universidade de Santiago de Compostela and Instituto Galego de Fisica de Altas Enerxias (IGFAE), 15782 Santiago de Compostela (Spain); Instituto de Fisica de La Plata (IFLP), Universidad Nacional de La Plata, La Plata (Argentina); Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile); Portugues, R. [Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)
2006-07-03
This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
New dualities of supersymmetric gauge theories
2016-01-01
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures. The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have ...
Virtual Gravity and the Duality of Reality
Harokopos, E
2003-01-01
It is shown that a hypothesis about gravity having a virtual cause implies there are two primary reference frames, a reality and a functional virtual reality and an equivalence principle relating the two is postulated. A mathematical expression relating the primary reference frames to the state of reality provides an explanation of particle-wave duality and resolves the controversy about the speed of gravity. A model for motion, time and particle formation is briefly discussed, in which the hypothesis about the virtual cause of gravity and supporting postulates are valid. It is further shown that such model provides solutions to unsolved paradoxes and a unification of consistent but contradictory ancient theories of matter and motion. Finally, a reference is made about the basis for devising experiments and testing the predictions of the model.
Duality transformations for general abelian systems
International Nuclear Information System (INIS)
Savit, R.
1982-01-01
We describe the general structure of duality transformations for a very broad set of abelian statistical and field theoretic systems. This includes theories with many different types of fields and a large variety of kinds of interactions including, but not limited to nearest neighbor, next nearest neighbor, multi-spin interactions, etc. We find that the dual form of a theory does not depend directly on the dimensionality of the theory, but rather on the number of fields and number of different kinds of interactions. The dual forms we find have a generalized gauge symmetry and posses the usual property of having a temperature (or coupling constant) which is inverted from that of the original theory. Our results reduce to the well-known results in those particular cases that have heretofore been studied. Our procedure also suggests variations capable of generating other forms of the dual theory which may be useful in various specific cases. (orig.)
Double field theory at SL(2) angles
Energy Technology Data Exchange (ETDEWEB)
Ciceri, Franz [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Dibitetto, Giuseppe [Institutionen för fysik och astronomi, University of Uppsala, Box 803, SE-751 08 Uppsala (Sweden); Fernandez-Melgarejo, J.J. [Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Jefferson Physical Laboratory, Harvard University,Cambridge, MA 02138 (United States); Guarino, Adolfo [Physique Théorique et Mathématique, Université Libre de Bruxellesand International Solvay Institutes,ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Inverso, Gianluca [Center for Mathematical Analysis, Geometry and Dynamical Systems,Department of Mathematics, Instituto Superior Tecnico,Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
2017-05-05
An extended field theory is presented that captures the full SL(2)×O(6,6+n) duality group of four-dimensional half-maximal supergravities. The theory has section constraints whose two inequivalent solutions correspond to minimal D=10 supergravity and chiral half-maximal D=6 supergravity, respectively coupled to vector and tensor multiplets. The relation with O(6,6+n) (heterotic) double field theory is thoroughly discussed. Non-Abelian interactions as well as background fluxes are captured by a deformation of the generalised diffeomorphisms. Finally, making use of the SL(2) duality structure, it is shown how to generate gaugings with non-trivial de Roo-Wagemans angles via generalised Scherk-Schwarz ansätze. Such gaugings allow for moduli stabilisation including the SL(2) dilaton.
Quiver gauge theory and extended electric-magnetic duality
International Nuclear Information System (INIS)
Maruyoshi, Kazunobu
2009-01-01
We construct N = 1 A-D-E quiver gauge theory with the gauge kinetic term which depends on the adjoint chiral superfields, as a low energy effective theory on D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The field-dependent gauge kinetic term can be engineered by introducing B-field which holomorphically varies on the base space (complex plane) of Calabi-Yau. We consider Weyl reflection on A-D-E node, which acts non-trivially on the gauge kinetic term. It is known that Weyl reflection is related to N = 1 electric-magnetic duality. Therefore, the non-trivial action implies an extension of the electric-magnetic duality to the case with the field-dependent gauge kinetic term. We show that this extended duality is consistent from the field theoretical point of view. We also consider the duality map of the operators.
The Duality Principle in Teaching Arithmetic and Geometric Series
Yeshurun, Shraga
1978-01-01
The author discusses the use of the duality principle in combination with the hierarchy of algebraic operations in helping students to retain and use definitions and rules for arithmetic and geometric sequences and series. (MN)
Particle-vortex duality in topological insulators and superconductors
Energy Technology Data Exchange (ETDEWEB)
Murugan, Jeff [The Laboratory for Quantum Gravity & Strings, Department of Mathematics and Applied Mathematics, University of Cape Town,Private Bag, Rondebosch, 7700 (South Africa); School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540 (United States); Nastase, Horatiu [Instituto de Física Teórica, UNESP-Universidade Estadual Paulista,R. Dr. Bento T. Ferraz 271, Bl. II, Sao Paulo 01140-070, SP (Brazil)
2017-05-31
We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path integral in the standard way, while in three dimensions, it takes the form of “self-duality in odd dimensions'. In this sense, it is closely related to the particle-vortex duality of planar systems. In particular, we use this to elaborate on Son’s conjecture that a three dimensional Dirac fermion that can be thought of as the surface mode of a four dimensional topological insulator is dual to a composite fermion.
New evidence for (0,2) target space duality
International Nuclear Information System (INIS)
Anderson, Lara B; Feng, He
2017-01-01
In the context of (0, 2) gauged linear sigma models, we explore chains of perturbatively dual heterotic string compactifications. The notion of target space duality originates in non-geometric phases and can be used to generate distinct GLSMs with shared geometric phases leading to apparently identical target space theories. To date, this duality has largely been studied at the level of counting states in the effective theories. We extend this analysis to the effective potential and loci of enhanced symmetry in dual theories. By engineering vector bundles with non-trivial constraints arising from slope-stability (i.e. D-terms) and holomorphy (i.e. F-terms) the detailed structure of the vacuum space of the dual theories can be explored. Our results give new evidence that GLSM target space duality may provide important hints towards a more complete understanding of (0, 2) string dualities. (paper)
What's the point? Hole-ography in Poincare AdS
International Nuclear Information System (INIS)
Espindola, Ricardo; Gueijosa, Alberto; Landetta, Alberto; Pedraza, Juan F.
2018-01-01
In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS 3 via hole-ography, i.e., in terms of differential entropy of the dual CFT 2 . Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.)
What's the point? Hole-ography in Poincare AdS
Energy Technology Data Exchange (ETDEWEB)
Espindola, Ricardo [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); University of Southampton, Mathematical Sciences and STAG Research Centre, Southampton (United Kingdom); Gueijosa, Alberto; Landetta, Alberto [Universidad Nacional Autonoma de Mexico, Departamento de Fisica de Altas Energias, Instituto de Ciencias Nucleares, Mexico City (Mexico); Pedraza, Juan F. [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands)
2018-01-15
In the context of the AdS/CFT correspondence, we study bulk reconstruction of the Poincare wedge of AdS{sub 3} via hole-ography, i.e., in terms of differential entropy of the dual CFT{sub 2}. Previous work had considered the reconstruction of closed or open spacelike curves in global AdS, and of infinitely extended spacelike curves in Poincare AdS that are subject to a periodicity condition at infinity. Working first at constant time, we find that a closed curve in Poincare is described in the CFT by a family of intervals that covers the spatial axis at least twice. We also show how to reconstruct open curves, points and distances, and obtain a CFT action whose extremization leads to bulk points. We then generalize all of these results to the case of curves that vary in time, and discover that generic curves have segments that cannot be reconstructed using the standard hole-ographic construction. This happens because, for the nonreconstructible segments, the tangent geodesics fail to be fully contained within the Poincare wedge. We show that a previously discovered variant of the hole-ographic method allows us to overcome this challenge, by reorienting the geodesics touching the bulk curve to ensure that they all remain within the wedge. Our conclusion is that all spacelike curves in Poincare AdS can be completely reconstructed with CFT data, and each curve has in fact an infinite number of representations within the CFT. (orig.)
Twist deformations leading to κ-Poincaré Hopf algebra and their application to physics
International Nuclear Information System (INIS)
Jurić, Tajron; Meljanac, Stjepan; Samsarov, Andjelo
2016-01-01
We consider two twist operators that lead to kappa-Poincaré Hopf algebra, the first being an Abelian one and the second corresponding to a light-like kappa-deformation of Poincaré algebra. The adventage of the second one is that it is expressed solely in terms of Poincaré generators. In contrast to this, the Abelian twist goes out of the boundaries of Poincaré algebra and runs into envelope of the general linear algebra. Some of the physical applications of these two different twist operators are considered. In particular, we use the Abelian twist to construct the statistics flip operator compatible with the action of deformed symmetry group. Furthermore, we use the light-like twist operator to define a star product and subsequently to formulate a free scalar field theory compatible with kappa-Poincaré Hopf algebra and appropriate for considering the interacting ϕ 4 scalar field model on kappa-deformed space. (paper)
Directory of Open Access Journals (Sweden)
Milovanović Branislav
2007-01-01
Full Text Available Introduction: There are different proofs about association of autonomic nervous system dysfunction, especially nonlinear parameters, with higher mortality after myocardial infarction. Objective The objective of the study was to determine predictive value of Poincare plot as nonlinear parameter and other significant standard risk predictors: ejection fraction of the left ventricle, late potentials, ventricular arrhythmias, and QT interval. Method The study included 1081 patients with mean follow up of 28 months (ranging fom 0-80 months. End-point of the study was cardiovascular mortality. The following diagnostic methods were used during the second week: ECG with commercial software Schiller AT-10: short time spectral analysis of RR variability with analysis of Poincare plot as nonlinear parameter and late potentials; 24-hour ambulatory ECG monitoring: QT interval, RR interval, QT/RR slope, ventricular arrhythmias (Lown >II; echocardiography examinations: systolic disorder (defined as EF<40 %. Results There were 103 (9.52% cardiovascular deaths during the follow-up. In univariate analysis, the following parameters were significantly correlated with mortality: mean RR interval < 800 ms, QT and RR interval space relationship as mean RR interval < 800 ms and QT interval > 350 ms, positive late potentials, systolic dysfunction, Poincare plot as a point, ventricular arrhythmias (Lown > II. In multivariate analysis, the significant risk predictors were: Poincare plot as a point and mean RR interval lower than 800 ms. Conclusion Mean RR interval lower than 800 ms and nonlinear and space presentation of RR interval as a point Poincare plot were multivariate risk predictors.
Wave–particle duality in a Raman atom interferometer
International Nuclear Information System (INIS)
Jia Ai-Ai; Yang Jun; Yan Shu-Hua; Hu Qing-Qing; Luo Yu-Kun; Zhu Shi-Yao
2015-01-01
We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ − π − π/2 type of atom interferometer, we find that the visibility (V) and predictability (P) still satisfy the duality relation, P 2 + V 2 ≤ 1. (paper)
Tree-loop duality relation beyond single poles
Energy Technology Data Exchange (ETDEWEB)
Bierenbaum, Isabella [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Buchta, Sebastian; Draggiotis, Petros; Malamos, Ioannis; Rodrigo, German [Valencia Univ. Paterna (Spain). Inst. de Fisica Corpuscular
2012-11-15
We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
Duality symmetries and the Type II string effective action
International Nuclear Information System (INIS)
Bergshoeff, E.
1996-01-01
We discuss the duality symmetries of Type II string effective actions in nine, ten and eleven dimensions. As a by-product we give a covariant action underlying the ten-dimensional Type IIB supergravity theory. We apply duality symmetries to construct dyonic Type II string solutions in six dimensions and their reformulation as solutions of the ten-dimensional Type IIB theory in ten dimensions. (orig.)
Dualities for multi-state probabilistic cellular automata
International Nuclear Information System (INIS)
López, F Javier; Sanz, Gerardo; Sobottka, Marcelo
2008-01-01
In this paper a new form of duality for probabilistic cellular automata (PCA) is introduced. Using this duality, an ergodicity result for processes having a dual is proved. Also, conditions on the probabilities defining the evolution of the processes for the existence of a dual are provided. The results are applied to wide classes of PCA which include multi-opinion voter models, competition models and the Domany–Kinzel model
Efficiency and Generalized Convex Duality for Nondifferentiable Multiobjective Programs
Directory of Open Access Journals (Sweden)
Bae KwanDeok
2010-01-01
Full Text Available We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly efficient solutions are presented. We formulate Mond-Weir-type and Wolfe-type dual problems and establish weak and strong duality theorems for efficient solutions by using suitable generalized convexity conditions. Some special cases of our duality results are given.
Duality quantum algorithm efficiently simulates open quantum systems
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-01-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm. PMID:27464855
MIMO processing based on higher-order Poincaré spheres
Fernandes, Gil M.; Muga, Nelson J.; Pinto, Armando N.
2017-08-01
A multi-input multi-output (MIMO) algorithm based on higher-order Poincaré spheres is demonstrated for space-division multiplexing (SDM) systems. The MIMO algorithm is modulation format agnostic, robust to frequency offset and does not require training sequences. In this approach, the space-multiplexed signal is decomposed in sets of two tributary signals, with each set represented in a higher-order Poincaré sphere. For any arbitrary complex modulation format, the samples of two tributaries can be represented in a given higher-order Poincaré sphere with a symmetry plane. The crosstalk along propagation changes the spatial orientation of this plane and, therefore, it can be compensated by computing and realigning the best fit plane. We show how the transmitted signal can be successfully recovered using this procedure for all possible combinations of tributaries. Moreover, we analyze the convergence speed for the MIMO technique considering several optical-to-noise ratios.
Conventionalism about what? Where Duhem and Poincaré part ways.
Ivanova, Milena
2015-12-01
This paper examines whether, and in what contexts, Duhem's and Poincaré's views can be regarded as conventionalist or structural realist. After analysing the three different contexts in which conventionalism is attributed to them-in the context of the aim of science, the underdetermination problem and the epistemological status of certain principles-I show that neither Duhem's nor Poincaré's arguments can be regarded as conventionalist. I argue that Duhem and Poincaré offer different solutions to the problem of theory choice, differ in their stances towards scientific knowledge and the status of scientific principles, making their epistemological claims substantially different. Copyright © 2015 Elsevier Ltd. All rights reserved.
Casimir energy between two parallel plates and projective representation of the Poincaré group
Akita, Takamaru; Matsunaga, Mamoru
2016-06-01
The Casimir effect is a physical manifestation of zero point energy of quantum vacuum. In a relativistic quantum field theory, Poincaré symmetry of the theory seems, at first sight, to imply that nonzero vacuum energy is inconsistent with translational invariance of the vacuum. In the setting of two uniform boundary plates at rest, quantum fields outside the plates have (1 +2 )-dimensional Poincaré symmetry. Taking a massless scalar field as an example, we have examined the consistency between the Poincaré symmetry and the existence of the vacuum energy. We note that, in quantum theory, symmetries are represented projectively in general and show that the Casimir energy is connected to central charges appearing in the algebra of generators in the projective representations.
Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.
2009-01-01
Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.
Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond
Energy Technology Data Exchange (ETDEWEB)
Fuentealba, Oscar [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Matulich, Javier; Troncoso, Ricardo [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile)
2015-09-01
An extension of the Poincaré group with half-integer spin generators is explicitly constructed. We start discussing the case of three spacetime dimensions, and as an application, it is shown that hypergravity can be formulated so as to incorporate this structure as its local gauge symmetry. Since the algebra admits a nontrivial Casimir operator, the theory can be described in terms of gauge fields associated to the extension of the Poincaré group with a Chern-Simons action. The algebra is also shown to admit an infinite-dimensional non-linear extension, that in the case of fermionic spin-3/2 generators, corresponds to a subset of a contraction of two copies of WB{sub 2}. Finally, we show how the Poincaré group can be extended with half-integer spin generators for d≥3 dimensions.
Magnetic vortices in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Strydom, Migael
2014-07-18
We study strongly-coupled phenomena using gauge/gravity duality, with a particular focus on vortex solutions produced by magnetic field and time-dependent problems in holographic models. The main result is the discovery of a counter-intuitive effect where a strong non-abelian magnetic field induces the formation of a triangular vortex lattice ground state in a simple holographic model. Gauge/gravity duality is a powerful theoretical tool that has been used to study strongly-coupled systems ranging from the quark-gluon plasma produced at particle colliders to condensed matter theories. The most important idea is that of duality: a strongly coupled quantum field theory can be studied by investigating the properties of a particular gravity background described by Einstein's equations. One gravity background we study in this dissertation is AdS-Schwarzschild with an SU(2) gauge field. We switch on the gauge field component that gives the field theory an external magnetic field. When the magnetic field is above a critical value, we find that the system is unstable, indicating a superconducting phase transition. We find the instability in two ways. Firstly, we do a quasinormal mode analysis, studying fluctuations about the background. Secondly, we rewrite the equations in Schroedinger form and numerically find that, as the magnetic field is increased, the potential deepens until it is capable of supporting a bound state. Next we show that the resulting superconducting ground state is a triangular vortex lattice. This is done by performing a perturbative expansion in a small parameter proportional to the condensate size. After solving the equations to third order, we use the holographic dictionary to calculate the total energy of different lattice solutions and identify the minimum energy state. In addition, we show that the result holds in an AdS-hard wall model as well, which is dual to a confining theory. Next we extend the simple gravity model to include a
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
Euler-Poincaré Reduction of Externally Forced Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action....... Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
The Poincaré Half-Plane for Informationally-Complete POVMs
Planat, Michel
2017-12-01
It has been shown that classes of (minimal asymmetric) informationally complete POVMs in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states [M. Planat and Z. Gedik, R. Soc. open sci. 4, 170387 (2017)]. The latter states may also be derived starting from the Poincar\\'e upper half-plane model H. For doing this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates whose some of the eigenstates are the seeked fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen-Specker theorem.
Heterotic-type II string duality and the H-monopole problem
Girardello, L; Zaffaroni, A
1996-01-01
Since T-duality has been proved only perturbatively and most of the heterotic states map into solitonic, non-perturbative, type II states, the 6-dimensional string-string duality between the heterotic string and the type II string is not sufficient to prove the S-duality of the former, in terms of the known T-duality of the latter. We nevertheless show in detail that perturbative T-duality, together with the heterotic-type II duality, does imply the existence of heterotic H-monopoles, with the correct multiplicity and multiplet structure. This construction is valid at a generic point in the moduli space of heterotic toroidal compactifications.
DEFF Research Database (Denmark)
Lützen, Jesper
2007-01-01
Artiklen analyserer kantianske, empiricistiske og konventionalistiske tendenser i Heinrich Hertz's Prinzipien der Mechanik (1894) og sammenligner dem med tilsvarende tendenser i Henri Poincaré's La science et l'hypothèse (1902). Derved belyses Poincaré's reaktion på kantianismen...
The bicovariant differential calculus on the κ-Poincare group and on the κ-Minkowski space
International Nuclear Information System (INIS)
Kosinski, P.; Maslanka, P.; Sobczyk, J.
1996-01-01
The bicovariant differential calculus on the four-dimensional κ-Poincare group and the corresponding Lie-algebra-like structure are described. The differential calculus on the n-dimensional κ-Minkowski space covariant under the action of the κ-Poincare group was constructed. 5 refs
Disentangling the f(R)-duality
Energy Technology Data Exchange (ETDEWEB)
Broy, Benedict J.; Westphal, Alexander [Deutsches Elektronen-Synchrotron DESY, Theory Group, Hamburg, 22603 Germany (Germany); Pedro, Francisco G., E-mail: benedict.broy@desy.de, E-mail: francisco.pedro@desy.de, E-mail: alexander.westphal@desy.de [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, Madrid, 28049 Spain (Spain)
2015-03-01
Motivated by UV realisations of Starobinsky-like inflation models, we study generic exponential plateau-like potentials to understand whether an exact f(R)-formulation may still be obtained when the asymptotic shift-symmetry of the potential is broken for larger field values. Potentials which break the shift symmetry with rising exponentials at large field values only allow for corresponding f(R)-descriptions with a leading order term R{sup n} with 1
Disentangling the f(R)-duality
Energy Technology Data Exchange (ETDEWEB)
Broy, Benedict J. [Deutsches Elektronen-Synchrotron DESY, Theory Group, Hamburg, 22603 (Germany); Pedro, Francisco G. [Departamento de Física Teórica and Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, Madrid, 28049 (Spain); Westphal, Alexander [Deutsches Elektronen-Synchrotron DESY, Theory Group, Hamburg, 22603 (Germany)
2015-03-16
Motivated by UV realisations of Starobinsky-like inflation models, we study generic exponential plateau-like potentials to understand whether an exact f(R)-formulation may still be obtained when the asymptotic shift-symmetry of the potential is broken for larger field values. Potentials which break the shift symmetry with rising exponentials at large field values only allow for corresponding f(R)-descriptions with a leading order term R{sup n} with 1
Alexandrov, Sergei
2012-01-01
In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.
Alexandrov, Sergei; Pioline, Boris
2012-08-01
In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space {{M}_H} must carry an isometric action of the modular group SL(2 , {Z} ), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of {{M}_H} , and construct a general class of SL(2 , {Z} )-invariant quaternion-Kähler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include {{M}_H} corrected by D3-D1-D(-1)-instantons (with five-brane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional {N} = {2} gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.
International Nuclear Information System (INIS)
Marklund, T.
1978-01-01
The most commonly used methods of assessing the scoliotic deviation measure angles that are not clearly defined in relation to the anatomy of the patient. In order to give an anatomic basis for such measurements it is proposed to define the scoliotic deviation as the deviation the vertebral column makes with the sagittal plane. Both the Cobb and the Ferguson angles may be based on this definition. The present methods of measurement are then attempts to measure these angles. If the plane of these angles is parallel to the film, the measurement will be correct. Errors in the measurements may be incurred by the projection. A hypothetical projection, called a 'rectified orthogonal projection', is presented, which correctly represents all scoliotic angles in accordance with these principles. It can be constructed in practice with the aid of a computer and by performing measurements on two projections of the vertebral column; a scoliotic curve can be represented independent of the kyphosis and lordosis. (Auth.)
Hard scattering and gauge/string duality
International Nuclear Information System (INIS)
Polchinski, Joseph; Strassler, Matthew J.
2002-01-01
We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions
Multiple fibrations in Calabi-Yau geometry and string dualities
Energy Technology Data Exchange (ETDEWEB)
Anderson, Lara B.; Gao, Xin; Gray, James; Lee, Seung-Joo [Physics Department, Virginia Tech,Robeson Hall, Blacksburg, VA 24061 (United States)
2016-10-19
In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA, and heterotic string theories. Our results include many M-/F-theory correspondences in which distinct F-theory vacua — associated to different elliptic fibrations of the same CY n-fold — give rise to the same M-theory limit in one dimension lower. Examples include 5-dimensional correspondences between 6-dimensional theories with Abelian, non-Abelian and superconformal structure, as well as examples of higher rank Mordell-Weil geometries. In addition, in the context of heterotic/F-theory duality, we investigate the role played by multiple K3- and elliptic fibrations in known and novel string dualities in 8-, 6- and 4-dimensional theories. Here we systematically summarize nested fibration structures and comment on the roles they play in T-duality, mirror symmetry, and 4-dimensional compactifications of F-theory with G-flux. This investigation of duality structures is made possible by geometric tools developed in a companion paper http://arxiv.org/abs/1608.07554.
Stringy horizons and generalized FZZ duality in perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Giribet, Gaston [Martin Fisher School of Physics, Brandeis University,Waltham, Massachusetts 02453 (United States); Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET,Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina)
2017-02-14
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n−2 winding modes actually coincide with the correlation functions in the SL(2,ℝ)/U(1) gauged WZW model that include n−2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference https://www.doi.org/10.1007/JHEP10(2016)157. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
Poincare group and relativistic wave equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)
1997-09-07
Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)
The foundations of chaos revisited from Poincaré to recent advancements
2016-01-01
With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory.
Controlled generation of higher-order Poincaré sphere beams from a laser
CSIR Research Space (South Africa)
Naidoo, Darryl
2016-03-01
Full Text Available . 10: 327-332 Controlled generation of higher-order Poincaré sphere beams from a laser Naidoo D Roux FS Dudley A Litvin I Piccirillo B Marrucci L Forbes A ABSTRACT: The angular momentum of light can be described by positions on a...
Geometry as an Object of Experience: The Missed Debate between Poincare and Einstein
Hacyan, Shahen
2009-01-01
According to Poincare, a geometry cannot be an object of experience since any geometrical experiment must be realized with physical objects, such as rulers and light rays, and it is only their properties that can be tested. This position was apparently refuted by general relativity and the successful confirmation of its predictions by astronomical…
Multiscale Poincaré plots for visualizing the structure of heartbeat time series.
Henriques, Teresa S; Mariani, Sara; Burykin, Anton; Rodrigues, Filipa; Silva, Tiago F; Goldberger, Ary L
2016-02-09
Poincaré delay maps are widely used in the analysis of cardiac interbeat interval (RR) dynamics. To facilitate visualization of the structure of these time series, we introduce multiscale Poincaré (MSP) plots. Starting with the original RR time series, the method employs a coarse-graining procedure to create a family of time series, each of which represents the system's dynamics in a different time scale. Next, the Poincaré plots are constructed for the original and the coarse-grained time series. Finally, as an optional adjunct, color can be added to each point to represent its normalized frequency. We illustrate the MSP method on simulated Gaussian white and 1/f noise time series. The MSP plots of 1/f noise time series reveal relative conservation of the phase space area over multiple time scales, while those of white noise show a marked reduction in area. We also show how MSP plots can be used to illustrate the loss of complexity when heartbeat time series from healthy subjects are compared with those from patients with chronic (congestive) heart failure syndrome or with atrial fibrillation. This generalized multiscale approach to Poincaré plots may be useful in visualizing other types of time series.
The bicovariant differential calculus on the κ-Poincare and κ-Weyl groups
International Nuclear Information System (INIS)
Przanowski, K.
1997-01-01
The bicovariant differential calculus on four-dimensional κ-Poincare group and corresponding Lie-algebra-like structure for any metric tensor are described. The bicovariant differential calculus on four-dimensional κ-Weyl group and corresponding Lie-algebra-like structure for any metric tensor in the reference frame in which g 00 = 0 are considered. (author). 6 refs
Heart rate variability analysed by Poincaré plot in patients with metabolic syndrome
Czech Academy of Sciences Publication Activity Database
Kubíčková, A.; Kozumplík, J.; Nováková, Z.; Plachý, M.; Jurák, Pavel; Lipoldová, J.
2016-01-01
Roč. 49, č. 1 (2016), s. 23-28 ISSN 0022-0736 R&D Projects: GA ČR GAP102/12/2034 Institutional support: RVO:68081731 Keywords : heart rate variability * metabolic syndrome * Poincaré plot * tilt table test * controlled breathing Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.514, year: 2016
A comment on continuous spin representations of the Poincare group and perturbative string theory
Energy Technology Data Exchange (ETDEWEB)
Font, A. [Departamento de Fisica, Centro de Fisica Teorica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Caracas (Venezuela, Bolivarian Republic of); Quevedo, F. [Abdus Salam ICTP, Trieste (Italy); DAMTP/CMS, University of Cambridge, Wilberforce Road, Cambridge (United Kingdom); Theisen, S. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany)
2014-11-04
We make a simple observation that the massless continuous spin representations of the Poincare group are not present in perturbative string theory constructions. This represents one of the very few model-independent low-energy consequences of these models. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Poincaré invariance in low-energy EFTs for QCD
Directory of Open Access Journals (Sweden)
Hwang Sungmin
2017-01-01
Full Text Available We present the calculations on deriving constraints between the Wilson coefficients in non-relativistic quantum chromodynamics and potential non-relativistic quantum chromodynamics by exploiting the symmetry of its fundamental theory, Poincaré invariance in particular. Implications of the constraints are briefly discussed in the context of the effective string theory.
Representations of the Poincare group, position operator and the bi-local model
International Nuclear Information System (INIS)
Sohkawa, Tohru
1978-01-01
We propose two types of representations of the Poincare group which give general frameworks for introduction of internal degrees of freedom of a particle. The bi-local model recently proposed by Takabayasi is constructed through our frameworks. In this study, new covariant and non-covariant position operators are introduced and discussed. (author)
Return times dynamics: role of the Poincare section in numerical analysis
International Nuclear Information System (INIS)
Pavlov, Alexey N.; Dumsky, Dmitry V.
2003-01-01
We study how different measures estimated from return time sequences are sensitive to choice of the Poincare section in the case of chaotic dynamics. We show that scaling characteristics of point processes are highly dependent on the secant plane. We focus on dynamical properties of a chaotic regime being more stable to displacements of the section than metrical characteristics
Geometry of the Poincaré compactification of a four-dimensional food-web system
Czech Academy of Sciences Publication Activity Database
Priyadarshi, Anupam; Banerjee, S.; Gakkhar, S.
2014-01-01
Roč. 226, JAN 1 (2014), s. 229-237 ISSN 0096-3003 R&D Projects: GA MŠk(CZ) EE2.3.30.0032 Institutional support: RVO:60077344 Keywords : Poincaré compactification * global dynamics * boundedness Subject RIV: EH - Ecology, Behaviour Impact factor: 1.551, year: 2014 http://www.sciencedirect.com/science/article/pii/S0096300313011247
Spectral properties of Pauli operators on the Poincare upper-half plane
International Nuclear Information System (INIS)
Inahama, Yuzuru; Shirai, Shin-ichi
2003-01-01
We investigate the essential spectrum of the Pauli operators (and the Dirac and the Schroedinger operators) with magnetic fields on the Poincare upper-half plane. The magnetic fields under consideration are asymptotically constant (which may be equal to zero), or diverge at infinity. Moreover, the Aharonov-Casher type result is also considered
Magnetic bottles on the Poincaré half-plane: spectral asymptotics.
Morame , Abderemane; Truc , Francoise
2008-01-01
We consider a magnetic Laplacian $-\\Delta_A=(id+A)^{\\star} (id+A)$ on the Poincaré upper-half plane $mathbb{H}$ when the magnetic field $dA$ is infinite at the infinity such that $-\\Delta_A$ has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.
Laughlin states on the Poincare half-plane and its quantum group symmetry
Alimohammadi, M.; Sadjadi, H. Mohseni
1996-01-01
We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE.
Degeneracy of the lowest Landau level and suq(2) on the Poincare half plane
International Nuclear Information System (INIS)
Jellal, A.
2000-01-01
It is shown that the presence of the quantum group symmetry su q (2) in the quantum Hall effect on the Poincare upper half plane the degeneracy of the lowest Landau level. It is also shown that the relation between the degeneracy and the cyclic representation of su q (2) appears in accordance with q being a kth root of unity. (Authors)
S-duality constraint on higher-derivative couplings
International Nuclear Information System (INIS)
Garousi, Mohammad R.
2014-01-01
The Riemann curvature correction to the type II supergravity at eight-derivative level in string frame is given as e"−"2"ϕ(t_8t_8R"4+(1/4)ϵ_8ϵ_8R"4). For constant dilaton, it has been extended in the literature to the S-duality invariant form by extending the dilaton factor in the Einstein frame to the non-holomorphic Eisenstein series. For non-constant dilaton, however, there are various couplings in the Einstein frame which are not consistent with the S-duality. By constructing the tensors t_2_n from Born-Infeld action, we include the appropriate Ricci and scalar curvatures as well as the dilaton couplings to make the above action to be consistent with the S-duality
Unification of type-II strings and T duality.
Hohm, Olaf; Kwak, Seung Ki; Zwiebach, Barton
2011-10-21
We present a unified description of the low-energy limits of type-II string theories. This is achieved by a formulation that doubles the space-time coordinates in order to realize the T-duality group O(10,10) geometrically. The Ramond-Ramond fields are described by a spinor of O(10,10), which couples to the gravitational fields via the Spin(10,10) representative of the so-called generalized metric. This theory, which is supplemented by a T-duality covariant self-duality constraint, unifies the type-II theories in that each of them is obtained for a particular subspace of the doubled space. © 2011 American Physical Society
Heterotic/Type-II duality and its field theory avatars
International Nuclear Information System (INIS)
Kiritsis, Elias
1999-01-01
In these lecture notes, I will describe heterotic/type-II duality in six and four dimensions. When supersymmetry is the maximal N=4 it will be shown that the duality reduces in the field theory limit to the Montonen-Olive duality of N=4 Super Yang-Mills theory. We will consider further compactifications of type II theory on Calabi-Yau manifolds. We will understand the physical meaning of geometric conifold singularities and the dynamics of conifold transitions. When the CY manifold is a K3 fibration we will argue that the type-II ground-state is dual to the heterotic theory compactified on K3xT 2 . This allows an exact computation of the low effective action. Taking the field theory limit, α ' →0, we will recover the Seiberg-Witten non-perturbative solution of N=2 gauge theory
p-brane dyons and electric-magnetic duality
International Nuclear Information System (INIS)
Deser, S.; Henneaux, M.; Teitelboim, C.
1998-01-01
We discuss dyons, charge quantization and electric-magnetic duality for self-interacting, abelian, p-form theories in the space-time dimensions D=2(p+1) where dyons can be present. The corresponding quantization conditions and duality properties are strikingly different depending on whether p is odd or even. If p is odd one has the familiar e anti g-g anti e=2πnℎ, whereas for even p one finds the opposite relative sign, e anti g+g anti e=2πnℎ. These conditions are obtained by introducing Dirac strings and taking due account of the multiple connectedness of the configuration space of the strings and the dyons. A two-potential formulation of the theory that treats the electric and magnetic sources on the same footing is also given. Our results hold for arbitrary gauge invariant self-interaction of the fields and are valid irrespective of their duality properties. (orig.)
Duality for heavy-quark systems. II. Coupled channels
International Nuclear Information System (INIS)
Durand, B.; Durand, L.
1981-01-01
We derive the duality relation approx. = which relates a suitable energy average of the physical coupled-channel cross section sigma=sigma(e + e - →hadrons) to the same average of the cross section sigma/sub bound/ for the production of bound qq-bar states in a single-channel confining potential. The average is equated by our previous work to the average cross section for production of a qq-bar pair moving freely in the nonconfining color Coulomb potential. Thus, approx. = . The corrections to these duality relations are calculable. We give an exactly solvable coupled-two-channel model and use it to verify duality for both weak and strong coupling
S-duality constraint on higher-derivative couplings
Energy Technology Data Exchange (ETDEWEB)
Garousi, Mohammad R. [Department of Physics, Ferdowsi University of Mashhad,P.O. Box 1436, Mashhad (Iran, Islamic Republic of)
2014-05-22
The Riemann curvature correction to the type II supergravity at eight-derivative level in string frame is given as e{sup −2ϕ}(t{sub 8}t{sub 8}R{sup 4}+(1/4)ϵ{sub 8}ϵ{sub 8}R{sup 4}). For constant dilaton, it has been extended in the literature to the S-duality invariant form by extending the dilaton factor in the Einstein frame to the non-holomorphic Eisenstein series. For non-constant dilaton, however, there are various couplings in the Einstein frame which are not consistent with the S-duality. By constructing the tensors t{sub 2n} from Born-Infeld action, we include the appropriate Ricci and scalar curvatures as well as the dilaton couplings to make the above action to be consistent with the S-duality.
Canonical duality theory unified methodology for multidisciplinary study
Latorre, Vittorio; Ruan, Ning
2017-01-01
This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in comp...
On Various R-duals and the Duality Principle
DEFF Research Database (Denmark)
Stoeva, Diana T.; Christensen, Ole
2016-01-01
to a characterization of frames in terms of associated Riesz sequences; however, it is still an open question whether this abstract theory is a generalization of the duality principle. In this paper we prove that a modified version of the R-duals leads to a generalization of the duality principle that keeps all......The duality principle states that a Gabor system is a frame if and only if the corresponding adjoint Gabor system is a Riesz sequence. In general Hilbert spaces and without the assumption of any particular structure, Casazza, Kutyniok and Lammers have introduced the so-called R-duals that also lead...... the attractive properties of the R-duals. In order to provide extra insight into the relations between a given sequence and its R-duals, we characterize all the types of R-duals that are available in the literature for the special case where the underlying sequence is a Riesz basis....
N = (4,4 Supersymmetry and T-Duality
Directory of Open Access Journals (Sweden)
Malin Göteman
2012-10-01
Full Text Available A sigma model with four-dimensional target space parametrized by chiral and twisted chiral N =(2,2 superfields can be extended to N =(4,4 supersymmetry off-shell, but this is not true for a model of semichiral fields, where the N = (4,4 supersymmetry can only be realized on-shell. The two models can be related to each other by T-duality. In this paper we perform a duality transformation from a chiral and twisted chiral model with off-shell N = (4,4 supersymmetry to a semichiral model. We find that additional non-linear terms must be added to the original transformations to obtain a semichiral model with N =(4,4 supersymmetry, and that the algebra closes on-shell as a direct consequence of the T-duality.
DUALITY IN SMALL AND MEDIUM ENTERPRISE ACCOUNTING PRACTICES
Directory of Open Access Journals (Sweden)
Fadilla Cahyaningtyas
2017-12-01
Full Text Available This research is aimed to comprehend the accounting practice and its benefit in triggering one of the most credible SMEs in Malang City to succeed, SME Garuda Jaya. The analytical tool used in this research is transcendental phenomenology. Based on data analysis, two kinds of accounting practices are: (1 accounting practice of mind and memory; and (2 accounting notation to the arrangement of basic financial statements in the form of balance sheets and Profit/ Loss (L / R. both practical accounting establishes duality practices, a practice that combines two distinct and different things into integral and appropriate things to do an accounting practice. Therefore, first, duality practices seek to make synergistic social and economic value. Second, the practice of duality establishes the integration of "masculine" and "feminist" characters to achieve business success, which not only places the orientation into the material aspects of earning income but also on environmental and social responsibility.
Hyperasymptotics and quark-hadron duality violations in QCD
Boito, Diogo; Caprini, Irinel; Golterman, Maarten; Maltman, Kim; Peris, Santiago
2018-03-01
We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex q2 plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality-violating contributions. Starting with the assumption that for QCD at Nc=∞ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite Nc.
Aspects of U-duality in matrix theory
International Nuclear Information System (INIS)
Blau, M.; O'Loughlin, M.
1997-12-01
We explore various aspects of implementing the full M-theory U-duality group E d+1 , and thus Lorentz invariance, in the finite N matrix theory (DLCQ of M-theory) describing toroidal IIA-compactifications on d-tori: (1) We generalize the analysis of Elitzur et al. (hep-th/9707217) from E d to E d+1 and identify the highest weight states unifying the momentum and flux E d -multiplets into one E d+1 -orbit, (2) We identify the new symmetries, in particular the Weyl group symmetry associated to the (d+1)'th node of the E d+1 Dynkin diagram, with Nahm-duality-like symmetries (N-duality) exchanging the rank N of the matrix theory gauge group with other (electric, magnetic, ...) quantum numbers. (3) We describe the action of N-duality on BPS bound states, thus making testable predictions for the Lorentz invariance of matrix theory. (4) We discuss the problems that arise in the matrix theory limit for BPS states with no top-dimensional branes, i.e. configurations with N = 0. (5) We show that N-duality maps the matrix theory SYM picture to the matrix string picture and argue that, for d even, the latter should be thought of as an M-theory membrane description (which appears to be well defined even for d > 5). (6) We find a compact and unified expression for a U-duality invariant of E d+1 for all d and show that in d = 5,6 it reduces to the black hole entropy cubic E 6 - and quartic E 7 -invariants respectively. (7) Finally, we describe some of the solitonic states in d = 6,7 and give an example (a 'rolled-up' Taub-NUT 6-brane) of a configuration exhibiting the unusual 1/g 3 s -behaviour. (author)
N = 1 quasi self-duality in the N = 2 Yang-Mills theory
International Nuclear Information System (INIS)
Pavlik, O.V.; Yatsun, V.A.
1998-01-01
The system of first-order equations-quasi self-duality equations-for component fields of the N = 2 SUSY Yang-Mills theory is suggested, which leads to equations of motion and reduces to self-duality equations if scalar fields vanish. The symmetries of quasi self-duality equations are studied
Duality and bosonization in Schwinger–Keldysh formulation
International Nuclear Information System (INIS)
Saraví, R E Gamboa; Naón, C M; Schaposnik, F A
2014-01-01
We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger–Keldysh time closed contour technique, to handle the non-equilibrium situation. The duality approach to bosonization that we present is valid for D ≥ 2 space–time dimensions leading for D = 2 to exact results. In this last case we present the bosonization rules for fermion currents, calculate current–current correlation functions and establish the connection between the fermionic and bosonic distribution functions in a generic, non-equilibrium situation. (paper)
Thermal duality and Hagedorn transition from p-adic strings.
Biswas, Tirthabir; Cembranos, Jose A R; Kapusta, Joseph I
2010-01-15
We develop the finite temperature theory of p-adic string models. We find that the thermal properties of these nonlocal field theories can be interpreted either as contributions of standard thermal modes with energies proportional to the temperature, or inverse thermal modes with energies proportional to the inverse of the temperature, leading to a thermal duality at leading order (genus one) analogous to the well-known T duality of string theory. The p-adic strings also recover the asymptotic limits (high and low temperature) for arbitrary genus that purely stringy calculations have yielded. We also discuss our findings surrounding the nature of the Hagedorn transition.
Quantitative Boltzmann-Gibbs Principles via Orthogonal Polynomial Duality
Ayala, Mario; Carinci, Gioia; Redig, Frank
2018-06-01
We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann-Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.
Path integral formulation of the Hodge duality on the brane
International Nuclear Information System (INIS)
Hahn, Sang-Ok; Kiem, Youngjai; Kim, Yoonbai; Oh, Phillial
2001-01-01
In the warped compactification with a single Randall-Sundrum brane, a puzzling claim has been made that scalar fields can be bound to the brane but their Hodge dual higher-rank antisymmetric tensors cannot. By explicitly requiring the Hodge duality, a prescription to resolve this puzzle was recently proposed by Duff and Liu. In this Brief Report, we implement the Hodge duality via the path integral formulation in the presence of the background gravity fields of warped compactifications. It is shown that the prescription of Duff and Liu can be naturally understood within this framework
Quark-hadron duality of nucleon spin structure function
International Nuclear Information System (INIS)
Dong, Y.B.
2005-01-01
Bloom-Gilman quark-hadron duality of nuclear spin structure function is studied by comparing the integral of g 1 from perturbative QCD prediction in the scaling region to the moment of g 1 in the resonance region. The spin structure function in the resonance region is estimated by the parametrization forms of non-resonance background and of resonance contributions. The uncertainties of our calculations due to those parametrization forms are discussed. Moreover, the effect of the Δ(1232)-resonance in the first resonance region and the role of the resonances in the second resonance region are explicitly shown. Elastic peak contribution to the duality is also analyzed. (orig.)
Interpreting multiple dualities conjectured from superconformal index identities
Khmelnitsky, A
2010-01-01
We consider field theory side of new multiple Seiberg dualities conjectured within superconformal index matching approach. We study the case of SU(2) supersymmetric QCD and find that the numerous conjectured duals are different faces of handful of master theories. These different faces are inequivalent to each other in a very peculiar sense. Some master theories are fully known; we construct superpotentials for others. We confirm that all index identities correspond to theories flowing to one and the same theory in the infrared, thus supporting the conjecture of index matching for Seiberg dual theories. However, none of the index identities considered in this paper actually implies an entirely new, unknown duality.
Entanglement entropy and duality in AdS4
Directory of Open Access Journals (Sweden)
Ioannis Bakas
2015-07-01
Full Text Available Small variations of the entanglement entropy δS and the expectation value of the modular Hamiltonian δE are computed holographically for circular entangling curves in the boundary of AdS4, using gravitational perturbations with general boundary conditions in spherical coordinates. Agreement with the first law of thermodynamics, δS=δE, requires that the line element of the entangling curve remains constant. In this context, we also find a manifestation of electric–magnetic duality for the entanglement entropy and the corresponding modular Hamiltonian, following from the holographic energy–momentum/Cotton tensor duality.
Local beam angle optimization with linear programming and gradient search
International Nuclear Information System (INIS)
Craft, David
2007-01-01
The optimization of beam angles in IMRT planning is still an open problem, with literature focusing on heuristic strategies and exhaustive searches on discrete angle grids. We show how a beam angle set can be locally refined in a continuous manner using gradient-based optimization in the beam angle space. The gradient is derived using linear programming duality theory. Applying this local search to 100 random initial angle sets of a phantom pancreatic case demonstrates the method, and highlights the many-local-minima aspect of the BAO problem. Due to this function structure, we recommend a search strategy of a thorough global search followed by local refinement at promising beam angle sets. Extensions to nonlinear IMRT formulations are discussed. (note)
Duality of female employment in Pakistan.
Kazi, S; Raza, B
1991-01-01
The trends in the level and pattern of women's employment in Pakistan in terms of supply and demand factors which influence women's participation in the labor market are discussed. Women's labor participation is underestimated in official sources such as the Labor Force Survey (LFS) and the Population Census. Figures which were obtained from micro level surveys and the Agricultural Census, show the duality of employment at the top and bottom socioeconomically. LFS data show the female share of the professional work force to have risen from 15.5% to 18.3% between 1984-95 and 1987-88, which translates to 33% of teachers and 25% of physicians being women. Urban female participation rates have increased only slightly from 3 to 5% between 1971 and 72 and 1987-88, based on LFS data, while informal sector surveys have shown an increase of workers who are women who have never worked before in the formal sector. In manufacturing, the female work force remains low at 5% in factories in the Punjab and Sindh, but only 20% were in regular employment compared with 50% of men. Agricultural work on the family farm has increased from 35% in 1972 and 42% in 1980. Increases are also shown in more recent LF surveys. Constraints on both male and female employment are the recent (1978-79 and 1986-87) shift to capital investment in agriculture with tubewells and tractors and in manufacturing. Women's movement into agriculture may be precipitated by men's out migration to urban areas or the Gulf region into other nonfarm occupations. In manufacturing there is exploitation of workers through low overhead costs of temporary or part time help. Supply constraints for women involve cultural restrictions, household responsibilities, and low levels of education and skills. Women enter the work force out of financial need. Data on female-headed households are scarce, but a Karachi survey finds that most female-headed households belong to the poorest strata and women work when family size
Superstrings, conformal field theories and holographic duality
International Nuclear Information System (INIS)
Benichou, R.
2009-06-01
The first half of this work is dedicated to the study of non-compact Gepner models.The Landau-Ginzburg description provides an easy and direct access to the geometry of the singularity associated to the non-compact Gepner models. Using these tools, we are able to give an intuitive account of the chiral rings of the models, and of the massless moduli in particular. By studying orbifolds of the singular linear dilaton models, we describe mirror pairs of non-compact Gepner models by suitably adapting the Greene-Plesser construction of mirror pairs for the compact case. For particular models, we take a large level, low curvature limit in which we can analyze corrections to a flat space orbifold approximation of the non-compact Gepner models. We have also studied bound states in N=2 Liouville theory with boundary and deep throat D-branes. We have shown that the bound states can give rise to massless vector and hyper multiplets in a low-energy gauge theory on D-branes deep inside the throat. The second half of this work deals with the issue of the quantization of the string in the presence of Ramond-Ramond backgrounds. Using the pure spinor formalism on the world-sheet, we derive the T-duality rules for all target space couplings in an efficient manner. The world-sheet path integral derivation is a proof of the equivalence of the T-dual Ramond-Ramond backgrounds which is valid non-perturbatively in the string length over the curvature radius and to all orders in perturbation theory in the string coupling. Sigma models on supergroup manifolds are relevant for quantifying string in various Anti-de-Sitter space-time with Ramond-Ramond backgrounds. We show that the conformal current algebra is realized in non-linear sigma models on supergroup manifolds with vanishing dual Coxeter number, with or without a Wess-Zumino term. The current algebra is computed. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting
Applications of Space-Time Duality
Plansinis, Brent W.
The concept of space-time duality is based on a mathematical analogy between paraxial diffraction and narrowband dispersion, and has led to the development of temporal imaging systems. The first part of this thesis focuses on the development of a temporal imaging system for the Laboratory for Laser Energetics. Using an electro-optic phase modulator as a time lens, a time-to-frequency converter is constructed capable of imaging pulses between 3 and 12 ps. Numerical simulations show how this system can be improved to image the 1-30 ps range used in OMEGA-EP. By adjusting the timing between the pulse and the sinusoidal clock of the phase modulator, the pulse spectrum can be selectively narrowed, broadened, or shifted. An experimental demonstration of this effect achieved spectral narrowing and broadening by a factor of 2. Numerical simulations show narrowing by a factor of 8 is possible with modern phase modulators. The second part of this thesis explores the space-time analog of reflection and refraction from a moving refractive index boundary. From a physics perspective, a temporal boundary breaks translational symmetry in time, requiring the momentum of the photon to remain unchanged while its energy may change. This leads to a shifting and splitting of the pulse spectrum as the boundary is crossed. Equations for the reflected and transmitted frequencies and a condition for total internal reflection are found. Two of these boundaries form a temporal waveguide, which confines the pulse to a narrow temporal window. These waveguides have a finite number of modes, which do not change during propagation. A single-mode waveguide can be created, allowing only a single pulse shape to form within the waveguide. Temporal reflection and refraction produce a frequency dependent phase shift on the incident pulse, leading to interference fringes between the incident light and the reflected light. In a waveguide, this leads to self-imaging, where the pulse shape reforms
Complex Correlation Measure: a novel descriptor for Poincaré plot
Directory of Open Access Journals (Sweden)
Gubbi Jayavardhana
2009-08-01
Full Text Available Abstract Background Poincaré plot is one of the important techniques used for visually representing the heart rate variability. It is valuable due to its ability to display nonlinear aspects of the data sequence. However, the problem lies in capturing temporal information of the plot quantitatively. The standard descriptors used in quantifying the Poincaré plot (SD1, SD2 measure the gross variability of the time series data. Determination of advanced methods for capturing temporal properties pose a significant challenge. In this paper, we propose a novel descriptor "Complex Correlation Measure (CCM" to quantify the temporal aspect of the Poincaré plot. In contrast to SD1 and SD2, the CCM incorporates point-to-point variation of the signal. Methods First, we have derived expressions for CCM. Then the sensitivity of descriptors has been shown by measuring all descriptors before and after surrogation of the signal. For each case study, lag-1 Poincaré plots were constructed for three groups of subjects (Arrhythmia, Congestive Heart Failure (CHF and those with Normal Sinus Rhythm (NSR, and the new measure CCM was computed along with SD1 and SD2. ANOVA analysis distribution was used to define the level of significance of mean and variance of SD1, SD2 and CCM for different groups of subjects. Results CCM is defined based on the autocorrelation at different lags of the time series, hence giving an in depth measurement of the correlation structure of the Poincaré plot. A surrogate analysis was performed, and the sensitivity of the proposed descriptor was found to be higher as compared to the standard descriptors. Two case studies were conducted for recognizing arrhythmia and congestive heart failure (CHF subjects from those with NSR, using the Physionet database and demonstrated the usefulness of the proposed descriptors in biomedical applications. CCM was found to be a more significant (p = 6.28E-18 parameter than SD1 and SD2 in discriminating
Electric-magnetic duality in non-Abelian gauge theories
International Nuclear Information System (INIS)
Mizrachi, L.
1982-03-01
The duality transformation of the vacuum expectation value of the operator which creates magnetic vortices (the 't Hooft loop operator in the Higgs phase) is performed in the radial gauge (xsub(μ)Asub(μ)sup(a)(x)=0). It is found that in the weak coupling region (small g) of a pure Yang-Mills theory the dual operator creates electric vortices whose strength is 1/g. The theory is self dual in this region, and the effective coupling of the dual Lagrangian is 1/g. Thus the above duality transformation reduces to electric-magnetic duality where the electric field in the 't Hooft loop operator transforms into a magnetic field in the dual operator. In a spontaneously broken gauge theory these results are valid only within the region where the vortices (or the monopoles) are concentrated, or in directions of the algebra space of unbroken symmetry, as self duality holds only for this subset of fields. In the strong coupling region a strong coupling expansion in powers of 1/g is suggested. (author)
On R-duals and the duality principle
DEFF Research Database (Denmark)
Christensen, Ole; Stoeva, Diana
2015-01-01
. In this paper we discuss the relationship between the R-duals and a variant, called R-duals of type III, introduced in 2014. In contrast to the original R-duals, it is known that the R-duals of type III generalize the duality principle for all Gabor frames, but we believe that a smaller and more convenient...
Electric–magnetic duality of lattice systems with topological order
Energy Technology Data Exchange (ETDEWEB)
Buerschaper, Oliver [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5 (Canada); Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching (Germany); Christandl, Matthias [Institute for Theoretical Physics, ETH Zurich, 8093 Zurich (Switzerland); Kong, Liang, E-mail: kong.fan.liang@gmail.com [Institute for Advanced Study (Science Hall), Tsinghua University, Beijing 100084 (China); Department of Mathematics and Statistics University of New Hampshire, Durham, NH 03824 (United States); Aguado, Miguel [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching (Germany)
2013-11-11
We investigate the duality structure of quantum lattice systems with topological order, a collective order also appearing in fractional quantum Hall systems. We define electromagnetic (EM) duality for all of Kitaev's quantum double models based on discrete gauge theories with Abelian and non-Abelian groups, and identify its natural habitat as a new class of topological models based on Hopf algebras. We interpret these as extended string-net models, whereupon Levin and Wen's string-nets, which describe all intrinsic topological orders on the lattice with parity and time-reversal invariance, arise as magnetic and electric projections of the extended models. We conjecture that all string-net models can be extended in an analogous way, using more general algebraic and tensor-categorical structures, such that EM duality continues to hold. We also identify this EM duality with an invertible domain wall. Physical applications include topology measurements in the form of pairs of dual tensor networks.
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
Directory of Open Access Journals (Sweden)
D. H. Fang
2013-01-01
Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.
A D-induced duality and its applications
J. Brinkhuis (Jan); S. Zhang (Shuzhong)
2003-01-01
textabstractThis paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a
Duality and modular class of a Nambu-Poisson structure
International Nuclear Information System (INIS)
Ibanez, R.; Leon, M. de; Lopez, B.; Marrero, J.C.; Padron, E.
2001-01-01
In this paper we introduce cohomology and homology theories for Nambu-Poisson manifolds. Also we study the relation between the existence of a duality for these theories and the vanishing of a particular Nambu-Poisson cohomology class, the modular class. The case of a regular Nambu-Poisson structure and some singular examples are discussed. (author)
Duality and hidden symmetries in interacting particle systems
Giardinà, C.; Kurchan, J.; Redig, F.H.J.; Vafayi, K.
2009-01-01
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the "hidden" symmetries are easily derived.
Gaugino condensation, loop corrections and S-duality constraint
International Nuclear Information System (INIS)
Saririan, K.; California Univ., Berkeley, CA
1996-11-01
This talk is a brief review of gaugino condensation in superstring effective field theories and some related issues (such as renormalization of the gauge coupling in the effective supergravity theories and modular anomaly cancellation). As a specific example, we discuss a model containing perturbative (1-loop) corrections to the Kaehler potential and approximate S-duality symmetry
Duality of roles and corporate governance in Greece
Directory of Open Access Journals (Sweden)
Themistokles Lazarides
2009-01-01
Full Text Available Duality of the role of President of the Board of Directors (BoD and CEO has been regarded as a good practice of corporate governance. These two roles are the ones with the most power an authority within the corporation. The paper depicts the formulating factors of duality of roles in Greece. Literature has linked duality with performance, organizational stability, ownership concentration and balance of power and control within the firm. The paper, using a Probit regression analysis, examines whether these relationships are valid in Greece. Statistical – econometric analysis has shown that financial performance is not related with concentration of power and control. The same conclusion is can be drawn for ownership concentration. There is a trend of change but this trend hasn’t the same dynamic or driving factors as the ones that are reported by Kirkbride and Letza (2002 and Muth and Donaldson (1998. The hypothesis posed by Heracleous (2001 and Baliga, 6oyer and Rao (1996 are more likely to be true in the case of Greece. Overall, duality in Greece is affected by the historical development of the firm, its organizational scheme and even more by the balance of power and control within the firm.
Unity from duality: gravity, gauge theory and strings
International Nuclear Information System (INIS)
Bachas, C.; Bilal, A.; Douglas, M.; Nekrasov, N.; David, F.
2002-01-01
The 76. session of the summer school in theoretical physics was devoted to recent developments in string theory, gauge theories and quantum gravity. Superstring theory is the leading candidate for a unified theory of all fundamental physical forces and elementary particles. The discovery of dualities and of important tools such as D-branes, has greatly reinforced this point of view. This document gathers the papers of 9 lectures: 1) supergravity, 2) supersymmetric gauge theories, 3) an introduction to duality symmetries, 4) large N field theories and gravity, 5) D-branes on the conifold and N = 1 gauge/gravity dualities, 6) de Sitter space, 7) string compactification with N = 1 supersymmetry, 8) open strings and non-commutative gauge theories, and 9) condensates near the Argyres-Douglas point in SU(2) gauge theory with broken N = 2 supersymmetry, and of 8 seminars: 1) quantum field theory with extra dimensions, 2) special holonomy spaces and M-theory, 3) four dimensional non-critical strings, 4) U-opportunities: why ten equal to ten?, 5) exact answers to approximate questions - non-commutative dipoles, open Wilson lines and UV-IR duality, 6) open-string models with broken supersymmetry, 7) on a field theory of open strings, tachyon condensation and closed strings, and 8) exceptional magic. (A.C.)
Superspace actions and duality transformations for N=2 tensor multiplets
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Ogievetsky, V.
1985-01-01
General actions for self-interacting N=2 tensor multiplets are considered in the harmonic superspace approach. All of them are shown to be equivalent, by superfield duality transformations, to some restricted class of the hypermultiplets actions. In particular, the improved tensor multiplet theory is dual to a free hypermultiplet one. Superspace couplings of these improved matter multiplets against conformal supergravity are also constructed
A one-loop test of string duality
International Nuclear Information System (INIS)
Vafa, C.
1995-01-01
We test Type IIA-heterotic string duality in six dimensions by showing that the sigma model anomaly of the heterotic string is generated by a combination of a tree level and a string one-loop correction on the Type IIA side. (orig.)
Wave-particle duality in a quark model
International Nuclear Information System (INIS)
Gudder, S.P.
1984-01-01
A quark model based on finite-dimensional quantum mechanics is presented. Observables associated with color, flavor, charge, and spin are considered. Using these observables, quark and baryon Hamiltonians are constructed. Wave-particle dualities in this model are pointed out. (Auth.)
Superdualities, brane tensions and massive IIA/IIB duality
International Nuclear Information System (INIS)
Lavrinenko, I.V.; Lue, H.; Pope, C.N.; Stelle, K.S.
1999-01-01
The gauge transformations of p-form fields in supergravity theories acquire a non-commuting character when one introduces potentials both for the theory's original field strengths and for their duals. This has previously been shown in the 'doubled' formalism for maximal supergravities, where a generalised duality relation between original and dual field strengths replaces the equations of motion. In the doubled formalism, the gauge transformations generate a superalgebra, and the corresponding symmetries have accordingly been called 'superdualities'. The corresponding Noether charges form a representation of the cohomology ring on the space-time manifold. In this paper, we show that the gauge symmetry superalgebra implies certain non-trivial relations among the various p-brane tensions, which can straightforwardly be read off from the superalgebra commutation relations. This provides an elegant derivation of the brane-tension relations purely within a given theory, without the need to make use of duality relations between different theories, such as the type IIA/IIB T-duality, although the results are consistent with such dualities. We present the complete set of brane-tension relations in M-theory, in the type IIA and type IIB theories, and in all the lower-dimensional maximal supergravities. We also construct a doubled formalism for massive type IIA supergravity, and this enables us to obtain the brane-tension relations involving the D8-brane, purely within the framework of the massive IIA theory. We also obtain explicit transformations for the nine-dimensional T-duality between the massive type IIA theory and the Scherk-Schwarz reduced type IIB theory
Segmented Poincaré plot analysis for risk stratification in patients with dilated cardiomyopathy.
Voss, A; Fischer, C; Schroeder, R; Figulla, H R; Goernig, M
2010-01-01
The prognostic value of heart rate variability in patients with dilated cardiomyopathy (DCM) is limited and does not contribute to risk stratification although the dynamics of ventricular repolarization differs considerably between DCM patients and healthy subjects. Neither linear nor nonlinear methods of heart rate variability analysis could discriminate between patients at high and low risk for sudden cardiac death. The aim of this study was to analyze the suitability of the new developed segmented Poincaré plot analysis (SPPA) to enhance risk stratification in DCM. In contrast to the usual applied Poincaré plot analysis the SPPA retains nonlinear features from investigated beat-to-beat interval time series. Main features of SPPA are the rotation of cloud of points and their succeeded variability depended segmentation. Significant row and column probabilities were calculated from the segments and led to discrimination (up to pplot analysis of heart rate variability was able to contribute to risk stratification in patients suffering from DCM.
Poincare invariant gravity with local supersymmetry as a gauge theory for the M-algebra
International Nuclear Information System (INIS)
Hassaine, Mokhtar; Troncoso, Ricardo; Zanelli, Jorge
2004-01-01
Here we consider a gravitational action having local Poincare invariance which is given by the dimensional continuation of the Euler density in ten dimensions. It is shown that the local supersymmetric extension of this action requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. The resulting action is shown to describe a gauge theory for the M-algebra, and is not the eleven-dimensional supergravity theory of Cremmer-Julia-Scherk. The theory admits a class of vacuum solutions of the form S10-dxXd+1, where Xd+1 is a warped product of R with a d-dimensional spacetime. It is shown that a nontrivial propagator for the graviton exists only for d=4 and positive cosmological constant. Perturbations of the metric around this solution reproduce linearized General Relativity around four-dimensional de Sitter spacetime
Deformed conformal and super-Poincare symmetries in the non- (anti-) commutative spaces
International Nuclear Information System (INIS)
Banerjee, R.; Lee, C.; Siwach, S.
2006-01-01
Generators of the super-Poincare algebra in the non- (anti-) commutative superspace are represented using appropriate higher derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the conformal and superconformal symmetry generators in the deformed spaces. This construction is obtained by generalizing the recent work of Wess et al. on the Poincare generators in the θ-deformed Minkowski space, or by using the substitution rules we derived on the basis of the phase-space structures of non- (anti-) commutative-space variables. Even with the non-zero deformation parameters the algebras remain unchanged although the comultiplication rules are deformed. The transformation of the fields under deformed symmetry is also discussed. Our construction can be used for systematic development of field theories in the deformed spaces. (orig.)
Poincare group, SU(3) and V-A in leptonic decay
International Nuclear Information System (INIS)
Boehm, A.
1975-07-01
From as few assumptions as possible about the relations between the Poincare group, the particle classifying SU(3) and V-A we derive properties of the K/sub l 3 / and K/sub L 2 / decays. From the assumed relation between SU(3) and the Poincare group and the first class condition it follows that the formfactor ratio Xi of K/sub l 3 / decay is Xi = --0.57, and that a value of Xi = 0 is in disagreement with very general and well accepted theoretical assumptions. Assuming universality of V-A, the Cabibbo suppression is derived from the relations between SU(3) and V-A as a consequence of the brokenness of SU(3). (U.S.)
N-particle effective generators of the Poincare group derived from a field theory
International Nuclear Information System (INIS)
Krueger, A.; Gloeckle, W.
1999-01-01
In quantum mechanics the principle of relativity is guaranteed by unitary operators being associated with inhomogeneous Lorentz transformations ensuring that quantum mechanical expectation values remain unchanged. In field theory the ten generators of inhomogeneous Lorentz transformations can be derived from a scalar Lagrangian density describing the physical system of interest. They obey the well known Poincare Lie algebra. For interacting systems some of the generators become operators allowing for particle production or annihilation so that the generators act on the full Fock space. However, given a field theory on the whole Fock space we prove that it is possible to construct generators acting on a subspace with a finite number of particles by one and the same unitary transformation of all generators leaving the Poincare algebra valid. In this manner it is in principle possible to derive a relativistically invariant theory of interacting particles on a Hilbert space with a finite number of particles from a field theoretical Lagrangian. Refs. 3 (author)
Monodromía y ecuaciones fuchsianas en la obra de H. Poincaré
Directory of Open Access Journals (Sweden)
Aroca Hernández-Ros, José Manuel
2004-08-01
Full Text Available Las cinco memorias de Poincaré sobre funciones y grupos fuchsianos publicadas en Acta Mathematica entre 1882 y 1884 constituyen la culminación de la teoría geométrica de funciones y el origen de un gran número de problemas de la Matemática actual. La cuarta memoria, dedicada a los grupos de monodromía de las ecuaciones diferenciales lineales de tipo Fuchs, es la menos conocida pese a contener resultados interesantes tanto en torno al problema de Riemann-Hilbert como a la estructura de los espacios de moduli de curvas algebraicas. En esta nota, expuesta en un ciclo de conferencias sobre Poincaré en su sesquicentenario, organizado en la Real Academia de Ciencias, se exponen las conexiones de esta memoria con resultados recientes de la teoría de Galois diferencial.…
Synthesis of full Poincaré beams by means of uniaxial crystals
Piquero, G.; Monroy, L.; Santarsiero, M.; Alonzo, M.; de Sande, J. C. G.
2018-06-01
A simple optical system is proposed to generate full-Poincaré beams (FPBs), i.e. beams presenting all possible states of (total) polarization across their transverse section. The method consists in focusing a uniformly polarized laser beam onto a uniaxial crystal having its optic axis parallel to the propagation axis of the impinging beam. A simple approximated model is used to obtain the analytical expression of the beam polarization at the output of the crystal. The output beam is then proved to be a FPB. By changing the polarization state of the input field, full-Poincaré beams are still obtained, but presenting different distributions of the polarization state across the beam section. Experimental results are reported, showing an excellent agreement with the theoretical predictions.
Thermodynamics of pion gas using states predicted from κ-deformed Poincare algebra
International Nuclear Information System (INIS)
Cordeiro, Claudete E.; Delfino, Antonio; Dey, Jishnu
1995-01-01
K-deformed Poincare algebra, which preserves rotational and translational symmetries, can successfully predict the angular and radial excited states of the pion. At high temperature, T these states can be excited in the pion gas, in addition to the usual momentum excitation. We exploit this to look at pion free energy finding it increases linearly with T. The energy per particle and the entropy show evidence of a smooth phase transition after T=0.2 GeV. (author)
W-realization of Lie algebras. Application to so(4,2) and Poincare algebras
International Nuclear Information System (INIS)
Barbarin, F.; Ragoucy, E.; Sorba, P.
1996-05-01
The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a 'canonical' differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author)
Analogue of the Witten effect in the Poincare gauge theory of gravity
International Nuclear Information System (INIS)
Mielke, E.W.
1985-03-01
The gravitational contribution to the chiral anomaly is analysed in the framework of the Poincare gauge theory. It is shown that an additional CP-violating term 8*RR in the effective Lagrangian is equivalent to a shift in the mass of the Taub-NUT metric as felt by fermions. This analogue of the Witten effect is discussed in conjunction with the appearance of torsion in recently found exact solutions. (author)
On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
International Nuclear Information System (INIS)
Burdik, C.; Pashnev, A.; Tsulaya, M.
2001-01-01
The Lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is used adopted to the systems of the second class constraints by the construction of auxiliary representations of the algebras of constraints in terms of Verma modules
Geometry, heat equation and path integrals on the Poincare upper half-plane
International Nuclear Information System (INIS)
Kubo, Reijiro.
1987-08-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation δf/δt = Δ H f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (author)
Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane
Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University
1988-01-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation ∂f/∂t=Δ_Hf is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrodinger equation is also valid for our case.
Non-critical Poincare invariant bosonic string backgrounds and closed string tachyons
International Nuclear Information System (INIS)
Alvarez, Enrique; Gomez, Cesar; Hernandez, Lorenzo
2001-01-01
A new family of non critical bosonic string backgrounds in arbitrary space-time dimension D and with ISO(1,D-2) Poincare invariance are presented. The metric warping factor and dilaton agree asymptotically with the linear dilaton background. The closed string tachyon equation of motion enjoys, in the linear approximation, an exact solution of 'kink' type interpolating between different expectation values. A renormalization group flow interpretation, based on a closed string tachyon potential of type -T 2 e -T , is suggested
Comparison of numerical approaches to solve a Poincare-covariant Faddeev equation
International Nuclear Information System (INIS)
Alkofer, R.; Eichmann, G.; Krassnigg, A.; Schwinzerl, M.
2006-01-01
Full text: The quark core of Baryons can be described with the help of the numerical solution of the Poincare-Faddeev equation. Hereby the used elements, as e.g. the quark propagator are taken from non-perturbative studies of Landau gauge QCD. Different numerical approaches to solve in this way the relativistic three quark problem are compared and benchmarked results for the efficiency of different algorithms are presented. (author)
Relativistic dynamics of quasistable states. I. Perturbation theory for the Poincare group
International Nuclear Information System (INIS)
Wickramasekara, S.
2009-01-01
We propose a theory of resonances by combining the S-matrix approach with the Bakamjian-Thomas (BT) construction. Characterization of resonances by the poles of the S-matrix has many advantages. Foremost among them is perhaps the gauge invariance of the definitions of resonance mass and width, a problem with which some definitions based on field theoretical approaches suffer. The BT construction provides a general framework for constructing Poincare generators for an interacting quantum system. While much of what we develop here can be cast in the language of quantum field theory, in the spirit of BT construction, which does not assume the existence of local field mediating interactions, we will work at the fundamental level of an interacting Poincare algebra. Our construction shows that a subset of this Poincare algebra integrates to a representation of the semigroup of causal transformations of relativistic space-time. These representations are characterized by the spin and S-matrix complex pole position of the resonance. The state vectors that transform under these representations also show an exact exponential decay, the signature of a decaying state. In this sense, the semigroup representations developed here tie together resonances and decaying states into a single theoretical description.
Automatic recognition of cardiac arrhythmias based on the geometric patterns of Poincaré plots
International Nuclear Information System (INIS)
Zhang, Lijuan; Guo, Tianci; Xi, Bin; Fan, Yang; Wang, Kun; Bi, Jiacheng; Wang, Ying
2015-01-01
The Poincaré plot emerges as an effective tool for assessing cardiovascular autonomic regulation. It displays nonlinear characteristics of heart rate variability (HRV) from electrocardiographic (ECG) recordings and gives a global view of the long range of ECG signals. In the telemedicine or computer-aided diagnosis system, it would offer significant auxiliary information for diagnosis if the patterns of the Poincaré plots can be automatically classified. Therefore, we developed an automatic classification system to distinguish five geometric patterns of the Poincaré plots from four types of cardiac arrhythmias. The statistics features are designed on measurements and an ensemble classifier of three types of neural networks is proposed. Aiming at the difficulty to set a proper threshold for classifying the multiple categories, the threshold selection strategy is analyzed. 24 h ECG monitoring recordings from 674 patients, which have four types of cardiac arrhythmias, are adopted for recognition. For comparison, Support Vector Machine (SVM) classifiers with linear and Gaussian kernels are also applied. The experiment results demonstrate the effectiveness of the extracted features and the better performance of the designed classifier. Our study can be applied to diagnose the corresponding sinus rhythm and arrhythmia substrates disease automatically in the telemedicine and computer-aided diagnosis system. (paper)
Energy Technology Data Exchange (ETDEWEB)
Jemcov, A.; Matovic, M.D. [Queen`s Univ., Kingston, Ontario (Canada)
1996-12-31
This paper examines the sparse representation and preconditioning of a discrete Steklov-Poincare operator which arises in domain decomposition methods. A non-overlapping domain decomposition method is applied to a second order self-adjoint elliptic operator (Poisson equation), with homogeneous boundary conditions, as a model problem. It is shown that the discrete Steklov-Poincare operator allows sparse representation with a bounded condition number in wavelet basis if the transformation is followed by thresholding and resealing. These two steps combined enable the effective use of Krylov subspace methods as an iterative solution procedure for the system of linear equations. Finding the solution of an interface problem in domain decomposition methods, known as a Schur complement problem, has been shown to be equivalent to the discrete form of Steklov-Poincare operator. A common way to obtain Schur complement matrix is by ordering the matrix of discrete differential operator in subdomain node groups then block eliminating interface nodes. The result is a dense matrix which corresponds to the interface problem. This is equivalent to reducing the original problem to several smaller differential problems and one boundary integral equation problem for the subdomain interface.
On the Duality Principle by Casazza, Kutyniok, and Lammers
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2011-01-01
The R-dual sequences of a frame {f i } i∈I , introduced by Casazza, Kutyniok and Lammers in (J. Fourier Anal. Appl. 10(4):383–408, 2004), provide a powerful tool in the analysis of duality relations in general frame theory. In this paper we derive conditions for a sequence {ω j } j∈I to be an R......-dual of a given frame {f i } i∈I . In particular we show that the R-duals {ω j } j∈I can be characterized in terms of frame properties of an associated sequence {n i } i∈I . We also derive the duality results obtained for tight Gabor frames in (Casazza et al. in J. Fourier Anal. Appl. 10(4):383–408, 2004...
Pure Gravities via Color-Kinematics Duality for Fundamental Matter
Johansson, Henrik
2015-01-01
We give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality. Amplitudes are constructed using double copies of pure (super-)Yang-Mills parts and additional contributions from double copies of fundamental matter, which are treated as ghosts. The opposite-statistics states cancel the unwanted dilaton and axion in the bosonic theory, as well as the extra matter supermultiplets in supergravities. As a spinoff, we obtain a prescription for obtaining amplitudes in supergravities with arbitrary non-self-interacting matter. As a prerequisite, we extend the color-kinematics duality from the adjoint to the fundamental representation of the gauge group. We explain the numerator relations that the fundamental kinematic Lie algebra should satisfy. We give nontrivial evidence supporting our construction using explicit tree and loop amplitudes, as well as more general arguments.
Gauge theories, duality relations and the tensor hierarchy
International Nuclear Information System (INIS)
Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas
2009-01-01
We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.
Topological T-duality for torus bundles with monodromy
Baraglia, David
2015-05-01
We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for T-duals are shown to follow. We determine necessary and sufficient conditions for existence of a T-dual in the case of affine torus bundles. This is general enough to include all principal torus bundles as well as torus bundles with arbitrary monodromy representations. We show that isomorphisms in twisted cohomology, twisted K-theory and of Courant algebroids persist in this general setting. We also give an example where twisted K-theory groups can be computed by iterating T-duality.
On the duality-transformed Wilson loop operator
International Nuclear Information System (INIS)
Mizrachi, L.
1981-08-01
Duality transformation of the vacuum expectation value of the Wilson loop operator is performed in the radial gauge (xsub(μ)Asub(μ)sup(a)(x) = 0). It is found to be equal, up to a multiplicative constant, to , where O(c) is a line integral along the loop c (defining the Wilson loop operator) of a function of the dual field variables. In the weak coupling region self duality is recovered in the sense that the Lagrangian is local gauge invariant defined in terms of the dual gauge potentials but with g (the coupling constant) replaced by 1/g, and O(c) is simply the line integral of the dual gauge potentials. For large g, a strong coupling expansion is suggested (but the theory is not local gauge invariant). (author)
Duality transformation of a spontaneously broken gauge theory
International Nuclear Information System (INIS)
Mizrachi, L.
1981-04-01
Duality transformation for a spontaneously broken gauge theory is constructed in the CDS gauge (xsub(μ)Asub(μ)sup(a)=0). The dual theory is expressed in terms of dual potentials which satisfy the same gauge condition, but with g→ 1 /g. Generally the theory is not self dual but in the weak coupling region (small g), self duality is found for the subgroup which is not spontaneously broken or in regions where monopoles and vortices are concentrated (in agreement with t'Hooft's ideas that monopoles and vortices in the Georgi-Glashow model make it self dual). In the strong coupling regime a systematic strong coupling expansion can be written. For this region the dual theory is generally not local gauge invariant, but it is invariant under global gauge transformations. (author)
On Λ-Type Duality of Frames in Banach Spaces
Directory of Open Access Journals (Sweden)
Renu Chugh
2013-11-01
Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.
Heterotic/type I duality and D-brane instantons
Bachas, C.; Fabre, C.; Kiritsis, E.; Obers, N. A.; Vanhove, P.
1998-01-01
We study heterotic/type I duality in d = 8, 9 uncompactified dimensions. We consider the special ("BPS-saturated") F4 and R4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet instanton corrections in a form that can be motivated as arising from a D-brane instanton calculation on the type I side.
Heterotic/type I duality and D-brane instantons
International Nuclear Information System (INIS)
Bachas, C.; Fabre, C.; Vanhove, P.
1998-01-01
We study heterotic/type I duality in d=8,9 uncompactified dimensions. We consider the special (''BPS-saturated'') F 4 and R 4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet instanton corrections in a form that can be motivated as arising from a D-brane instanton calculation on the type I side. (orig.)
Heterotic / type-I duality and D-brane instantons
Bachas, C P; Kiritsis, Elias B; Obers, N A; Vanhove, P
1998-01-01
We study heterotic/type-I duality in d=8,9 uncompactified dimensions. We consider the special (``BPS saturated'') F^4 and R^4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet instanton corrections in a form that can be recognized easily as arising from a D-brane instanton calculation on the type-I side.
Gauge symmetry, T-duality and doubled geometry
Energy Technology Data Exchange (ETDEWEB)
Hull, C.M. [Imperial College London (United Kingdom). Inst. for Mathematical Sciences]|[Imperial College London (United Kingdom). Blackett Laboratory; Reid-Edwards, R.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2007-11-15
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a 'doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric. (orig.)
U-duality and D-brane combinatorics
Pioline, B
1998-01-01
We investigate D-brane instanton contributions to R^4 couplings in any toroidal compactification of type II theories. Starting from the 11D supergravity one-loop four-graviton amplitude computed by Green, Gutperle and Vanhove, we derive the non-perturbative O(e^{-1/\\lambda}) corrections to R^4 couplings by a sequence of T-dualities, and interpret them as precise configurations of bound states of D-branes wrapping cycles of the compactification torus. Dp-branes explicitely appear as fluxes on D(p+2)-branes, and as gauge instantons on D(p+4)-branes. Specific rules for weighting these contributions are obtained, which should carry over to more general situations. Furthermore, it is shown that U-duality in D<=6 relates these D-brane configurations to O(e^{-1/\\lambda^2}) instantons for which a geometric interpretation is still lacking.
Supersymmetry, p-brane duality, and hidden spacetime dimensions
International Nuclear Information System (INIS)
Bars, I.
1996-01-01
A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions in a theory that treats p-branes democratically. The maximal number of dimensions is 12, with signature (10,2), containing one space and one time dimension that are hidden from the point of view of perturbative ten-dimensional string theory or its compactifications. When the theory is compactified on R d-1,1 circle-times T c+1,1 with d+c+2=12, there are isometry groups that relate to the hidden dimensions as well as to duality. Their combined intersecting classification schemes provide some properties of nonperturbative states and their couplings. copyright 1996 The American Physical Society
Experimental observation of entanglement duality for identical particles
International Nuclear Information System (INIS)
Ma, J-J; Yuan, X-X; Zu, C; Chang, X-Y; Hou, P-Y; Duan, L-M
2014-01-01
It was shown recently that entanglement of identical particles has a feature called dualism (Bose and Home 2013 Phys. Rev. Lett. 110 140404), which is fundamentally connected with quantum indistinguishability. Here we report an experiment that observes the entanglement duality for the first time with two identical photons, which manifest polarization entanglement when labeled by different paths or path entanglement when labeled by polarization states. By adjusting the mismatch in frequency or arrival time of the entangled photons, we tune the photon indistinguishability from the quantum to the classical limit and observe that the entanglement duality disappears under the emergence of classical distinguishability, confirming it as a characteristic feature of quantum indistinguishable particles. (paper)
Gauge symmetry, T-duality and doubled geometry
International Nuclear Information System (INIS)
Hull, C.M.
2007-11-01
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a 'doubled space' in which each circle is supplemented by a T-dual circle to construct a geometry which is a doubled torus bundle over a circle. We discuss a conjectured extension to include T-duality on the base circle, and propose the introduction of a dual base coordinate, to give a doubled space which is locally the group manifold of the gauge group. Special cases include those in which the doubled group is a Drinfel'd double. This gives a framework to discuss backgrounds that are not even locally geometric. (orig.)
Karmakar, Chandan K; Khandoker, Ahsan H; Voss, Andreas; Palaniswami, Marimuthu
2011-03-03
A novel descriptor (Complex Correlation Measure (CCM)) for measuring the variability in the temporal structure of Poincaré plot has been developed to characterize or distinguish between Poincaré plots with similar shapes. This study was designed to assess the changes in temporal structure of the Poincaré plot using CCM during atropine infusion, 70° head-up tilt and scopolamine administration in healthy human subjects. CCM quantifies the point-to-point variation of the signal rather than gross description of the Poincaré plot. The physiological relevance of CCM was demonstrated by comparing the changes in CCM values with autonomic perturbation during all phases of the experiment. The sensitivities of short term variability (SD1), long term variability (SD2) and variability in temporal structure (CCM) were analyzed by changing the temporal structure by shuffling the sequences of points of the Poincaré plot. Surrogate analysis was used to show CCM as a measure of changes in temporal structure rather than random noise and sensitivity of CCM with changes in parasympathetic activity. CCM was found to be most sensitive to changes in temporal structure of the Poincaré plot as compared to SD1 and SD2. The values of all descriptors decreased with decrease in parasympathetic activity during atropine infusion and 70° head-up tilt phase. In contrast, values of all descriptors increased with increase in parasympathetic activity during scopolamine administration. The concordant reduction and enhancement in CCM values with parasympathetic activity indicates that the temporal variability of Poincaré plot is modulated by the parasympathetic activity which correlates with changes in CCM values. CCM is more sensitive than SD1 and SD2 to changes of parasympathetic activity.
A Call-Put Duality for Perpetual American Options
Alfonsi, Aurélien; Jourdain, Benjamin
2006-01-01
International audience; It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper investigates such a Call Put duality for perpetual American options. It turns out that the perpetual American Put price is equal to the perpetual American C...
Dualities and signatures of G++-invariant theories
International Nuclear Information System (INIS)
Buyl, Sophie de; Houart, Laurent; Tabti, Nassiba
2005-01-01
The G ++ -content of the formulation of gravity and M-theories as very-extended Kac-Moody invariant theories is further analysed. The different exotic phases of all the G ++ B -theories, which admit exact solutions describing intersecting branes smeared in all directions but one, are derived. This is achieved by analysing for all G ++ the signatures which are related to the conventional one (1,D-1) by 'dualities' generated by the Weyl reflections
Duality relation between charged elastic strings and superconducting cosmic strings
International Nuclear Information System (INIS)
Carter, B.
1989-01-01
The mechanical properties of macroscopic electromagnetically coupled string models in a flat or curved background are treated using a covariant formalism allowing the construction of a duality transformation that relates the category of uniform ''electric'' string models, constructed as the (nonconducting) charged generalisation of ordinary uncoupled (violin type) elastic strings, to a category of ''magnetic'' string models comprising recently discussed varieties of ''superconducting cosmic strings''. (orig.)
Nucleon structure functions, resonance form factors, and duality
International Nuclear Information System (INIS)
Davidovsky, V.V.; Struminsky, B.V.
2003-01-01
The behavior of nucleon structure functions in the resonance region is explored. For form factors that describe resonance production, expressions are obtained that are dependent on the photon virtuality Q 2 , which have a correct threshold behavior, and which take into account available experimental data on resonance decay. Resonance contributions to nucleon structure functions are calculated. The resulting expressions are used to investigate quark-hadron duality in electron-nucleon scattering by taking the example of the structure function F 2
The duality of tensions at the workplace for female leaders
Haidinger, Julia
2017-01-01
The qualitative research undertaken was set out to understand the challenges experienced by female leaders at the workplace. Therefore, semi-structured interviews with 12 female leaders in top management positions from different industries were conducted. As a consequence, a duality between tensions concerning 1) character traits, 2) beauty and 3) motherhood was confirmed through the experiences shared by the participants. Women identified these tensions as highly challenging and difficult to...
Dualities in ABJM matrix model from closed string viewpoint
Energy Technology Data Exchange (ETDEWEB)
Kiyoshige, Kazuki; Moriyama, Sanefumi [Department of Physics, Graduate School of Science, Osaka City University,3-3-138 Sugimoto, Sumiyoshi, Osaka 558-8585 (Japan)
2016-11-17
We propose a new formalism to study the ABJM matrix model. Contrary to expressing the fractional brane background with the Wilson loops in the open string formalism, we formulate the Wilson loop expectation value from the viewpoint of the closed string background. With this new formalism, we can prove some duality relations in the matrix model. /includegraphics[scale=0.7]{abstract.eps}.
Duality and corrections to the van Royen-Weisskopf formula
International Nuclear Information System (INIS)
Durand, B.; Durand, L.
1981-01-01
We propose that duality can be used in conjunction with QCD calculations of the cross section for e + e - → qanti q - to evaluate relativistic and radiative corrections to the leptonic widths of the psi and UPSILON states. We use this method to discuss relativistic corrections to the van Royen-Weisskopf formula for leptonic widths. We also point out that this formula is in error by an important factor 4m 2 sub(q)/M 2 sub(n). (orig.)
Non Abelian T-duality in Gauged Linear Sigma Models
Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto
2018-04-01
Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.
Trigonometric version of quantum–classical duality in integrable systems
Directory of Open Access Journals (Sweden)
M. Beketov
2016-02-01
Full Text Available We extend the quantum–classical duality to the trigonometric (hyperbolic case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars–Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix. In the rational version of the duality, the action variables of the Ruijsenaars–Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix. The limit corresponding to the classical Calogero–Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.
Dualities in the analysis of phage DNA packaging motors
Serwer, Philip; Jiang, Wen
2012-01-01
The DNA packaging motors of double-stranded DNA phages are models for analysis of all multi-molecular motors and for analysis of several fundamental aspects of biology, including early evolution, relationship of in vivo to in vitro biochemistry and targets for anti-virals. Work on phage DNA packaging motors both has produced and is producing dualities in the interpretation of data obtained by use of both traditional techniques and the more recently developed procedures of single-molecule analysis. The dualities include (1) reductive vs. accretive evolution, (2) rotation vs. stasis of sub-assemblies of the motor, (3) thermal ratcheting vs. power stroking in generating force, (4) complete motor vs. spark plug role for the packaging ATPase, (5) use of previously isolated vs. new intermediates for analysis of the intermediate states of the motor and (6) a motor with one cycle vs. a motor with two cycles. We provide background for these dualities, some of which are under-emphasized in the literature. We suggest directions for future research. PMID:23532204
Precision studies of duality in the 't Hooft model
International Nuclear Information System (INIS)
Lebed, Richard F.; Uraltsev, Nikolai G.
2000-01-01
We address the numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with N c →∞. The primary focus of these studies is the total semileptonic decay widths relevant for extracting |V cb | and |V ub |. We compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/m Q expansion arising from the operator product expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. We find the ''small velocity'' sum rules to be exceptionally well saturated already by the first excited state. We also obtain a convincing degree of duality in the differential distributions and in an analogue of R e + e - (s). Finally, we discuss possible lessons for semileptonic decays of actual heavy quarks in QCD
Precision Studies of Duality in the 't Hooft Model
International Nuclear Information System (INIS)
Richard F. Lebed; Nikolai G. Uraltsev
2000-01-01
The authors address numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with Nc ?8. The primary focus of these studies is total semileptonic decay widths relevant for extracting (Vcb) and (Vub). They compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/mQ expansion arising from the Operator Product Expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. They find the ''Small Velocity'' sum rules to be exceptionally well saturated already by the first excited state. They also obtain a convincing degree of duality in the differential distributions and in an analogue of Re+e-(s). Finally, they discuss possible lessons for semileptonic decays of actual heavy quarks in QCD
Open string T-duality in double space
Energy Technology Data Exchange (ETDEWEB)
Sazdovic, B. [University of Belgrade, Institute of Physics, Belgrade (Serbia)
2017-09-15
The role of double space is essential in the new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of the open string is missing in such an approach because until now there has been no appropriate formulation of open string T-duality. In the previous paper (Sazdovic, From geometry to non-geometry via T-duality, arXiv:1606.01938, 2017), we showed how to introduce vector gauge fields A{sup N}{sub a} and A{sup D}{sub i} at the end-points of an open string in order to enable open string invariance under local gauge transformations of the Kalb-Ramond field and its T-dual ''restricted general coordinate transformations''. We demonstrated that gauge fields A{sup N}{sub a} and A{sup D}{sub i} are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space. (orig.)
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
Casalderrey-Solana, Jorge; Mateos, David; Rajagopal, Krishna; Wiedemann, Urs Achim
2011-01-01
Over the last decade, both experimental and theoretical advances have brought the need for strong coupling techniques in the analysis of deconfined QCD matter and heavy ion collisions to the forefront. As a consequence, a fruitful interplay has developed between analyses of strongly-coupled non-abelian plasmas via the gauge/string duality (also referred to as the AdS/CFT correspondence) and the phenomenology of heavy ion collisions. We review some of the main insights gained from this interplay to date. To establish a common language, we start with an introduction to heavy ion phenomenology and finite-temperature QCD, and a corresponding introduction to important concepts and techniques in the gauge/string duality. These introductory sections are written for nonspecialists, with the goal of bringing readers ranging from beginning graduate students to experienced practitioners of either QCD or gauge/string duality to the point that they understand enough about both fields that they can then appreciate their in...
Five-brane superpotentials and heterotic/F-theory duality
International Nuclear Information System (INIS)
Grimm, Thomas W.; Ha, Tae-Won; Klemm, Albrecht; Klevers, Denis
2010-01-01
Under heterotic/F-theory duality it was argued that a wide class of heterotic five-branes is mapped into the geometry of an F-theory compactification manifold. In four-dimensional compactifications this identifies a five-brane wrapped on a curve in the base of an elliptically fibered Calabi-Yau threefold with a specific F-theory Calabi-Yau fourfold containing the blow-up of the five-brane curve. We argue that this duality can be reformulated by first constructing a non-Calabi-Yau heterotic threefold by blowing up the curve of the five-brane into a divisor with five-brane flux. Employing heterotic/F-theory duality this leads us to the construction of a Calabi-Yau fourfold and four-form flux. Moreover, we obtain an explicit map between the five-brane superpotential and an F-theory flux superpotential. The map of the open-closed deformation problem of a five-brane in a compact Calabi-Yau threefold into a deformation problem of complex structures on a dual Calabi-Yau fourfold with four-form flux provides a powerful tool to explicitly compute the five-brane superpotential.
S-matrix elements from T-duality
International Nuclear Information System (INIS)
Babaei Velni, Komeil; Garousi, Mohammad R.
2013-01-01
Recently it has been speculated that the S-matrix elements satisfy the Ward identity associated with the T-duality. This indicates that a group of S-matrix elements is invariant under the linear T-duality transformations on the external states. If one evaluates one component of such T-dual multiplet, then all other components may be found by the simple use of the linear T-duality. The assumption that fields must be independent of the Killing coordinate, however, may cause, in some cases, the T-dual multiplet not to be gauge invariant. In those cases, the S-matrix elements contain more than one T-dual multiplet which are intertwined by the gauge symmetry. In this paper, we apply the T-dual Ward identity on the S-matrix element of one RR (p−3)-form and two NSNS states on the world volume of a D p -brane to find its corresponding T-dual multiplet. In the case that the RR potential has two transverse indices, the T-dual multiplet is gauge invariant, however, in the case that it has one transverse index the multiplet is not gauge invariant. We find a new T-dual multiplet in this case by imposing the gauge symmetry. We show that the multiplets are reproduced by explicit calculation, and their low energy contact terms at order α ′2 are consistent with the existing couplings in the literature
Leo Esakia on duality in modal and intuitionistic logics
Bezhanishvili, Guram
2014-01-01
This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia's original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia's work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other re...
Open string T-duality in double space
International Nuclear Information System (INIS)
Sazdovic, B.
2017-01-01
The role of double space is essential in the new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of the open string is missing in such an approach because until now there has been no appropriate formulation of open string T-duality. In the previous paper (Sazdovic, From geometry to non-geometry via T-duality, arXiv:1606.01938, 2017), we showed how to introduce vector gauge fields A"N_a and A"D_i at the end-points of an open string in order to enable open string invariance under local gauge transformations of the Kalb-Ramond field and its T-dual ''restricted general coordinate transformations''. We demonstrated that gauge fields A"N_a and A"D_i are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space. (orig.)
Trigonometric version of quantum–classical duality in integrable systems
Energy Technology Data Exchange (ETDEWEB)
Beketov, M., E-mail: beketov@phystech.edu [MIPT, Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Liashyk, A., E-mail: a.liashyk@gmail.com [National Research University Higher School of Economics, Myasnitskaya str. 20, 101000, Moscow (Russian Federation); BITP, Metrolohichna str. 14-b, 03680, Kiev (Ukraine); Zabrodin, A., E-mail: zabrodin@itep.ru [National Research University Higher School of Economics, Myasnitskaya str. 20, 101000, Moscow (Russian Federation); Institute of Biochemical Physics, Kosygina str. 4, 119991, Moscow (Russian Federation); ITEP, Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); Zotov, A., E-mail: zotov@mi.ras.ru [Steklov Mathematical Institute, RAS, Gubkina str. 8, 119991, Moscow (Russian Federation); ITEP, Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT, Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation)
2016-02-15
We extend the quantum–classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars–Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars–Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero–Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.
Temperature duality on Riemann surface and cosmological solutions for genus g = 1 and 2
International Nuclear Information System (INIS)
Yan Jun; Wang Shunjin
1999-01-01
A bosonic string model at finite temperature on the gravitation g μν and the dilaton φ background field is examined. Moreover, the duality relation of energy momentum tensor on high genus Riemann surface is derived. At the same time, the temperature duality invariance for the action of string gas matter is proved in 4-D Robertson-Walker metric, the string cosmological solutions and temperature duality of the equations of motion for genus g = 1 and 2 are also investigated
Exact Boson-Fermion Duality on a 3D Euclidean Lattice
Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao; Raghu, S.
2018-01-01
The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.
La correspondance entre Henri Poincaré, les astronomes, et les géodésiens
Walter, Scott A; Krömer, Ralf; Schiavon, Martina; Kromer, Ralf; Kr Mer, Ralf
2008-01-01
Les lettres du troisième volume de la Correspondance de Poincaré scandent toute son œuvre astronomique, allant de ses premiers mémoires sur les courbes définies par une équation différentielle (1881), jusqu'aux analyses des hypothèses cosmogoniques (1911). Encore très jeune, Poincaré s'est fait remarquer pour sa maîtrise des questions de la mécanique céleste, de tel sorte que les astronomes et les géodésiens l'ont souvent interpellé, y compris O. Callandreau, C.V.L. Charlier, G.H. Darwin, F.R. Helmert, A. Lindstedt, A.M. Lyapunov, Simon Newcomb, Karl Schwarzschild et F. Tisserand. Avec ses correspondants, Poincaré abordaient les questions principales de l'astronomie mathématique, du célèbre problème des trois corps à la théorie des perturbations et aux figures d'équilibre des masses fluides en rotation. La correspondance de Poincaré éditée et annotée dans ce volume concerne, au-delà des mémoires mathématiques, l'activité de Poincaré en tant que Professeur d'astronomie mathéma...
Shi, Ping; Hu, Sijung; Yu, Hongliu
2018-02-01
The aim of this study was to analyze the recovery of heart rate variability (HRV) after treadmill exercise and to investigate the autonomic nervous system response after exercise. Frequency domain indices, i.e., LF(ms 2 ), HF(ms 2 ), LF(n.u.), HF(n.u.) and LF/HF, and lagged Poincaré plot width (SD1 m ) and length (SD2 m ) were introduced for comparison between the baseline period (Pre-E) before treadmill running and two periods after treadmill running (Post-E1 and Post-E2). The correlations between lagged Poincaré plot indices and frequency domain indices were applied to reveal the long-range correlation between linear and nonlinear indices during the recovery of HRV. The results suggested entirely attenuated autonomic nervous activity to the heart following the treadmill exercise. After the treadmill running, the sympathetic nerves achieved dominance and the parasympathetic activity was suppressed, which lasted for more than 4 min. The correlation coefficients between lagged Poincaré plot indices and spectral power indices could separate not only Pre-E and two sessions after the treadmill running, but also the two sessions in recovery periods, i.e., Post-E1 and Post-E2. Lagged Poincaré plot as an innovative nonlinear method showed a better performance over linear frequency domain analysis and conventional nonlinear Poincaré plot.
Hsu, Che-Hao; Tsai, Ming-Ya; Huang, Go-Shine; Lin, Tso-Chou; Chen, Kuen-Pao; Ho, Shung-Tai; Shyu, Liang-Yu; Li, Chi-Yuan
2012-03-01
Beat-to-beat heart rate variability (HRV) is caused by the fluctuating balance of sympathetic and parasympathetic tone. The Poincaré plot has been used to evaluate HRV. In this study, we validate that this new method may qualitatively and quantitatively assess the sympathovagal fluctuation in patients during induction of anesthesia with sevoflurane. Twenty-eight young patients were allocated for the study. The patients received a tilt test and on the next day they sustained anesthesia induced with inhaled anesthetics. Electrocardiography signals from the patients were relayed to an analogue-digital converter. The Poincaré plot is quantified by measuring SD1, SD2, and SD1/SD2. Power spectral analyses were performed and LF, HF and HF/LF were calculated. The LF power and the SD2 of the Poincaré plot increased while subjects were tilt-up from the supine position. Additionally, a significant correlation were found between LF and SD2, HF and SD1 (p plot respectively. However, the LF, SD2 and LF/HF increased; the HF, SD1 and SD1/SD2 ratio decreased after intubation stimulation. Poincaré plot and power spectral analysis of HRV during tilt test and sevoflurane induction significantly correlate. Poincaré plot analysis is easier and more sensitive at evaluating the sympathovagal balance and observing the beat-to-beat HRV. Copyright © 2012. Published by Elsevier B.V.
Manifestly super-Poincare covariant quantization of the Green-Schwarz superstring
International Nuclear Information System (INIS)
Nissimov, E.R.; Pacheva, S.J.
1987-11-01
The Green-Schwarz (GS) superstring is reformulated in a physically equivalent way by embedding it into a larger system containing additional fermionic string- as well as bosonic harmonic variables and possessing additional gauge invariances. The main feature of the new GS superstring system is that it contains covariant and functionally independent first-class constraints only. This allows straightforward application of the BFV-BRST formalism for a manifestly super-Poincare covariant canonical quantization. The corresponding BRST charge turns out to be of second rank and, therefore, the BFV-BRST action contains fourth order ghost terms. (author). 20 refs
Three particle Poincare states and SU(6) x SU(3) as a classification group for baryons
International Nuclear Information System (INIS)
Buccella, F.; Sciarrino, A.; Sorba, P.
1975-05-01
A complete set of democratic quantum numbers is introduced to classify the states of an irreducible unitary representation (IUR) of the Poincare group obtained from the decomposition of the direct products of three I.U.R. Such states are identified with the baryon states constituted of three free relativistic quarks. The transformation from current to constituent quarks is then easily reobtained. Moreover, the group SU(6) x SU(3) appears naturally as a collinear classification group for baryons. Results similar to those of the symmetric harmonic oscillator quark model are obtained [fr
Non-vanishing of Taylor coefficients and Poincaré series
DEFF Research Database (Denmark)
O'Sullivan, C.; Risager, Morten S.
2013-01-01
We prove recursive formulas for the Taylor coefficients of cusp forms, such as Ramanujan's Delta function, at points in the upper half-plane. This allows us to show the non-vanishing of all Taylor coefficients of Delta at CM points of small discriminant as well as the non-vanishing of certain...... Poincaré series. At a "generic" point, all Taylor coefficients are shown to be non-zero. Some conjectures on the Taylor coefficients of Delta at CM points are stated....
New torsion black hole solutions in Poincaré gauge theory
Energy Technology Data Exchange (ETDEWEB)
Cembranos, Jose A.R.; Valcarcel, Jorge Gigante, E-mail: cembra@fis.ucm.es, E-mail: jorgegigante@ucm.es [Departamento de Física Teórica I, Universidad Complutense de Madrid, Av. Complutense s/n, E-28040 Madrid (Spain)
2017-01-01
We derive a new exact static and spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with dynamical massless torsion. This theory is built in such a form that allows to recover General Relativity when the first Bianchi identity of the model is fulfilled by the total curvature. The solution shows a Reissner-Nordström type geometry with a Coulomb-like curvature provided by the torsion field. It is also shown the existence of a generalized Reissner-Nordström-de Sitter solution when additional electromagnetic fields and/or a cosmological constant are coupled to gravity.
q-deformed conformal and Poincare algebras on quantum 4-spinors
International Nuclear Information System (INIS)
Kobayashi, Tatsuo; Uematsu, Tsuneo
1993-01-01
We investigate quantum deformation of conformal algebras by constructing the quantum space for sl q (4). The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformed su(2, 2) algebra from the deformed sl(4) algebra using the quantum 4-spinor and its conjugate spinor. The quantum 6-vector in so q (4, 2) is constructed as a tensor product of two sets of 4-spinors. We obtain the q-deformed conformal algebra with the suitable assignment of the generators which satisfy the reality condition. The deformed Poincare algebra is derived through a contraction procedure. (orig.)
W-realization of Lie algebras. Application to so(4,2) and Poincare algebras
Energy Technology Data Exchange (ETDEWEB)
Barbarin, F.; Ragoucy, E.; Sorba, P.
1996-05-01
The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a `canonical` differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author). 12 refs.
On the generating function of Poincare plots defining one dimensional perturbed Hamiltonian systems
International Nuclear Information System (INIS)
Montvai, A.
1989-01-01
A simple numerical method has been devised, for deriving the generating function of an arbitrary, one dimensional Hamiltonian system represented by its Poincare plot. In this case, the plot to be numerically processed is an area preserving transformation of a two-dimensional surface onto itself. Although the method in its present form is capable of treating only this case, there are no principal restrictions excluding the analysis of systems with higher dimensionality as well. As an example, the generating function of the motion of alpha particles in a nonsymmetric, toroidal magnetic field is derived and studied numerically. (orig.)
Power of the Poincaré group: elucidating the hidden symmetries in focal conic domains.
Alexander, Gareth P; Chen, Bryan Gin-Ge; Matsumoto, Elisabetta A; Kamien, Randall D
2010-06-25
Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincaré symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures, and tilt-grain boundaries.
Power of the Poincare Group: Elucidating the Hidden Symmetries in Focal Conic Domains
International Nuclear Information System (INIS)
Alexander, Gareth P.; Chen, Bryan Gin-ge; Matsumoto, Elisabetta A.; Kamien, Randall D.
2010-01-01
Focal conic domains are typically the 'smoking gun' by which smectic liquid crystalline phases are identified. The geometry of the equally spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincare symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures, and tilt-grain boundaries.
The Poincare group as the symmetry group of canonical general relativity
International Nuclear Information System (INIS)
Beig, R.; Murchadha, N. o
1986-01-01
This work reconsiders the formulation, due to Regge and Teitelboim, of the phase space approach to General Relativity in the asymptotically flat context, phrasing it in the language of symplectic geometry. The necessary boundary conditions at spatial infinity are spelled out in detail. Precise meaning is given to the statement that, as a result of these boundary conditions, the Poincare group acts as a symmetry group on the phase space of G.R. This situation is compared with the spi-picture of Ashtekar and Hansen, where a larger asymptotic symmetry group is obtained. (Author)
International Nuclear Information System (INIS)
Schroeck, Franklin E.
2008-01-01
The quarks have always been a puzzle, as have the particles' mass and mass/spin relations as they seemed to have no coordinates in configuration space and/or momentum space. The solution to this seems to lie in the marriage of ordinary Poincare group representations with a non-associative algebra made through a demisemidirect product. Then, the work of G. Dixon applies; so, we may obtain all the relations between masses, mass and spin, and the attribution of position and momentum to quarks--this in spite of the old restriction that the Poincare group cannot be extended to a larger group by any means (including the (semi)direct product) to get even the mass relations. Finally, we will briefly discuss a possible connection between the phase space representations of the Poincare group and the phase space representations of the object we will obtain. This will take us into Leibniz (co)homology.
q-Poincaré supersymmetry in AdS5/CFT4
Borsato, Riccardo; Torrielli, Alessandro
2018-03-01
We consider the exact S-matrix governing the planar spectral problem for strings on AdS5 ×S5 and N = 4 super Yang-Mills, and we show that it is invariant under a novel "boost" symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu (2 | 2) symmetry, and to conclude that the S-matrix is invariant under a q-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine algebra Uq (sl2 ˆ) in Drinfeld's second realisation.
Fischer, Claudia; Voss, Andreas
2014-01-01
Hypertensive pregnancy disorders affect 6 to 8 percent of all pregnancies which can cause severe complications for the mother and the fetus. The aim of this study was to develop a new method suitable for a three dimensional coupling analysis. Therefore, the three-dimensional segmented Poincaré plot analysis (SPPA3) is introduced that represents the Poincare analysis based on a cubic box model representation. The box representing the three dimensional phase space is (based on the SPPA method) subdivided into 12×12×12 equal cubelets according to the predefined range of signals and all single probabilities of occurring points in a specific cubelet related to the total number of points are calculated. From 10 healthy non-pregnant women, 66 healthy pregnant women and 56 hypertensive pregnant women suffering from chronic hypertension, gestational hypertension and preeclampsia, 30 minutes of beat-to-beat intervals (BBI), noninvasive blood pressure and respiration (RESP) were continuously recorded and analyzed. Couplings between the different signals were analyzed. The ability of SPPA3 for a screening could be confirmed by multivariate discriminant analysis differentiating between all pregnant woman and preeclampsia (index BBI3_SBP9_RESP6/ BBI8_SBP11_RESP4 leads to an area under the ROC curve of AUC=91.2%). In conclusion, SPPA3 could be a useful method for enhanced risk stratification in pregnant women.
Advanced Poincaré plot analysis differentiates between hypertensive pregnancy disorders.
Seeck, A; Baumert, M; Fischer, C; Khandoker, A; Faber, R; Voss, A
2011-10-01
Hypertensive pregnancy disorders affect 6% to 8% of all pregnancies and can result in severe complications for the mother and the foetus of which pre-eclampsia (PE) has the worst perinatal outcome. Several studies suggested that the autonomic nervous system plays an important role in the process of developing hypertensive pregnancy disorders, especially PE. The aim of this retrospective study was to investigate whether women with PE could be differentiated from women with various other hypertensive pregnancy disorders, by employing an enhanced Poincaré plot analysis (PPA), the segmented Poincaré plot analysis (SPPA), to their beat-to-beat interval and blood pressure signals. Sixty-nine pregnant women with hypertensive disorders (29 PE, 40 with chronic or gestational hypertension) were included. The SPPA as well as the traditional PPA found significant differences between PE and other hypertensive disorders of diastolic blood pressure (p analysis demonstrated that indices derived from SPPA are more suitable for differentiation between chronic and gestational hypertension and PE than those from traditional PPA (area under the ROC curve 0.85 versus 0.69). Therefore this procedure could contribute to the differential diagnosis of hypertensive pregnancy disorders.
Voss, Andreas; Fischer, Claudia; Schroeder, Rico; Figulla, Hans R; Goernig, Matthias
2012-07-01
The objectives of this study were to introduce a new type of heart-rate variability analysis improving risk stratification in patients with idiopathic dilated cardiomyopathy (DCM) and to provide additional information about impaired heart beat generation in these patients. Beat-to-beat intervals (BBI) of 30-min ECGs recorded from 91 DCM patients and 21 healthy subjects were analyzed applying the lagged segmented Poincaré plot analysis (LSPPA) method. LSPPA includes the Poincaré plot reconstruction with lags of 1-100, rotating the cloud of points, its normalized segmentation adapted to their standard deviations, and finally, a frequency-dependent clustering. The lags were combined into eight different clusters representing specific frequency bands within 0.012-1.153 Hz. Statistical differences between low- and high-risk DCM could be found within the clusters II-VIII (e.g., cluster IV: 0.033-0.038 Hz; p = 0.0002; sensitivity = 85.7 %; specificity = 71.4 %). The multivariate statistics led to a sensitivity of 92.9 %, specificity of 85.7 % and an area under the curve of 92.1 % discriminating these patient groups. We introduced the LSPPA method to investigate time correlations in BBI time series. We found that LSPPA contributes considerably to risk stratification in DCM and yields the highest discriminant power in the low and very low-frequency bands.
q-Poincaré supersymmetry in AdS5/CFT4
Directory of Open Access Journals (Sweden)
Riccardo Borsato
2018-03-01
Full Text Available We consider the exact S-matrix governing the planar spectral problem for strings on AdS5×S5 and N=4 super Yang–Mills, and we show that it is invariant under a novel “boost” symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu(2|2 symmetry, and to conclude that the S-matrix is invariant under a q-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory and weak-coupling (spin-chain description of the gauge theory limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine algebra Uq(sl2ˆ in Drinfeld's second realisation.
Covariant representation theory of the Poincaré algebra and some of its extensions
Boels, Rutger
2010-01-01
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the Poincaré algebra quantum numbers of the particles involved. Technically, this is most easily done using the well-known four dimensional spinor helicity method. In this article a natural generalization to all dimensions higher than four is obtained based on a covariant version of the representation theory of the Poincaré algebra. Covariant expressions for all possible polarization states, both bosonic and fermionic, are constructed. For the fermionic states the analysis leads directly to pure spinors. The natural extension to the representation theory of the on-shell supersymmetry algebra results in an elementary derivation of the supersymmetry Ward identities for scattering amplitudes with massless or massive legs in any integer dimension from four onwards. As a proof-of-concept application a higher dimensional analog of the vanishing helicity-equal amplitudes in four dimensions is presented in (super) Yang-Mills theory, Einstein (super-)gravity and superstring theory in a flat background.
International Nuclear Information System (INIS)
Warnock, R.L.; Ellison, J.A.; Univ. of New Mexico, Albuquerque, NM
1997-08-01
Data from orbits of a symplectic integrator can be interpolated so as to construct an approximation to the generating function of a Poincare map. The time required to compute an orbit of the symplectic map induced by the generator can be much less than the time to follow the same orbit by symplectic integration. The construction has been carried out previously for full-turn maps of large particle accelerators, and a big saving in time (for instance a factor of 60) has been demonstrated. A shortcoming of the work to date arose from the use of canonical polar coordinates, which precluded map construction in small regions of phase space near coordinate singularities. This paper shows that Cartesian coordinates can also be used, thus avoiding singularities. The generator is represented in a basis of tensor product B-splines. Under weak conditions the spline expansion converges uniformly as the mesh is refined, approaching the exact generator of the Poincare map as defined by the symplectic integrator, in some parallelepiped of phase space centered at the origin
Advanced Poincaré plot analysis differentiates between hypertensive pregnancy disorders
International Nuclear Information System (INIS)
Seeck, A; Fischer, C; Voss, A; Baumert, M; Khandoker, A; Faber, R
2011-01-01
Hypertensive pregnancy disorders affect 6% to 8% of all pregnancies and can result in severe complications for the mother and the foetus of which pre-eclampsia (PE) has the worst perinatal outcome. Several studies suggested that the autonomic nervous system plays an important role in the process of developing hypertensive pregnancy disorders, especially PE. The aim of this retrospective study was to investigate whether women with PE could be differentiated from women with various other hypertensive pregnancy disorders, by employing an enhanced Poincaré plot analysis (PPA), the segmented Poincaré plot analysis (SPPA), to their beat-to-beat interval and blood pressure signals. Sixty-nine pregnant women with hypertensive disorders (29 PE, 40 with chronic or gestational hypertension) were included. The SPPA as well as the traditional PPA found significant differences between PE and other hypertensive disorders of diastolic blood pressure (p < 0.001 versus p < 0.001) but only the SPPA method revealed significant differences (p < 0.001) also of the systolic blood pressure. Further on, linear discrimination analysis demonstrated that indices derived from SPPA are more suitable for differentiation between chronic and gestational hypertension and PE than those from traditional PPA (area under the ROC curve 0.85 versus 0.69). Therefore this procedure could contribute to the differential diagnosis of hypertensive pregnancy disorders
Electric-magnetic duality as a secondary symmetry
International Nuclear Information System (INIS)
Brandt, R.A.; Young, K.
1980-01-01
In both the abelian and non-abelian classical point magnetic monopole theories, electric current conservation is a consequence of gauge invariance, but, since there is no magnetic gauge group, magnetic current conservation is not a Noether-type conservation law. In the abelian models, the equations of motion (but not the lagrangian) are invariant to the duality rotations in electric-magnetic charge space, but this is not the case in the non-abelian models. In an attempt to understand these and related points, we introduce a generalization of Noether's theorem. Consider a physical system described by a set of variables THETA and characterized by a lagrangian density L(THETA). A transormation law THETA → G THETA which leaves L invariant leads to a conserved current Jsub(μ)(THETA). We then call G a primary symmetry. A second transformation law THETA → D THETA which leaves the equations of motion, but not L, invariant then leads to another conserved current Jsub(μ)(D THETA). We then call D a secondary symmetra. Our main point is that Jsub(μ) (D THETA) may be conserved even if the equations of motion are not invariant under D. All that is required is that the change of the equations of motion under D is perpendicular (in the field space) to the change of the fields under G. Then we call D an incomplete secondary symmetry. We show that in both the abelian and non-abelian monopole theories, duality is an incomplete secondary symmetry whose associated conservation law is magnetic current conservation. Thus it is the interpretation of duality as a secondary symmetry which explains magnetic current conservation and which generalizes from the abelian theories to the non-abelian ones. This suggests that magnetic current conservation may remain valid in quantum field theory. (orig.)
Duality in an asset exchange model for wealth distribution
Li, Jie; Boghosian, Bruce M.
2018-05-01
Asset exchange models are agent-based economic models with binary transactions. Previous investigations have augmented these models with mechanisms for wealth redistribution, quantified by a parameter χ, and for trading bias favoring wealthier agents, quantified by a parameter ζ. By deriving and analyzing a Fokker-Planck equation for a particular asset exchange model thus augmented, it has been shown that it exhibits a second-order phase transition at ζ / χ = 1, between regimes with and without partial wealth condensation. In the "subcritical" regime with ζ / χ 1, a fraction 1 - χ / ζ of the wealth is condensed. Intuitively, one may associate the supercritical, wealth-condensed regime as reflecting the presence of "oligarchy," by which we mean that an infinitesimal fraction of the total agents hold a finite fraction of the total wealth in the continuum limit. In this paper, we further elucidate the phase behavior of this model - and hence of the generalized solutions of the Fokker-Planck equation that describes it - by demonstrating the existence of a remarkable symmetry between its supercritical and subcritical regimes in the steady-state. Noting that the replacement { ζ → χ , χ → ζ } , which clearly has the effect of inverting the order parameter ζ / χ, provides a one-to-one correspondence between the subcritical and supercritical states, we demonstrate that the wealth distribution of the subcritical state is identical to that of the corresponding supercritical state when the oligarchy is removed from the latter. We demonstrate this result analytically, both from the microscopic agent-level model and from its macroscopic Fokker-Planck description, as well as numerically. We argue that this symmetry is a kind of duality, analogous to the famous Kramers-Wannier duality between the subcritical and supercritical states of the Ising model, and to the Maldacena duality that underlies AdS/CFT theory.
In search of balance – managing the dualities of HRM: an overview of the issues
Boselie, J.P.P.E.F.|info:eu-repo/dai/nl/177012277; Brewster, C.; Paauwe, J.
2009-01-01
Purpose – The purpose of this paper is to provide an overview of the human resource management (HRM) literature that builds up to our current concern with dualities, paradoxes, ambiguities, and balance issues; and to introduce the six papers in this special issue on managing the dualities in HRM.
Metaphorical Duality: High School Subject Departments as Both Communities and Organizations
Melville, Wayne; Wallace, John
2007-01-01
This article investigates the metaphorical duality that exists when school subject departments are concurrently conceptualized as both communities and organizations. Employing a narrative methodology, we use the metaphorical duality to examine the manner in which science teachers negotiate two key aspects of their work; professional learning and…
Korman, Jonathan; McCann, Robert J.; Seis, Christian
2013-01-01
A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality theorem for capacity-constrained optimal transport as an infinite-dimensional application.
A case study of an organisation development of duality
DEFF Research Database (Denmark)
Andreassen, Mads R.; Gertsen, Frank
2008-01-01
This paper seeks to comprehend what the organisational circumstances (conditions) look like that induces an organisation to develop its exploitation and exploration capabilities to duality. This is done by studying changes in the organisational characteristics in a Danish manufacturer...... of accessories for house windows during the expansion leading to global operation. The study comprises 2½ years of detailed study and a retrospective study of approximately 30 years. The data collection was mainly based on semi-structured interviews. The findings add a new approach to continuous innovation...... theory by uncovering how organisational conditions affect the development and integration of exploitation and exploration capabilities....
The Bloom-Gilman duality and leading logarithms
International Nuclear Information System (INIS)
Carlson, C.E.; Mukhopadhyay, N.C.
1994-01-01
The existing inclusive electroproduction data base allows the authors a look at the issue of the relative behaviors of background and resonance excitations, a part of the Bloom-Gilman duality. These data lack accuracy at high Q 2 but establish PQCD scaling in the resonance region and even allow the authors a glimpse at the leading logarithmic corrections due to the gluon radiation and its possible quenching at large W and x. These should inspire better quality experimental tests at facilities like CEBAF II
Numerical implementation of the loop-tree duality method
Energy Technology Data Exchange (ETDEWEB)
Buchta, Sebastian; Rodrigo, German [Universitat de Valencia-Consejo Superior de Investigaciones Cientificas, Parc Cientific, Instituto de Fisica Corpuscular, Valencia (Spain); Chachamis, Grigorios [Universidad Autonoma de Madrid, Instituto de Fisica Teorica UAM/CSIC, Madrid (Spain); Draggiotis, Petros [Institute of Nuclear and Particle Physics, NCSR ' ' Demokritos' ' , Agia Paraskevi (Greece)
2017-05-15
We present a first numerical implementation of the loop-tree duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs. (orig.)
Legendre Duality of Spherical and Gaussian Spin Glasses
International Nuclear Information System (INIS)
Genovese, Giuseppe; Tantari, Daniele
2015-01-01
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model
N=1 field theory duality from M theory
International Nuclear Information System (INIS)
Schmaltz, M.; Sundrum, R.
1998-01-01
We investigate Seiberg close-quote s N=1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in type IIA string theory is given an elegant derivation from M theory. copyright 1998 The American Physical Society
Coherence Generalises Duality: A Logical Explanation of Multiparty Session Types
DEFF Research Database (Denmark)
Carbone, Marco; Lindley, Sam; Montesi, Fabrizio
2016-01-01
the duality of classical linear logic (relating two types) with a more general notion of coherence (relating an arbitrary number of types). This paper introduces variants of CP and MCP, plus a new intermediate calculus of Globally-governed Classical Processes (GCP). We show a tight relation between......Wadler introduced Classical Processes (CP), a calculus based on a propositions-as-types correspondence between propositions of classical linear logic and session types. Carbone et al. introduced Multiparty Classical Processes, a calculus that generalises CP to multiparty session types, by replacing...
Legendre Duality of Spherical and Gaussian Spin Glasses
Energy Technology Data Exchange (ETDEWEB)
Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)
2015-12-15
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
Absolute X-distribution and self-duality
Alexandru, Andrei; Horváth, Ivan
2011-01-01
Various models of QCD vacuum predict that it is dominated by excitations that are predominantly self-dual or anti-self-dual. In this work we look at the tendency for self-duality in the case of pure-glue SU(3) gauge theory using the overlap-based definition of the field-strength tensor. To gauge this property, we use the absolute X-distribution method which is designed to quantify the dynamical tendency for polarization for arbitrary random variables that can be decomposed in a pair of orthog...
Topological twist in four dimensions, R-duality and hyperinstantons
International Nuclear Information System (INIS)
Anselmi, D.; Fre, P.
1993-01-01
In this paper we continue the programme of topologically twisting N=2 theories in D=4, focusing on the coupling of vector multiplets to N=2 supergravity. We show that in the minimal case, namely when the special gometry prepotential F(X) is a quadratic polynomial, the theory has a so far unknown on-shell U(1) symmetry, that we name R-duality. R-duality is a generalization of the chiral-dual on-shell symmetry of N=2 pure supergravity and of the R-symmetry of N=2 super Yang-Mills theory. Thanks to this, the theory can be topologically twisted and topologically shifted, precisely as pure N=2 supergravity, to yield a natural coupling of topological gravity to topological Yang-Mills theory. The gauge-fixing condition that emerges from the twisting is the self-duality condition on the gauge field strength and on the spin connection. Hence our theory reduces to intersection theory in the moduli-space of gauge instantons living in gravitational instanton backgrounds. We remark that, for deep properties of the parent N=2 theory, the topological Yang-Mills theory we obtain by taking the flat space limit of our gravity-coupled lagrangian is different from the Donaldson theory constructed by Witten. Whether this difference is substantial and what its geometrical implications may be is yet to be seen. We also discuss the topological twist of the hypermultiplets leading to topological quaternionic sigma-models. The instantons of these models, named by us hyperinstantons, correspond to a notion of triholomorphic mappings discussed in the paper. In all cases the new ghost number is the sum of the old ghost number plus the R-duality charge. The observables described by the theory are briefly discussed. In conclusion, the topological twist of the complete N=2 theory defines intersection theory in the moduli-space of gauge instantons plus gravitational instantons plus hyperinstantons. This is possibly a new subject for further mathematical investigation. (orig.)
Duality and BPS spectra in N = 2 supersymmetric QCD
International Nuclear Information System (INIS)
Ferrari, F.
1997-01-01
I review, with some pedagogy, two different approaches to the computation of BPS spectra in N = 2 supersymmetric QCD with gauge group SU(2). The first one is semiclassical and has been widely used in the literature. The second one makes use of constraints coming from the non perturbative, global structure of the Coulomb branch of these theories. The second method allows for a description of discontinuities in the BPS spectra at strong coupling, and should lead to accurate test of duality conjectures in N = 2 theories. (orig.)
Geometric approach to a massive p form duality
International Nuclear Information System (INIS)
Arias, Pio J.; Leal, Lorenzo; Perez-Mosquera, J. C.
2003-01-01
Massive theories of Abelian p forms are quantized in a generalized path representation that leads to a description of the phase space in terms of a pair of dual nonlocal operators analogous to the Wilson loop and the 't Hooft disorder operators. Special attention is devoted to the study of the duality between the topologically massive and self-dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one nonlocal operator suffices to describe the observables
Causality and unitarity via the tree-loop duality relation
Energy Technology Data Exchange (ETDEWEB)
Tomboulis, E.T. [Mani L. Bhaumik Institute for Theoretical Physics,Department of Physics and Astronomy, UCLA,Los Angeles, CA 90095-1547 (United States)
2017-05-29
The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a representation of a graph in terms of lower order cut graphs. Extracting the absorptive part gives then the general unitarity relation (Cutkosky rule). The derivation, being carried out directly in momentum space, holds for any local (polynomial) hermitian interaction vertices. This is in contrast to the technical difficulties arising from contact terms in the spacetime approach based on the largest time equation.
Orientifolds and duality cascades: confinement before the wall
Argurio, Riccardo; Bertolini, Matteo
2018-02-01
We consider D-branes at orientifold singularities and discuss two properties of the corresponding low energy four-dimensional effective theories which are not shared, generically, by other Calabi-Yau singularities. The first property is that duality cascades are finite and, unlike ordinary ones, do not require an infinite number of degrees of freedom to be UV-completed. The second is that orientifolds tend to stabilize runaway directions. These two properties can have interesting implications and widen in an intriguing way the variety of gauge theories one can describe using D-branes.
Supersymmetric quantum corrections and Poisson-Lie T-duality
International Nuclear Information System (INIS)
Assaoui, F.; Lhallabi, T.; Abdus Salam International Centre for Theoretical Physics, Trieste
2000-07-01
The quantum actions of the (4,4) supersymmetric non-linear sigma model and its dual in the Abelian case are constructed by using the background superfield method. The propagators of the quantum superfield and its dual and the gauge fixing actions of the original and dual (4,4) supersymmetric sigma models are determined. On the other hand, the BRST transformations are used to obtain the quantum dual action of the (4,4) supersymmetric nonlinear sigma model in the sense of Poisson-Lie T-duality. (author)
Symmetries of the Schrodinger Equation and Algebra/Superalgebra Duality
International Nuclear Information System (INIS)
Toppan, Francesco
2014-12-01
Some key features of the symmetries of the Schroedinger equation that are common to a much broader class of dynamical systems (some under construction) are illustrated. I discuss the algebra/superalgebra duality involving rst and second-order differential operators. It provides different viewpoints for the spectrum-generating subalgebras. The representation dependent notion of on-shell symmetry is introduced. The difference in associating the time derivative symmetry operator with either a root or a Cartan generator of the sl(2) subalgebra is discussed. In application to one-dimensional Lagrangian superconformal sigma-models it implies superconformal actions which are either supersymmetric or non-supersymmetric. (author)
Punctuated eternal inflation via AdS/CFT duality
International Nuclear Information System (INIS)
Lowe, David A.; Roy, Shubho
2010-01-01
The work is an attempt to model a scenario of inflation in the framework of anti-de Sitter/conformal field theory duality, a potentially complete nonperturbative description of quantum gravity. We study bubble geometries with de Sitter interiors within an ambient Schwarzschild anti-de Sitter black hole spacetime and the properties of the corresponding states in the dual conformal field theory. It is argued the viable bubble states can be identified with a subset of the black hole microstates. Consistency checks are performed and a number of implications regarding cosmology are discussed including how the key problems or paradoxes of conventional eternal inflation are overcome in this scenario.
Short-time perturbation theory and nonrelativistic duality
International Nuclear Information System (INIS)
Whitenton, J.B.; Durand, B.; Durand, L.
1983-01-01
We give a simple proof of the nonrelativistic duality relation 2 sigma/sub bound/>roughly-equal 2 sigma/sub free/> for appropriate energy averages of the cross sections for e + e - →(qq-bar bound states) and e + e - →(free qq-bar pair), and calculate the corrections to the relation by relating W 2 sigma to the Fourier transform of the Feynman propagation function and developing a short-time perturbation series for that function. We illustrate our results in detail for simple power-law potentials and potentials which involve combinations of powers
Duality and BPS spectra in N = 2 supersymmetric QCD
Energy Technology Data Exchange (ETDEWEB)
Ferrari, F. [Ecole Normale Superieure, 75 - Paris (France). Lab. de Physique Theorique
1997-05-01
I review, with some pedagogy, two different approaches to the computation of BPS spectra in N = 2 supersymmetric QCD with gauge group SU(2). The first one is semiclassical and has been widely used in the literature. The second one makes use of constraints coming from the non perturbative, global structure of the Coulomb branch of these theories. The second method allows for a description of discontinuities in the BPS spectra at strong coupling, and should lead to accurate test of duality conjectures in N = 2 theories. (orig.).
Duality in a Supersymmetric Gauge Theory From a Perturbative Viewpoint
DEFF Research Database (Denmark)
Ryttov, Thomas A.; Shrock, Robert
2018-01-01
points of the renormalization group emerge in scheme-independent series expansions in the electric and magnetic theories. We further demonstrate that truncations of these series expansions to modest order yield very accurate approximations to these quantities and suggest possible implications......We study duality in N ¼ 1 supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral superfields, and the quantities a, c, a=c, and b at superconformal fixed...
The Bloom-Gilman duality and leading logarithms
Energy Technology Data Exchange (ETDEWEB)
Carlson, C.E. [College of William and Mary, Williamsburg, VA (United States); Mukhopadhyay, N.C. [Rensselaer Polytechnic Inst., Troy, NY (United States)
1994-04-01
The existing inclusive electroproduction data base allows the authors a look at the issue of the relative behaviors of background and resonance excitations, a part of the Bloom-Gilman duality. These data lack accuracy at high Q{sup 2} but establish PQCD scaling in the resonance region and even allow the authors a glimpse at the leading logarithmic corrections due to the gluon radiation and its possible quenching at large W and x. These should inspire better quality experimental tests at facilities like CEBAF II.
The Hall module of an exact category with duality
Young, Matthew B.
2012-01-01
We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced sigma-analogue of the quantum Kac-Moody algebra attached to the quiver. For finite type quivers, we explicitly determin...
Duality of quasilocal gravitational energy and charges with nonorthogonal boundaries
International Nuclear Information System (INIS)
Kim, Sung-Won; Kim, Won Tae; Oh, John J.; Yee, Ki Hyuk
2003-01-01
We study the duality of quasilocal energy and charges with nonorthogonal boundaries in the (2+1)-dimensional low-energy string theory. Quasilocal quantities shown in previous work and also some new variables arising from considering the nonorthogonal boundaries are presented, and the boost relations between these quantities are discussed. Moreover, we show that the dual properties of quasilocal variables, such as quasilocal energy density, momentum densities, surface stress densities, dilaton pressure densities, and Neveu-Schwarz charge density, are still valid in the moving observer's frame
Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity
Ceresole, Anna T; Ferrara, Sergio; Van Proeyen, A; Ceresole, A; D'Auria, R; Ferrara, S; Van Proeyen, A
1995-01-01
We consider duality transformations in N=2, d=4 Yang-Mills theory coupled to N=2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy `classical and quantum duality symmetries' (monodromies), incorporating T and S dualities. In particular, we shall be able to study theories (like N=2 heterotic strings) which are formulated in symplectic basis where a `holomorphic prepotential' F does not exist, and yet give general expressions for all relevant physical quantities. Duality transformations and symmetries for the N=1 matter coupled Yang--Mills supergravity system are also exhibited. The implications of duality symmetry on all N>2 extended supergravities are briefly mentioned. We finally give the general form of the central charge and the N=2 semiclassical spectrum of the dyonic BPS saturated states (as it comes by truncation of the N=4 spectrum).
Core-Shell Particles as Building Blocks for Systems with High Duality Symmetry
Rahimzadegan, Aso; Rockstuhl, Carsten; Fernandez-Corbaton, Ivan
2018-05-01
Material electromagnetic duality symmetry requires a system to have equal electric and magnetic responses. Intrinsically dual materials that meet the duality conditions at the level of the constitutive relations do not exist in many frequency bands. Nevertheless, discrete objects like metallic helices and homogeneous dielectric spheres can be engineered to approximate the dual behavior. We exploit the extra degrees of freedom of a core-shell dielectric sphere in a particle optimization procedure. The duality symmetry of the resulting particle is more than 1 order of magnitude better than previously reported nonmagnetic objects. We use T -matrix-based multiscattering techniques to show that the improvement is transferred onto the duality symmetry of composite objects when the core-shell particle is used as a building block instead of homogeneous spheres. These results are relevant for the fashioning of systems with high duality symmetry, which are required for some technologically important effects.
New Results on Testing Duality in Spin Structure from Jefferson Lab
Energy Technology Data Exchange (ETDEWEB)
Nilanga Liyanage
2005-10-01
The Bloom-Gilman duality has been experimentally demonstrated for spin independent structure functions. Duality is observed when the smooth scaling curve at high momentum transfer is an average over the resonance bumps at lower momentum transfer, but at the same value of scaling variable x. Signs of quark-hadron duality for the spin Dependant structure function g1 of the proton has been recently reported by the Hermes collaboration. Experimental Halls A, B and C at Jefferson lab have recently measured spin structure functions in the resonance region for the proton and the neutron. Data from these experiments combined with Deep-Inelastic-Scattering data provide a precision test of quark-hadron duality predictions for spin structure functions for both the proton and the neutron. This will be one of the first precision tests of spin and flavor dependence of quark-hadron duality.
Section sigma models coupled to symplectic duality bundles on Lorentzian four-manifolds
Lazaroiu, C. I.; Shahbazi, C. S.
2018-06-01
We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion π over space-time, whose total space carries a Lorentzian metric making the fibers into totally-geodesic connected Riemannian submanifolds. In particular, π is a fiber bundle endowed with a complete Ehresmann connection whose transport acts through isometries between the fibers. In turn, the Abelian gauge fields are "twisted" by a flat symplectic vector bundle defined over the total space of π. This vector bundle is endowed with a vertical taming which locally encodes the gauge couplings and theta angles of the theory and gives rise to the notion of twisted self-duality, of crucial importance to construct the theory. When the Ehresmann connection of π is integrable, we show that our theories are locally equivalent to ordinary Einstein-Scalar-Maxwell theories and hence provide a global non-trivial extension of the universal bosonic sector of four-dimensional supergravity. In this case, we show using a special trivializing atlas of π that global solutions of such models can be interpreted as classical "locally-geometric" U-folds. In the non-integrable case, our theories differ locally from ordinary Einstein-Scalar-Maxwell theories and may provide a geometric description of classical U-folds which are "locally non-geometric".
Bukhvostov–Lipatov model and quantum-classical duality
Directory of Open Access Journals (Sweden)
Vladimir V. Bazhanov
2018-02-01
Full Text Available The Bukhvostov–Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1+1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O(3 non-linear sigma model. In our previous work [arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov–Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.
U-duality multiplets and nonperturbative superstring states
International Nuclear Information System (INIS)
Bars, I.; Yankielowicz, S.
1996-01-01
We employ an algebraic approach for unifying perturbative and nonperturbative superstring states on an equal footing, in the form of U-duality multiplets, at all excited string levels. In compactified type-IIA supertring theory we present evidence that the multiplet is labeled by two spaces, open-quote open-quote index close-quote close-quote space and open-quote open-quote base close-quote close-quote space, on which U acts without mixing them. Both spaces are nonperturbative extensions of similar spaces that label perturbative T-duality multiplets. Base space consists of all the central charges of the 11D SUSY algebra, while index space corresponds to representations of the maximal compact subgroup K improper-subset U. This structure predicts the quantum numbers of the nonperturbative states. We also discuss whether and how U multiplets may coexist with 11-dimensional multiplets that are associated with an additional nonperturbative 11D structure that seems to be lurking behind in the underlying theory. copyright 1996 The American Physical Society
Bukhvostov-Lipatov model and quantum-classical duality
Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.
2018-02-01
The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1 + 1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model. In our previous work [arxiv:arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.
S-duality invariant perturbation theory improved by holography
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Abhishek [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); Honda, Masazumi [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 7610001 (Israel); Thakur, Somyadip [Tata Institute of Fundamental Research,Mumbai 400005 (India)
2017-04-26
We study anomalous dimensions of unprotected low twist operators in the four-dimensional SU (N)N=4 supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling τ. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the N=4 superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points τ=i and τ=e{sup iπ/3}. It turns out that our interpolating functions have maximum at τ=e{sup iπ/3}, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.
Duality covariant type IIB supersymmetry and nonperturbative consequences
Bars, Itzhak
1997-01-01
Type-IIB supersymmetric theories have an SL(2,Z) invariance, known as U-duality, which controls the non-perturbative behavior of the theory. Under SL(2,Z) the supercharges are doublets, implying that the bosonic charges would be singlets or triplets. However, among the bosonic charges there are doublet strings and doublet fivebranes which are in conflict with the doublet property of the supercharges. It is shown that the conflict is resolved by structure constants that depend on moduli, such as the tau parameter, which transform under the same SL(2,Z). The resulting superalgebra encodes the non-perturbative duality properties of the theory and is valid for any value of the string coupling constant. The usefulness of the formalism is illustrated by applying it to purely algebraic computations of the tension of (p,q) strings, and the mass and entropy of extremal blackholes constructed from D-1-branes and D-5-branes. In the latter case the non-perturbative coupling dependence of the BPS mass and metric is comput...
Duality covariant type-IIB supersymmetry and nonperturbative consequences
International Nuclear Information System (INIS)
Bars, I.
1997-01-01
Type-IIB supersymmetric theories have an SL(2,Z) invariance, known as U duality, which controls the nonperturbative behavior of the theory. Under SL(2,Z) the supercharges are doublets, implying that the bosonic charges would be singlets or triplets. However, among the bosonic charges there are doublet strings and doublet five-branes which are in conflict with the doublet property of the supercharges. It is shown that the conflict is resolved by structure constants that depend on moduli, such as the tau parameter, which transform under the same SL(2,Z). The resulting superalgebra encodes the nonperturbative duality properties of the theory and is valid for any value of the string coupling constant. The usefulness of the formalism is illustrated by applying it to purely algebraic computations of the tension of (p,q) strings, and the mass and entropy of extremal black holes constructed from D-1-branes and D-5-branes. In the latter case the nonperturbative coupling dependence of the BPS mass and renormalization is computed for the first time in this paper. It is further argued that the moduli dependence of the superalgebra provides hints for four more dimensions beyond ten, such that the superalgebra is embedded in a fundamental theory which would be covariant under SO(11,3). An outline is given for a matrix theory in 14 dimensions that would be consistent with M(atrix) theory as well as with the above observations. copyright 1997 The American Physical Society
Heterotic String/F-theory Duality from Mirror Symmetry
Berglund, Per
1998-01-01
We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds $X_{n+1}$ to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of these data as valid classical solutions of the heterotic string compactified on Z_n proves F-theory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n+1-fold $X_{n+1}$ a toric n fold Z_n together with a specific family of sheafs on it. This allows for a systematic construction of phenomenologically interesting d=4 N=1 heterotic vacua, e.g. on deformations of the tangent bundle, with grand unified and SU(3)\\times SU(2) gauge groups. As another application we find non-perturbative gauge enhancements of the heterotic string on singular Calabi-Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds.
Duality between k-essence and Rastall gravity
Energy Technology Data Exchange (ETDEWEB)
Bronnikov, Kirill A. [VNIIMS, Moscow (Russian Federation); RUDN University, Institute of Gravitation and Cosmology, Moscow (Russian Federation); National Research Nuclear University ' ' MEPhI' ' , Moscow (Russian Federation); Fabris, Julio C. [National Research Nuclear University ' ' MEPhI' ' , Moscow (Russian Federation); Universidade Federal do Espirito Santo, Vitoria, ES (Brazil); Piattella, Oliver F.; Rodrigues, Denis C.; Santos, Edison C. [Universidade Federal do Espirito Santo, Vitoria, ES (Brazil)
2017-06-15
The k-essence theory with a power-law function of (∂φ){sup 2} and Rastall's non-conservative theory of gravity with a scalar field are shown to have the same solutions for the metric under the assumption that both the metric and the scalar fields depend on a single coordinate. This equivalence (called k-R duality) holds for static configurations with various symmetries (spherical, plane, cylindrical, etc.) and all homogeneous cosmologies. In the presence of matter, Rastall's theory requires additional assumptions on how the stress-energy tensor non-conservation is distributed between different contributions. Two versions of such non-conservation are considered in the case of isotropic spatially flat cosmological models with a perfect fluid: one (R1) in which there is no coupling between the scalar field and the fluid, and another (R2) in which the fluid separately obeys the usual conservation law. In version R1 it is shown that k-R duality holds not only for the cosmological models themselves but also for their adiabatic perturbations. In version R2, among other results, a particular model is singled out that reproduces the same cosmological expansion history as the standard ΛCDM model but predicts different behaviors of small fluctuations in the k-essence and Rastall frameworks. (orig.)
Duality and modular invariance in rational conformal field theories
International Nuclear Information System (INIS)
Li Miao.
1990-03-01
We investigate the polynomial equations which should be satisfied by the duality data for a rational conformal field theory. We show that by these duality data we can construct some vector spaces which are isomorphic to the spaces of conformal blocks. One can construct explicitly the inner product for the former if one deals with a unitary theory. These vector spaces endowed with an inner product are the algebraic reminiscences of the Hilbert spaces in a Chern-Simons theory. As by-products, we show that the polynomial equations involving the modular transformations for the one-point blocks on the torus are not independent. And along the way, we discuss the reconstruction of the quantum group in a rational conformal theory. Finally, we discuss the solution of structure constants for a physical theory. Making some assumption, we obtain a neat solution. And this solution in turn implies that the quantum groups of the left sector and of the right sector must be the same, although the chiral algebras need not to be the same. Some examples are given. (orig.)
T-duality orbifolds of heterotic Narain compactifications
Energy Technology Data Exchange (ETDEWEB)
Nibbelink, Stefan Groot [School of Engineering and Applied Sciences, Rotterdam University of Applied Sciences,G.J. de Jonghweg 4-6, 3015 GG Rotterdam (Netherlands); Vaudrevange, Patrick K.S. [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Physik Department T30, Technische Universität München,James-Franck-Straße, 85748 Garching (Germany)
2017-04-06
To obtain a unified framework for symmetric and asymmetric heterotic orbifold constructions we provide a systematic study of Narain compactifications orbifolded by finite order T-duality subgroups. We review the generalized vielbein that parametrizes the Narain moduli space (i.e. the metric, the B-field and the Wilson lines) and introduce a convenient basis of generators of the heterotic T-duality group. Using this we generalize the space group description of orbifolds to Narain orbifolds. This yields a unified, crystallographic description of the orbifold twists, shifts as well as Narain moduli. In particular, we derive a character formula that counts the number of unfixed Narain moduli after orbifolding. Moreover, we develop new machinery that may ultimately open up the possibility for a full classification of Narain orbifolds. This is done by generalizing the geometrical concepts of ℚ-, ℤ- and affine classes from the theory of crystallography to the Narain case. Finally, we give a variety of examples illustrating various aspects of Narain orbifolds, including novel T-folds.
International Nuclear Information System (INIS)
Fradkin, E.S.; Metsaev, R.R.
1996-02-01
Using the language of highest weight representations and the light cone formalism we construct a full list of cubic amplitudes of scattering for all bosonic massless representations of the Poincare group in any even space-time dimension. (author). 29 refs
Guzik, P.; Piskorski, J.; Krauze, T.; Schneider, R.; Wesseling, K.H.; Wykrȩtowicz, A.; Wysocki, H.
2007-01-01
Aim: To analyze the correlation of the Poincaré plot descriptors of RR intervals with standard measures of heart rate variability (HRV) and spontaneous baroreflex sensitivity (BRS). A physiological model of changing respiratory rates from 6 to 15 breaths/min provided a wide range of RR intervals for
International Nuclear Information System (INIS)
Inahama, Yuzuru; Shirai, Shin-ichi
2003-01-01
We study the essential spectrum of the magnetic Schroedinger operators on the Poincare upper-half plane and establish a hyperbolic analog of Iwatsuka's result [J. Math. Kyoto Univ. 23(3), 475-480 (1983)] on the stability of the essential spectrum under perturbations from constant magnetic fields
Directory of Open Access Journals (Sweden)
S.H. Chen
1996-01-01
Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.
Gauge/gravity duality. A road towards reality
International Nuclear Information System (INIS)
Kerner, Patrick
2012-01-01
In this dissertation we use gauge/gravity duality to investigate various phenomena of strongly coupled systems. In particular, we consider applications of the duality to real-world systems such as condensed matter systems and the quark-gluon plasma created by heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Gauge/gravity duality which originates from string theory relates strongly coupled gauge theories to weakly coupled gravity theories. This duality allows for computations of non-perturbative results on the field theory side by perturbative calculations on the gravity side. As we have learned in the recent years, the duality is especially suitable to describe hot and dense plasmas as well as real-time processes related to transport properties or spectral functions. Unfortunately, so far there is no dual gravity description modeling every aspect of a strongly coupled real-world system. However, there are many gravity duals which describe several phenomena. The general idea of this thesis is to study different gravity duals in order to develop a gravity description of hot and dense plasmas. In particular, we focus on physics in thermal equilibrium and close to equilibrium. Motivated by the experimentally observed mesonic resonances in the quark-gluon plasma, we first study quasinormal modes of a gravity dual which contains such resonances. The quasinormal modes on the gravity side are identified with the poles of the Green's function on the field theory side. By studying these quasinormal modes, we observe how quasiparticle resonances develop in a hot and dense plasma. We find interesting trajectories of quasinormal frequencies which may be found experimentally as the temperature and density is varied. In addition, we find an instability in the quasinormal mode spectrum at large chemical potential or magnetic field. At large chemical potential, this instability triggers the condensation of a field which breaks
Gauge/gravity duality. A road towards reality
Energy Technology Data Exchange (ETDEWEB)
Kerner, Patrick
2012-02-23
In this dissertation we use gauge/gravity duality to investigate various phenomena of strongly coupled systems. In particular, we consider applications of the duality to real-world systems such as condensed matter systems and the quark-gluon plasma created by heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Gauge/gravity duality which originates from string theory relates strongly coupled gauge theories to weakly coupled gravity theories. This duality allows for computations of non-perturbative results on the field theory side by perturbative calculations on the gravity side. As we have learned in the recent years, the duality is especially suitable to describe hot and dense plasmas as well as real-time processes related to transport properties or spectral functions. Unfortunately, so far there is no dual gravity description modeling every aspect of a strongly coupled real-world system. However, there are many gravity duals which describe several phenomena. The general idea of this thesis is to study different gravity duals in order to develop a gravity description of hot and dense plasmas. In particular, we focus on physics in thermal equilibrium and close to equilibrium. Motivated by the experimentally observed mesonic resonances in the quark-gluon plasma, we first study quasinormal modes of a gravity dual which contains such resonances. The quasinormal modes on the gravity side are identified with the poles of the Green's function on the field theory side. By studying these quasinormal modes, we observe how quasiparticle resonances develop in a hot and dense plasma. We find interesting trajectories of quasinormal frequencies which may be found experimentally as the temperature and density is varied. In addition, we find an instability in the quasinormal mode spectrum at large chemical potential or magnetic field. At large chemical potential, this instability triggers the condensation of a field which
Kaluza–Klein-type models of de Sitter and Poincaré gauge theories of gravity
International Nuclear Information System (INIS)
Lu Jiaan; Huang Chaoguang
2013-01-01
We construct Kaluza–Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincaré gauge theory of gravity, respectively. A manifestly gauge-invariant formalism has been given. The gravitational dynamics is constructed by the geometry of the de Sitter or Minkowski bundle and a global section which plays an important role in the gauge-invariant formalism. Unlike the old Kaluza–Klein-type models of gauge theory of gravity, a suitable cosmological term can be obtained in the Lagrangian of our models and the models in the spin-current-free and torsion-free limit will come back to general relativity with a corresponding cosmological term. We also generalize the results to the case with a variable cosmological term. (paper)
The Poincaré compactification of the MIC-Kepler problem with positive energies
Iwai, T
2001-01-01
The Poincare compactification and the symplectic reduction methods are first reviewed and then used to study the behaviour at infinity of the MIC (McIntosh-Cisneros)-Kepler problem at positive energies. The hyperbolic orbits leave the unstable equilibrium point set at infinity and tend eventually to the stable equilibrium point set at infinity. Both of these equilibrium point sets are diffeomorphic with S/sup 2/, the unit sphere in R/sup 3/. The hyperbolic orbits determine a map of the unstable equilibrium point set to the stable equilibrium point set in such a manner that the initial point (or the limit point as t to - infinity ) of an orbit is mapped to its final point (or the limit point as t to infinity ). This map is found explicitly as a rotation matrix which depends on the energy and the angular momentum of the orbits. (9 refs).
Robust Solvers for Symmetric Positive Definite Operators and Weighted Poincaré Inequalities
Efendiev, Yalchin
2012-01-01
An abstract setting for robustly preconditioning symmetric positive definite (SPD) operators is presented. The term "robust" refers to the property of the condition numbers of the preconditioned systems being independent of mesh parameters and problem parameters. Important instances of such problem parameters are in particular (highly varying) coefficients. The method belongs to the class of additive Schwarz preconditioners. The paper gives an overview of the results obtained in a recent paper by the authors. It, furthermore, focuses on the importance of weighted Poincaré inequalities, whose notion is extended to general SPD operators, for the analysis of stable decompositions. To demonstrate the applicability of the abstract preconditioner the scalar elliptic equation and the stream function formulation of Brinkman\\'s equations in two spatial dimensions are considered. Several numerical examples are presented. © 2012 Springer-Verlag.
The accelerating universe under Poincaré gauge theory of gravtiy
Directory of Open Access Journals (Sweden)
AO Xichen
2014-08-01
Full Text Available The accelerating expansion was discovered at the end of the last century, which violates humans′ fundamental intuition of gravity. Trying to explaining this weird observational fact became the principal task of cosmologists, who proposed various models. Among these models, gauge theories of gravity , for its solid theoretical foundation, attract widespread attention. In this paper, we study the cosmology based on the Poincaré gauge theory of gravity. We obtain the analytical solution which describes the evolution history of the universe. And we fit these analytical results to the Type Ia Supernova observation data, and obtain the best-fit value for model parameters and initial conditions, and the confidence level of these parameters.
Exceptional versus superPoincaré algebra as the defining symmetry of maximal supergravity
International Nuclear Information System (INIS)
Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta
2016-01-01
We describe how one may use either the superPoincaré algebra or the exceptional algebra to construct maximal supergravity theories in the light-cone formalism. The d=4 construction shows both symmetries albeit in a non-linearly realized manner. In d=11, we find that we have to choose which of these two symmetries to use, in constructing the theory. In order to understand the other “unused" symmetry, one has to perform a highly non-trivial field redefinition. We argue that this shows that one cannot trust counterterm arguments that do not take the full symmetry of the theory into account. Finally we discuss possible consequences for Superstring theory and M-theory.
Cosmology in Poincaré gauge gravity with a pseudoscalar torsion
Energy Technology Data Exchange (ETDEWEB)
Lu, Jianbo; Chee, Guoying [Department of Physics, Liaoning Normal University,Dalian 116029 (China)
2016-05-04
A cosmology of Poincare{sup ´} gauge theory is developed, where several properties of universe corresponding to the cosmological equations with the pseudoscalar torsion function are investigated. The cosmological constant is found to be the intrinsic torsion and curvature of the vacuum universe and is derived from the theory naturally rather than added artificially, i.e. the dark energy originates from geometry and includes the cosmological constant but differs from it. The cosmological constant puzzle, the coincidence and fine tuning problem are relieved naturally at the same time. By solving the cosmological equations, the analytic cosmological solution is obtained and can be compared with the ΛCDM model. In addition, the expressions of density parameters of the matter and the geometric dark energy are derived, and it is shown that the evolution of state equations for the geometric dark energy agrees with the current observational data. At last, the full equations of linear cosmological perturbations and the solutions are obtained.
Poincaré: el método, lo inconsciente y el caso Dreyfus
Directory of Open Access Journals (Sweden)
Miquel Escudero
2013-06-01
Full Text Available The last man who had an universal knowledge of mathematics and its applications died just a hundred years ago. He always said that mathematics should be encouraged for themselves, and its first aim was to enjoy them in the same way that painting and music allow us to. He did never pretend to be only a specialist, his way of working was to choose the ‘interesting’ facts. On the other hand, maybe we could find serendipity. It is worthwhile to know how to implement the unconscious machine, the unconscious ego beside the conscious ego. In the famous a aire Dreyfus, Poincare was asked for advise and he wrote a dossier about the graphological system that had been erroneously used.
Analytic simulation of the Poincare surface of sections for the diamagnetic Kepler problem
International Nuclear Information System (INIS)
Hasegawa, H.; Harada, A.; Okazaki, Y.
1984-01-01
The Poincare surface-of-section analysis which the authors previously reported on the diamagnetic Kepler problem (classical hydrogen atom in a uniform magnetic field) in a transition region from regular to chaotic motions is simulated by an analytic means, by taking intersections of the energy integral and the approximate integral Λ of Solovev to obtain sections of the two separate regions of the motion that exist in the limit of a weak magnetic field (B → 0). The origin of the unique hyperbolic point and the separatrix around which the onset of chaos takes place are thus identified. The invariant tori arising near the full chaos are shown to be simulated by this method but with modified parameter values in the expression Λ. (author)
Analytic simulation of the Poincare surface of sections for the diamagnetic Kepler problem
Energy Technology Data Exchange (ETDEWEB)
Hasegawa, H; Harada, A; Okazaki, Y [Kyoto Univ. (Japan). Dept. of Physics
1984-11-11
The Poincare surface-of-section analysis which the authors previously reported on the diamagnetic Kepler problem (classical hydrogen atom in a uniform magnetic field) in a transition region from regular to chaotic motions is simulated by an analytic means, by taking intersections of the energy integral and the approximate integral ..lambda.. of Solovev to obtain sections of the two separate regions of the motion that exist in the limit of a weak magnetic field (B ..-->.. 0). The origin of the unique hyperbolic point and the separatrix around which the onset of chaos takes place are thus identified. The invariant tori arising near the full chaos are shown to be simulated by this method but with modified parameter values in the expression ..lambda...
Flattening of the resonance spectrum of hadrons from κ-deformed Poincare algebra
International Nuclear Information System (INIS)
Dey, J.; Ferreira, P.L.; Tomio, L.; Choudhury, R.R.
1994-02-01
It was recently defined by Lukierski a κ-deformed Poincare algebra which is characterized by having the energy-momentum and angular momentum sub-algebras not deformed. Further Biedenharn showed that on gauging the κ-deformed electron with the electromagnetic field, one can set a limit on the allowed value of the deformation parameter ε ≡ 1/κ < 1 fm. It is shown that one gets Regge like angular excitations, J, of the mesons, non-strange and strange baryons, with a value of ε ∼ 0.082 fm and predict a flattening with J of the corresponding trajectories. The Regge fit improves on including deformation, particularly for the baryon spectrum. (author)
On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature
Hu, Xue
2018-06-01
In this paper, we discuss the mass aspect tensor and the rigidity of an asymptotically Poincaré-Einstein (APE) 4-manifold with harmonic curvature. We prove that the trace-free part of the mass aspect tensor of an APE 4-manifold with harmonic curvature and normalized Einstein conformal infinity is zero. As to the rigidity, we first show that a complete noncompact Riemannian 4-manifold with harmonic curvature and positive Yamabe constant as well as a L2-pinching condition is Einstein. As an application, we then obtain that an APE 4-manifold with harmonic curvature and positive Yamabe constant is isometric to the hyperbolic space provided that the L2-norm of the traceless Ricci tensor or the Weyl tensor is small enough and the conformal infinity is a standard round 3-sphere.
Super-Poincare covariant canonical formulation of superparticles and Green-Schwarz superstrings
International Nuclear Information System (INIS)
Nissimov, E.R.; Pacheva, S.J.
1987-11-01
First, a new unified covariant formulation simultaneously describing both superparticles and spinning particles is proposed. In this formulation both models emerge as different gauge fixings from a more general point-particle model with larger and gauge invariance. The general model possesses covariant and functionally independent first-class constraints only. Next, the above construction is generalized to the case of Green-Schwarz (GS) superstrings. This allows straightforward application of the Batalin-Fradkin-Vilkovisky (BFV) Becchi-Rouet-Stora-Tyutin (BRST) formalism for a manifestly super-Poincare covariant canonical quantization. The corresponding BRST charge turns out to be remarkably simple and is of rank one. It is used to construct a covariant BFV Hamiltonian for the GS superstring exhibiting explicit Parisi-Sourlas OSp(1,1/2) symmetry. (author). 21 refs
International Nuclear Information System (INIS)
Edelen, D.G.B.
1986-01-01
Homogeneous scaling of the group space of the Poincare group, P 10 , is shown to induce scalings of all geometric quantities associated with the local action of P 10 . The field equations for both the translation and the Lorentz rotation compensating fields reduce to O(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8πGc -4 . Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to break P 10 -gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system of P 10 -gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincare gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable
Superconformal quantum field theories in string. Gauge theory dualities
Energy Technology Data Exchange (ETDEWEB)
Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Superconformal quantum field theories in string. Gauge theory dualities
International Nuclear Information System (INIS)
Wiegandt, Konstantin
2012-01-01
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Holographic dark energy from fluid/gravity duality constraint by cosmological observations
Pourhassan, Behnam; Bonilla, Alexander; Faizal, Mir; Abreu, Everton M. C.
2018-06-01
In this paper, we obtain a holographic model of dark energy using the fluid/gravity duality. This model will be dual to a higher dimensional Schwarzschild black hole, and we would use fluid/gravity duality to relate to the parameters of this black hole to such a cosmological model. We will also analyze the thermodynamics of such a solution, and discuss the stability model. Finally, we use cosmological data to constraint the parametric space of this dark energy model. Thus, we will use observational data to perform cosmography for this holographic model based on fluid/gravity duality.
Chief Executive Officer Duality And Financial Performance of Firms In Nigeria
Directory of Open Access Journals (Sweden)
Dominic Ose Erah (B.Sc, M.Sc
2013-07-01
Full Text Available the work is centred on CEO Duality and Financial Performance of Firms in Nigeria. The objective of the study is to find out the relationship between CEO Duality and the Financial Performance of Firm. We adopted the use of secondary data from the Nigerian Stock Exchange Fact book drawn from various industries during the period 2001 – 2010 and the regression analysis with its Best Linear Unbiased Estimate (BLUES was employed to test our hypothesis. The findings of the study revealed that CEO Duality is harmful to the Financial Performance of a firm. The study proffered useful recommendations, which when implemented will help improve financial performance of firms in Nigeria.
On R-Duals and the Duality Principle in Gabor Analysis
DEFF Research Database (Denmark)
Stoeva, Diana T.; Christensen, Ole
2015-01-01
The concept of R-duals of a frame was introduced by Casazza, Kutyniok and Lammers in 2004, with the motivation to obtain a general version of the duality principle in Gabor analysis. For tight Gabor frames and Gabor Riesz bases the three authors were actually able to show that the duality principle...... these classes coincide with the R-duals by Casazza et al., which is desirable in the sense that the motivating case of tight Gabor frames already is well covered by these R-duals. On the other hand, all the introduced types of R-duals generalize the duality principle for larger classes of Gabor frames than just...
The inside–outside duality for inverse scattering problems with near field data
International Nuclear Information System (INIS)
Lechleiter, Armin; Peters, Stefan
2015-01-01
We derive an inside–outside duality for near field scattering data generated by time-harmonic scattering of acoustic point sources from a sound-soft scatterer. This duality in particular rigorously characterizes interior Dirichlet eigenvalues of the scattering object by near field operators for an interval of wave numbers. As a crucial new concept to prove this duality we exploit the numerical ranges of certain modifications of these near field operators. We also show that our theoretical results can be numerically used to approximate interior Dirichlet eigenvalues from multi-frequency near field measurements. (paper)
A Duality Theory for Non-convex Problems in the Calculus of Variations
Bouchitté, Guy; Fragalà, Ilaria
2018-02-01
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).
M5-branes, orientifolds, and S-duality
Energy Technology Data Exchange (ETDEWEB)
Hwang, Yoonseok [Department of Physics and Astronomy & Center for Theoretical Physics,Seoul National University, 1 Gwanak-ro, Seoul (Korea, Republic of); Kim, Joonho [School of Physics, Korea Institute for Advanced Study,85 Hoegiro, Seoul (Korea, Republic of); Kim, Seok [Department of Physics and Astronomy & Center for Theoretical Physics,Seoul National University, 1 Gwanak-ro, Seoul (Korea, Republic of)
2016-12-29
We study the instanton partition functions of 5d maximal super Yang-Mills theories with all classical gauge groups. They are computed from the ADHM quantum mechanics of the D0-D4-O4 systems. Our partition functions respect S-dualities of the circle compactified Yang-Mills theories and various orientifold backgrounds. We also compute and study the S{sup 5} partition functions that correspond to the 6d (2,0) superconformal indices. Our SO(2N) index takes the form of the vacuum character of W{sub D} algebra in a special limit, supporting the W algebra conjecture. We propose new indices for (2,0) theories with outer automorphism twists along the temporal circle, obtained from non-simply-laced SYMs on S{sup 5}.
Duality in Left-Right Symmetric Seesaw Mechanism
International Nuclear Information System (INIS)
Akhmedov, E.Kh.; Frigerio, M.
2006-01-01
We consider type I+II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m ν and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution f, there is a dual solution f-circumflex=m ν /v L -f, where v L is the vacuum expectation value of the triplet Higgs boson. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2 n . We develop an exact analytic method of solving the seesaw nonlinear matrix equation for f
Two-field Born–Infeld with diverse dualities
Directory of Open Access Journals (Sweden)
S. Ferrara
2016-11-01
Full Text Available We elaborate on how to build, in a systematic fashion, two-field Abelian extensions of the Born–Infeld Lagrangian. These models realize the non-trivial duality groups that are allowed in this case, namely U(2, SU(2 and U(1×U(1. For each class, we also construct an explicit example. They all involve an overall square root and reduce to the Born–Infeld model if the two fields are identified, but differ in quartic and higher interactions. The U(1×U(1 and SU(2 examples recover some recent results obtained with different techniques, and we show that the U(1×U(1 model admits an N=1 supersymmetric completion. The U(2 example includes some unusual terms that are not analytic at the origin of field space.
Eisenstein series for infinite-dimensional U-duality groups
Fleig, Philipp; Kleinschmidt, Axel
2012-06-01
We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.
De Sitter space in gauge/gravity duality
Directory of Open Access Journals (Sweden)
Lilia Anguelova
2015-10-01
Full Text Available We investigate gauge/gravity duality for gauge theories in de Sitter space. More precisely, we study a five-dimensional consistent truncation of type IIB supergravity, which encompasses a wide variety of gravity duals of strongly coupled gauge theories, including the Maldacena–Nunez solution and its walking deformations. We find several solutions of the 5d theory with dS4 spacetime and nontrivial profiles for (some of the scalars along the fifth (radial direction. In the process, we prove that one of the equations of motion becomes dependent on the others, for nontrivial warp factor. This dependence reduces the number of field equations and, thus, turns out to be crucial for the existence of solutions with (AdS4 spacetime. Finally, we comment on the implications of our dS4 solutions for building gravity duals of Glueball Inflation.
Superconductivity from gauge/gravity duality with flavor
International Nuclear Information System (INIS)
Ammon, Martin; Erdmenger, Johanna; Kaminski, Matthias; Kerner, Patrick
2009-01-01
We consider thermal strongly-coupled N=2 SYM theory with fundamental matter at finite isospin chemical potential. Using gauge/gravity duality, i.e. a probe of two flavor D7-branes embedded in the AdS black hole background, we find a critical temperature at which the system undergoes a second order phase transition. The critical exponent of this transition is one half and coincides with the result from mean field theory. In the thermodynamically favored phase, a flavor current acquires a vev and breaks an Abelian symmetry spontaneously. This new phase shows signatures known from superconductivity, such as an infinite dc conductivity and a gap in the frequency-dependent conductivity. The gravity setup allows for an explicit identification of the degrees of freedom in the dual field theory, as well as for a dual string picture of the condensation process.
Duality and braiding in twisted quantum field theory
International Nuclear Information System (INIS)
Riccardi, Mauro; Szabo, Richard J.
2008-01-01
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality
Coupling a QFT to a TQFT and duality
International Nuclear Information System (INIS)
Kapustin, Anton; Seiberg, Nathan
2014-01-01
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On ℝ d the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when we compactify ℝ d , and they are crucial in the context of electric-magnetic duality. We explore several examples including Dijkgraaf-Witten theories and their generalizations both in the continuum and on the lattice. When we couple them to ordinary quantum field theories the topological degrees of freedom allow us to express certain characteristic classes of gauge fields as integrals of local densities, thus simplifying the analysis of their physical consequences
Inflationary susceptibilities, duality and large-scale magnetic fields generation
Giovannini, Massimo
2013-01-01
We investigate what can be said about the interaction of scalar fields with Abelian gauge fields during a quasi-de Sitter phase of expansion and under the assumption that the electric and the magnetic susceptibilities do not coincide. The duality symmetry, transforming the magnetic susceptibility into the inverse of the electric susceptibility, exchanges the magnetic and electric power spectra. The mismatch between the two susceptibilities determines an effective refractive index affecting the evolution of the canonical fields. The constraints imposed by the duration of the inflationary phase and by the magnetogenesis requirements pin down the rate of variation of the susceptibilities that is consistent with the observations of the magnetic field strength over astrophysical and cosmological scales but avoids back-reaction problems. The parameter space of this magnetogenesis scenario is wider than in the case when the susceptibilities are equal, as it happens when the inflaton or some other spectator field is ...
Origin of Money: Dynamic Duality Between Necessity and Unnecessity
Tauchi, Yuka; Kamiura, Moto; Haruna, Taichi; Gunji, Yukio-Pegio
2008-10-01
We propose a mathematical model of economic agents to study origin of money. This multi-agent model is based on commodity theory of money, which says that a commodity used as money emerges from barter transaction. Each agent has a different value system which is given by a Heyting algebra, and exchanges one's commodities based on the value system. In each value system, necessity and unnecessity of commodities are expressed by some elements and their compliments on a Heyting Algebra. Moreover, the concept of the compliment is extended. Consequently, the duality of the necessity-unnecessity is weakened, and the exchanges of the commodities are promoted. The commodities which keeps being exchanged for a long time can correspond to money.
Fundamentals of convex analysis duality, separation, representation, and resolution
Panik, Michael J
1993-01-01
Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided. Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and comple...
Proving AGT conjecture as HS duality: Extension to five dimensions
International Nuclear Information System (INIS)
Mironov, A.; Morozov, A.; Shakirov, Sh.; Smirnov, A.
2012-01-01
We extend the proof from Mironov et al. (2011) , which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out to be straightforward: it is enough to substitute all relevant numbers by q-numbers in all the formulas, Dotsenko-Fateev integrals by the Jackson sums and the Jack polynomials by the MacDonald ones. The problem with extra poles in individual Nekrasov functions continues to exist, therefore, such a proof works only for β=1, i.e. for q=t in MacDonald's notation. For β≠1 the conformal blocks are related in this way to a non-Nekrasov decomposition of the LMNS partition function into a double sum over Young diagrams.
Brane configurations and 4D field theory dualities
International Nuclear Information System (INIS)
Brandhuber, A.; Sonnenschein, J.; Yankielowicz, S.
1997-01-01
We study brane configurations which correspond to field theories in four dimension with N=2 and N=1 supersymmetry. In particular we discuss brane motions that translate to Seiberg's duality in N=1 models recently studied by Elitzur, Giveon and Kutasov. We investigate, using the brane picture, the moduli spaces of the dual theories. Deformations of these models like mass terms and vacuum expectation values of scalar fields can be identified with positions of branes. The map of these deformations between the electric and dual magnetic theories is clarified. The models we study reproduce known field theory results and we provide an example of new dual pairs with N=1 supersymmetry. Possible relations between brane configurations and non-supersymmetric field theories are discussed. (orig.)
N=1 Mirror Symmetry and Open/Closed String Duality
Mayr, Peter
2002-01-01
We show that the exact N=1 superpotential of a class of 4d string compactifications is computed by the closed topological string compactified to two dimensions. A relation to the open topological string is used to define a special geometry for N=1 mirror symmetry. Flat coordinates, an N=1 mirror map for chiral multiplets and the exact instanton corrected superpotential are obtained from the periods of a system of differential equations. The result points to a new class of open/closed string dualities which map individual string world-sheets with boundary to ones without. It predicts an mathematically unexpected coincidence of the closed string Gromov-Witten invariants of one Calabi-Yau geometry with the open string invariants of the dual Calabi-Yau.
On hyperbolic U4 manifolds with local duality
International Nuclear Information System (INIS)
Wallner, R.P.
1982-01-01
We use the decomposition of the Riemann/Cartan curvature 2-forms Ωsup(ij) in terms of their irreducible parts under the Lorentz group to examine the irreducible content of self- and anti-self double dual curvature forms Ωsup(+-ij) and their further refinements involving left and right duals. In the case of local duality (i.e. Ωsup(ij) = Ωsup(+-ij) locally), some consequences to curvature and torsion are easily derived in this way. As Riemann/Cartan space-times (U 4 -space-times) are subject to generalized gravity theories, some (vacuum) field equations proposed there are also taken into considerations. As an application to the various decompositions of curvature and torsion we point out their utility in the search of exact solutions of U 4 -field equations. To simplify notations and calculations, the calculus of exterior forms is used throughout. (Author)
Deeply virtual Compton scattering from gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Costa, Miguel S.; Djuric, Marko [University of Porto (Portugal)
2013-04-15
We use gauge/gravity duality to study deeply virtual Compton scattering (DVCS) in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by the exchange of the pomeron. At strong coupling, the pomeron is described as the graviton Regge trajectory in AdS space, with a hard wall to mimic confinement effects. This model agrees with HERA data in a large kinematical range. The behavior of the DVCS cross section for very high energies, inside saturation, can be explained by a simple AdS black disk model. In a restricted kinematical window, this model agrees with HERA data as well.
Deeply virtual Compton scattering from gauge/gravity duality
International Nuclear Information System (INIS)
Costa, Miguel S.; Djurić, Marko
2013-01-01
We use gauge/gravity duality to study deeply virtual Compton scattering (DVCS) in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by the exchange of the pomeron. At strong coupling, the pomeron is described as the graviton Regge trajectory in AdS space, with a hard wall to mimic confinement effects. This model agrees with HERA data in a large kinematical range. The behavior of the DVCS cross section for very high energies, inside saturation, can be explained by a simple AdS black disk model. In a restricted kinematical window, this model agrees with HERA data as well.
Duality reconstruction algorithm for use in electrical impedance tomography
International Nuclear Information System (INIS)
Abdullah, M.Z.; Dickin, F.J.
1996-01-01
A duality reconstruction algorithm for solving the inverse problem in electrical impedance tomography (EIT) is described. In this method, an algorithm based on the Geselowitz compensation (GC) theorem is used first to reconstruct an approximate version of the image. It is then fed as a first guessed data to the modified Newton-Raphson (MNR) algorithm which iteratively correct the image until a final acceptable solution is reached. The implementation of the GC and MNR based algorithms using the finite element method will be discussed. Reconstructed images produced by the algorithm will also be presented. Consideration is also given to the most computationally intensive aspects of the algorithm, namely the inversion of the large and sparse matrices. The methods taken to approximately compute the inverse ot those matrices will be outlined. (author)
Approaches to emergent spacetime in gauge/gravity duality
Sully, James Kenneth
2013-08-01
In this thesis we explore approaches to emergent local spacetime in gauge/gravity duality. We first conjecture that every CFT with a large-N type limit and a parametrically large gap in the spectrum of single-trace operators has a local bulk dual. We defend this conjecture by counting consistent solutions to the four-point function in simple scalar models and matching to the number of local interaction terms in the bulk. Next, we proceed to explicitly construct local bulk operators using smearing functions. We argue that this construction allows one to probe inside black hole horizons for only short times. We then suggest that the failure to construct bulk operators inside a black hole at late times is indicative of a break-down of local effective field theory at the black hole horizon. We argue that the postulates of black hole complementarity are inconsistent and cannot be realized within gauge/gravity duality. We argue that the most conservative solution is a firewall at the black hole horizon and we critically explore alternative resolutions. We then examine the CGHS model of two-dimensional gravity to look for dynamical formation of firewalls. We find that the CGHS model does not exhibit firewalls, but rather contains long-lived remnants. We argue that, while this is consistent for the CGHS model, it cannot be so in higher-dimensional theories of gravity. Lastly, we turn to F-theory, and detail local and global obstructions to writing elliptic fibrations in Tate form. We determine more general possible forms.
Vosmaer, J.
2010-01-01
In this dissertation we discuss three subjects: canonical extensions of lattice-based algebras, Stone duality for distributive lattices with operators, and a generalization of the point-free Vietoris powerlocale construction.
Self-duality in Maxwell-Chern-Simons theories with non minimal coupling with matter field
Chandelier, F; Masson, T; Wallet, J C
2000-01-01
We consider a general class of non-local MCS models whose usual minimal coupling to a conserved current is supplemented with a (non-minimal) magnetic Pauli-type coupling. We find that the considered models exhibit a self-duality whenever the magnetic coupling constant reaches a special value: the partition function is invariant under a set of transformations among the parameter space (the duality transformations) while the original action and its dual counterpart have the same form. The duality transformations have a structure similar to the one underlying self-duality of the (2+1)-dimensional Z sub n - Abelian Higgs model with Chern-Simons and bare mass term.
Nuclearity, split-property and duality for the Klein-Gordon field in curved spacetime
International Nuclear Information System (INIS)
Verch, R.
1993-05-01
Nuclearity, Split-Property and Duality are establihed for the nets of von Neumann algebras associated with the representations of distinguished states of the massive Klein-Gordon field propagating in particular classes of curved spacetimes. (orig.)
String duality transformations in f(R) gravity from Noether symmetry approach
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore [Dipartimento di Fisica, Università di Napoli ' ' Federico II' ' , Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli (Italy); Gionti, Gabriele S.J. [Specola Vaticana, Vatican City, V-00120, Vatican City State (Vatican City State, Holy See); Vernieri, Daniele, E-mail: capozziello@na.inf.it, E-mail: ggionti@as.arizona.edu, E-mail: vernieri@iap.fr [Sorbonne Universités, UPMC Univ Paris 6 et CNRS, UMR 7095, Institut d' Astrophysique de Paris, GReCO, 98bis Bd Arago, 75014 Paris (France)
2016-01-01
We select f(R) gravity models that undergo scale factor duality transformations. As a starting point, we consider the tree-level effective gravitational action of bosonic String Theory coupled with the dilaton field. This theory inherits the Busher's duality of its parent String Theory. Using conformal transformations of the metric tensor, it is possible to map the tree-level dilaton-graviton string effective action into f(R) gravity, relating the dilaton field to the Ricci scalar curvature. Furthermore, the duality can be framed under the standard of Noether symmetries and exact cosmological solutions are derived. Using suitable changes of variables, the string-based f(R) Lagrangians are shown in cases where the duality transformation becomes a parity inversion.
String duality transformations in f(R) gravity from Noether symmetry approach
International Nuclear Information System (INIS)
Capozziello, Salvatore; Gionti, Gabriele S.J.; Vernieri, Daniele
2016-01-01
We select f(R) gravity models that undergo scale factor duality transformations. As a starting point, we consider the tree-level effective gravitational action of bosonic String Theory coupled with the dilaton field. This theory inherits the Busher's duality of its parent String Theory. Using conformal transformations of the metric tensor, it is possible to map the tree-level dilaton-graviton string effective action into f(R) gravity, relating the dilaton field to the Ricci scalar curvature. Furthermore, the duality can be framed under the standard of Noether symmetries and exact cosmological solutions are derived. Using suitable changes of variables, the string-based f(R) Lagrangians are shown in cases where the duality transformation becomes a parity inversion
Tunneling time distribution by means of Nelson's quantum mechanics and wave-particle duality
International Nuclear Information System (INIS)
Hara, Koh'ichiro; Ohba, Ichiro
2003-01-01
We calculate a tunneling time distribution by means of Nelson's quantum mechanics and investigate its statistical properties. The relationship between the average and deviation of tunneling time suggests the existence of 'wave-particle duality' in the tunneling phenomena
Duality for Multitime Multiobjective Ratio Variational Problems on First Order Jet Bundle
Directory of Open Access Journals (Sweden)
Mihai Postolache
2012-01-01
Full Text Available We consider a new class of multitime multiobjective variational problems of minimizing a vector of quotients of functionals of curvilinear integral type. Based on the efficiency conditions for multitime multiobjective ratio variational problems, we introduce a ratio dual of generalized Mond-Weir-Zalmai type, and under some assumptions of generalized convexity, duality theorems are stated. We prove our weak duality theorem for efficient solutions, showing that the value of the objective function of the primal cannot exceed the value of the dual. Direct and converse duality theorems are stated, underlying the connections between the values of the objective functions of the primal and dual programs. As special cases, duality results of Mond-Weir-Zalmai type for a multitime multiobjective variational problem are obtained. This work further develops our studies in (Pitea and Postolache (2011.
Introduction of the chronon in the theory of electron and the wave-particle duality
International Nuclear Information System (INIS)
Caldirola, P.
1984-01-01
The author summarizes the more important results obtained in the electron theory based on the chronon and stresses some peculiarities of the wave-particle duality directly connected with the introduction of the chronon. (Auth.)
Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions
Directory of Open Access Journals (Sweden)
J. Zhang
2010-01-01
Full Text Available We apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program. Our results extend and improve the corresponding results in the literature.
CEO Duality e performance. Il ruolo del controllo familiare in periodi di crisi
Tenuta, Paolo; Cambrea, Domenico Rocco; Iusi, Giorgio
2016-01-01
There are several studies in the literature which analyse the effect of CEO duality on corporate performance, reaching mixed conclusions. Using agency theory, stewardship theory and socio-emotional wealth theory perspectives, we examine the relationship between CEO duality and the performance of Italian publicly listed companies over the period 2003–2013. In addition, considering the presence of conflicting empirical evidence, which could lead to a positive effect rather than a negative one, ...
Marginal and non-commutative deformations via non-abelian T-duality
Energy Technology Data Exchange (ETDEWEB)
Hoare, Ben [Institut für Theoretische Physik, ETH Zürich,Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland); Thompson, Daniel C. [Theoretische Natuurkunde, Vrije Universiteit Brussel & The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)
2017-02-10
In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-β-deformations and non-commutative deformations of N=4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
S- and T-self-dualities in dilatonic f(R) theories
Energy Technology Data Exchange (ETDEWEB)
Rador, Tonguc [Bogazici University, Department of Physics, Istanbul (Turkey); Izmir Institute of Technology, Department of Physics, Izmir (Turkey)
2017-12-15
We search for theories, in general spacetime dimensions, that would incorporate a dilaton and higher powers of the scalar Ricci curvature such that they have exact S- or T-self-dualities. The theories we find are free of Ostrogradsky instabilities. We also show that within the framework we are confining ourselves, a theory of the form mentioned above cannot have both T- and S-dualities except for the case where the action is linear in the scalar curvature. (orig.)
Challenges in assessing college students' conception of duality: the case of infinity
Babarinsa-Ochiedike, Grace Olutayo
Interpreting students' views of infinity posits a challenge for researchers due to the dynamic nature of the conception. There is diversity and variation among students' process-object perceptions. The fluctuations between students' views however reveal an undeveloped duality conception. This study examined college students' conception of duality in understanding and representing infinity with the intent to design strategies that could guide researchers in categorizing students' views of infinity into different levels. Data for the study were collected from N=238 college students enrolled in Calculus sequence courses (Pre-Calculus, Calculus I through Calculus III) at one of the southwestern universities in the U.S. using self-report questionnaires and semi-structured individual task-based interviews. Data was triangulated using multiple measures analyzed by three independent experts using self-designed coding sheets to assess students' externalization of the duality conception of infinity. Results of this study reveal that college students' experiences in traditional Calculus sequence courses are not supportive of the development of duality conception. On the contrary, it strengthens the singularity perspective on fundamental ideas of mathematics such as infinity. The study also found that coding and assessing college students' conception of duality is a challenging and complex process due to the dynamic nature of the conception that is task-dependent and context-dependent. Practical significance of the study is that it helps to recognize misconceptions and starts addressing them so students will have a more comprehensive view of fundamental mathematical ideas as they progress through the Calculus coursework sequence. The developed duality concept development framework called Action-Process-Object-Duality (APOD) adapted from the APOS theory could guide educators and researchers as they engage in assessing students' conception of duality. The results of this study
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Dual formulation of covariant nonlinear duality-symmetric action of kappa-symmetric D3-brane
Vanichchapongjaroen, Pichet
2018-02-01
We study the construction of covariant nonlinear duality-symmetric actions in dual formulation. Essentially, the construction is the PST-covariantisation and nonlinearisation of Zwanziger action. The covariantisation made use of three auxiliary scalar fields. Apart from these, the construction proceed in a similar way to that of the standard formulation. For example, the theories can be extended to include interactions with external fields, and that the theories possess two local PST symmetries. We then explicitly demonstrate the construction of covariant nonlinear duality-symmetric actions in dual formulation of DBI theory, and D3-brane. For each of these theories, the twisted selfduality condition obtained from duality-symmetric actions are explicitly shown to match with the duality relation between field strength and its dual from the one-potential actions. Their on-shell actions between the duality-symmetric and the one-potential versions are also shown to match. We also explicitly prove kappa-symmetry of the covariant nonlinear duality-symmetric D3-brane action in dual formulation.
The quantum poisson-Lie T-duality and mirror symmetry
International Nuclear Information System (INIS)
Parkhomenko, S.E.
1999-01-01
Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also
Carmona, J. M.; Cortés, J. L.; Relancio, J. J.
2018-03-01
A new proposal for the notion of spacetime in a relativistic generalization of special relativity based on a modification of the composition law of momenta is presented. Locality of interactions is the principle which defines the spacetime structure for a system of particles. The formulation based on κ -Poincaré Hopf algebra is shown to be contained in this framework as a particular example.
Chaidas, Konstantinos; Tsaoussoglou, Marina; Theodorou, Emmanouel; Lianou, Loukia; Chrousos, George; Kaditis, Athanasios G
2014-08-01
Obstructive sleep apnea (OSA) in childhood is accompanied by sympathetic overflow unopposed by the parasympathetic tone. Complex methods like power spectral analysis of heart rate variability have been applied to study this imbalance. In this report, width of Poincaré scattergram of the R-R interval (parasympathetic tone) and morning urine norepinephrine concentration (sympathetic activity) were used to assess autonomic imbalance. Poincaré plot was obtained from the electrocardiographic channel of nocturnal polysomnography and its width was measured, and norepinephrine-to-creatinine concentration ratio was calculated in morning urine specimen. Twenty children with obstructive sleep apnea and moderate-to-severe nocturnal hypoxemia (oxygen saturation of hemoglobin [SpO(2)] nadir plot width (318.7 ± 139.3 ms) and higher ln-transformed urine norepinephrine-to-creatinine ratio (4.5 ± 0.6) than control subjects (484.2 ± 104.4 ms and 3.8 ± 0.4, respectively; P plot width (P = 0.02). Subjects with obstructive sleep apnea and moderate-to-severe nocturnal hypoxemia have enhanced sympathetic activity and reduced parasympathetic drive. Poincaré plot width and urine norepinephrine levels are simple measures of autonomic imbalance in pediatric obstructive sleep apnea. Copyright © 2014 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Morillo, Daniel S; Rojas, Juan L; Crespo, Luis F; León, Antonio; Gross, Nicole
2009-01-01
The analysis of oxygen desaturations is a basic variable in polysomnographic studies for the diagnosis of sleep apnea. Several algorithms operating in the time domain already exist for sleep apnea detection via pulse oximetry, but in a disadvantageous way—they achieve either a high sensitivity or a high specificity. The aim of this study was to assess whether an alternative analysis of arterial oxygen saturation (SaO 2 ) signals from overnight pulse oximetry could yield essential information on the diagnosis of sleep apnea hypopnea syndrome (SAHS). SaO 2 signals from 117 subjects were analyzed. The population was divided into a learning dataset (70 patients) and a test set (47 patients). The learning set was used for tuning thresholds among the applied Poincaré quantitative descriptors. Results showed that the presence of apnea events in SAHS patients caused an increase in the SD 1 Poincaré parameter. This conclusion was assessed prospectively using the test dataset. 90.9% sensitivity and 84.0% specificity were obtained in the test group. We conclude that Poincaré analysis could be useful in the study of SAHS, contributing to reduce the demand for polysomnographic studies in SAHS screening
International Nuclear Information System (INIS)
Gritli, Hassène; Belghith, Safya
2015-01-01
Highlights: • A numerical calculation method of the Lyapunov exponents in the compass-gait model under OGY control is proposed. • A new linearization method of the impulsive hybrid dynamics around a one-periodic hybrid limit cycle is achieved. • We develop a simple analytical expression of a controlled hybrid Poincaré map. • A dimension reduction of the hybrid Poincaré map is realized. • We describe the numerical computation procedure of the Lyapunov exponents via the designed hybrid Poincaré map. - Abstract: This paper aims at providing a numerical calculation method of the spectrum of Lyapunov exponents in a four-dimensional impulsive hybrid nonlinear dynamics of a passive compass-gait model under the OGY control approach by means of a controlled hybrid Poincaré map. We present a four-dimensional simplified analytical expression of such hybrid map obtained by linearizing the uncontrolled impulsive hybrid nonlinear dynamics around a desired one-periodic passive hybrid limit cycle. In order to compute the spectrum of Lyapunov exponents, a dimension reduction of the controlled hybrid Poincaré map is realized. The numerical calculation of the spectrum of Lyapunov exponents using the reduced-dimension controlled hybrid Poincaré map is given in detail. In order to show the effectiveness of the developed method, the spectrum of Lyapunov exponents is calculated as the slope (bifurcation) parameter varies and hence used to predict the walking dynamics behavior of the compass-gait model under the OGY control.