Institute of Scientific and Technical Information of China (English)
GUO TieXin; CHEN XinXiang
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules.First,the complicated stratification structure of a module over the algebra L(μ,K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory,thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules.Then,we give the representation theorem of weakly continuous canonical module homomorphisms,the theorem of existence of random Mackey structure,and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably difierent from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
Energy Technology Data Exchange (ETDEWEB)
Green, Daniel; /SLAC /Stanford U., Phys. Dept.; Lawrence, Albion; /Brandeis U.; McGreevy, John; /MIT, LNS; Morrison, David R.; /Duke U., CGTP /UC, Santa Barbara; Silverstein,; /SLAC /Stanford U., Phys. Dept.
2007-05-18
We show that string theory on a compact negatively curved manifold, preserving a U(1)b1 winding symmetry, grows at least b1 new effective dimensions as the space shrinks. The winding currents yield a ''D-dual'' description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b{sub 1}-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article,we make a review on the development of a newly proposed quantum computer,duality computer,or the duality quantum computer and the duality mode of quantum computers.The duality computer is based on the particle-wave duality principle of quantum mechanics.Compared to an ordinary quantum computer,the duality quantum computer is a quantum computer on the move and passing through a multi-slit.It offers more computing operations than is possible with an ordinary quantum computer.The most two distinct operations are:the quantum division operation and the quantum combiner operation.The division operation divides the wave function of a quantum computer into many attenuated,and identical parts.The combiner operation combines the wave functions in different parts into a single part.The duality mode is a way in which a quantum computer with some extra qubit resource simulates a duality computer.The main structure of duality quantum computer and duality mode,the duality mode,their mathematical description and algorithm designs are reviewed.
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
From Koszul duality to Poincaré duality
Indian Academy of Sciences (India)
Michel Dubois-Violette
2012-06-01
We discuss the notion of Poincaré duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincaré duality is pointed out for the existence of twisted potentials associated to Koszul algebras as well as for the extraction of a good generalization of Lie algebras among the quadratic-linear algebras.
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.
Duality Computing in Quantum Computers
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; LIU Yang
2008-01-01
In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.
Holographic duality and applications
Bea, Yago
2016-01-01
In this thesis we review some results on the generalization of the gauge/gravity duality to new cases by using T-duality and by including fundamental matter, finding applications to condensed matter physics. First, we construct new supersymmetric solutions of type IIA/B and eleven-dimensional supergravity by using non-abelian T-duality. Second, we construct a type IIA supergravity solution with D6-brane sources, dual to an unquenched massive flavored version of the ABJM theory. Third, we study a probe D6-brane with worldvolume gauge fields in the ABJM background, obtaining the dual description of a quantum Hall system. Moreover, we consider a system of a probe D6-brane in the ABJM background and study quantum phase transitions of its dual theory.
Gravitation and Duality Symmetry
D'Andrade, V C; Pereira, J G
2005-01-01
By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation does not present duality symmetry, there is a particular theory in which this symmetry is present. This theory is a self dual (or anti-self dual) teleparallel gravity in which, owing to the fact that it does not contribute to the gravitational interaction of fermions, the purely tensor part of torsion is assumed to vanish. The corresponding fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory will probably be much more amenable to renormalization than teleparallel gravity or general relativity. Although obtained in the context of teleparallel gravity, these results must also be true for general relativity.
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.)
Destructive Interference of Dualities
Wotzasek, C
1998-01-01
We show that the fusion of two (diffeomorphism) invariant self-dual scalars described by right and left chiral-WZW actions, produces a Hull non-mover field. After fusion, right and left moving modes disappear from the spectrum, displaying in this way the phenomenon of (destructive) quantum interference of dualities.
Duality group actions on fermions
Pantev, Tony; Sharpe, Eric
2016-11-01
In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL(2 , ℤ) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by ℤ2, to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and (briefly) four-dimensional N = 4 super Yang-Mills, and in each case, propose that the full duality group is a nontrivial ℤ2 extension of the duality group acting on bosonic degrees of freedom, to more accurately describe possible actions on fermions. We also walk through U-duality groups for toroidal compactifications to nine, eight, and seven dimensions, which enables us to perform cross-consistency tests of these proposals.
Duality group actions on fermions
Pantev, T
2016-01-01
In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL(2,Z) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by Z_2, to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and (briefly) four-dimensional N=4 super Yang-Mills, and in each case, propose that the full duality group is a nontrivial Z_2 extension of the duality group acting on bosonic degrees of freedom, to more accurately describe possible actions on fermions. We also walk through U-duality groups for toroidal compactifications to nine, eight, and seven dimensions, which enables us to perform cross-consistency tests of these proposals.
Quantitative wave-particle duality
Qureshi, Tabish
2016-07-01
The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is here described not just as two extreme cases of wave and particle characteristics, but in terms of quantitative measures of these characteristics, known to follow a duality relation. A very simple and intuitive derivation of a closely related duality relation is presented, which should be understandable to the introductory student.
Subdifferentials with respect to dualities
Energy Technology Data Exchange (ETDEWEB)
Martinez-Legaz, J.E.; Singer, I.
1994-12-31
Let X and W be two sets. We introduce and study the subdifferential of an extended real valued function defined on X at a point, with respect to a duality from the set of functions on X into the set of functions on W (by a duality we mean a mapping transforming infima into suprema). We also consider some particular cases as, e.g., when the duality is a (Fenchel-Moreau) conjugation.
Comparing dualities and gauge symmetries
De Haro, Sebastian; Teh, Nicholas; Butterfield, Jeremy N.
2017-08-01
We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4-6) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory.
Group dualities, T-dualities, and twisted K-theory
Mathai, Varghese
2016-01-01
This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K-groups, but that these K-groups are trivial except in the simplest case of SU(2) and SO(3). Along the way we compute explicitly the map on $H^3$ induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K-theory using the Segal spectral sequence, giving simpler computations of certain twisted K-theory groups of compact Lie groups relevant for D-brane charges in WZW theories and rank-level dualities. Finally we study a duality for orientifolds based on complex Lie groups with an involution.
Comparing Dualities and Gauge Symmetries
De Haro, Sebastian; Butterfield, Jeremy N
2016-01-01
We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4, 5 and 6) is much more specific. We give a result about gauge/gravity duality that shows its rela...
Hewson, S F
1997-01-01
We discuss the application of T-duality to massive supersymmetric sigma models. In particular (1,1) supersymmetric models with off-shell central charges reveal an interesting structure. The T-duality transformations of the BPS states of these theories are also discussed and an explicit example of Q-kinks is given.
Tinkertoys for Gaiotto Duality
Chacaltana, Oscar
2010-01-01
We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N=5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N=2 SCFTs.
Electromagnetic Duality and Entanglement Anomalies
Donnelly, William; Wall, Aron
2016-01-01
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of freedom rearranged in a nonlocal fashion. We study this phenomenon in the context of the electromagnetic duality of abelian $p$-forms. A careful calculation of the duality anomaly on an arbitrary $D$-dimensional manifold shows that the effective actions agree exactly in odd $D$, while in even $D$ they differ by a term proportional to the Euler number. Despite this anomaly, the trace of the stress tensor agrees between the dual theories. We also compute the change in the vacuum entanglement entropy under duality, relating this entanglement anomaly to the duality of an "edge mode" theory in two fewer dimensions. Previous work on this subject has led to conflicting results; we explain and resolve these discrepancies.
Brane actions and string dualities
Eyras, E; Lozano, Y; Ceresole, A; Kounnas, C; Lust, D; Theisen, S
1999-01-01
An effective action for the M9-brane is proposed. We study its relation with other branes via dualities. Among these, we find actions for branes which are not suggested by the central charges of the Type II superalgebras.
Meana, M L; Meana, Marco Laucelli; Peñalba, Jesús Puente
2000-01-01
We use the AdS/SYM correspondence to study the relevant effects ofcompactified dimensions on the D-brane dynamics. We present a detailed pictureof the T-duality transition between branes in type IIA and type IIBsupergravity. An analysis of the renormalization scheme coming from theexpectation values of background fields and the role of Wilson lines in it isgiven. We finally explore finite size effects and T-duality maps on thedescription of Wilson loops by supergravity.
The braneology of 3D dualities
Amariti, Antonio; Klare, Claudius; Orlando, Domenico; Reffert, Susanne
2015-01-01
In this paper we study the reduction of four-dimensional Seiberg duality to three dimensions from a brane perspective. We reproduce the non-perturbative dynamics of the three-dimensional field theory via a T-duality at finite radius and the action of Euclidean D-strings. In this way we also overcome certain issues regarding the brane description of Aharony duality. Moreover we apply our strategy to more general dualities, such as toric duality for M2-branes and dualities with adjoint matter fields.
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
Szyld, Martín
2011-01-01
The purpose of this work is twofold: to expose the existing similarities between the generalizations of the Tannaka and Galois theories, and on the other hand, to develop in detail our own treatment of part of the content of Joyal and Street [1] paper, generalizing from vector spaces to an abstract tensor category. We also develop in detail the proof of the Tannaka equivalence of categories in the case of vector spaces. Saavedra Rivano [2], Deligne and Milne [3] generalize classical Tannaka theory to the context of K-linear tensor (or monoidal) categories. They obtain a lifting-equivalence into a category of \\group representations" for a ?nite-dimensional vector space valued monoidal functor. This lifting theorem is similar to the one of Grothendieck Galois theory [4] for a ?nite sets valued functor. On the other hand, Joyal and Street [1] work on the algebraic side of the duality between algebra and geometry, and also obtain a lifting-equivalence, but now to the category of ?nite-dimensional comodules over a...
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.)
Supersymmetry, Duality And Holonomy
Wen, W
2005-01-01
In this thesis, I study various aspects of solutions to eleven-dimensional supergravity and its descendents. The former is at one corner of the moduli space of M-theory. While it is not clear how to formulate M-theory; it is equally interesting to see how far we can proceed from this low energy window. First of all, various techniques are applied to construct supergravity solutions preserving partial supersymmetry. A seven-dimensional membrane solution in the gauged supergravity is constructed by lifting a self-dual string in six dimensions, and its supersymmetric property is explored in certain detail. Then fractional BPS solutions from Sn × Sn reduction of six and ten-dimensional supergravities are constructed via the method of G-structures. The form of the solutions is totally determined by Laplace equations with specified boundary conditions. Secondly, the concept of duality is realized in two aspects. A certain type of *-theory, obtained from time-like T-dualization of the usual string and M-t...
Projective duality and homogeneous spaces
Tevelev, E A
2006-01-01
Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.
The Duality on Vector Optimization Problems
Institute of Scientific and Technical Information of China (English)
HUANG Long-guang
2012-01-01
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
Duality for cochain DG algebras
Jorgensen, Peter
2010-01-01
This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-commutative aspects. One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology. As an application, it is proved that if the canonical module $A / A^{\\geq 1}$ has a semi-free resolution where the cohomological degree of the generators is bounded above, then the same is t...
Brane Tilings and Specular Duality
Hanany, Amihay
2012-01-01
We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.
Duality in Dynamic Fuzzy Systems
Yoshida, Yuji
1995-01-01
This paper shows the resolvent equation, the maximum principle and the co-balayage theorem for a dynamic fuzzy system. We define a dual system for the dynamic fuzzy system, and gives a duality for Snell's optimal stopping problem by the dual system.
Pursuing Gravitational S-Duality
García-Compéan, H; Ramírez, C
1998-01-01
Recently a strong-weak coupling duality in non-abelian non-supersymmetric theories in four dimensions has been found. An analogous procedure is reviewed, which allows to find the `dual action' to the gauge theory of dynamical gravity constructed by the MacDowell-Mansouri model plus the superposition of a
Dualities in Covering Rough Operations
Institute of Scientific and Technical Information of China (English)
William Zhu
2006-01-01
Rough set theory is a technique of granular computing. In this paper, we study a type of generalized rough sets based on covering. There are several literatures[ 1,40-43 ] exploring covering-based rough sets. Our focus of this paper is on the dualities in rough operations.
Aspects of Duality in Cosmology
J., Gabriele Gionti S
2016-01-01
In the first part of this article, given the intent to stay at a popular level, it has been introduced and explained briefly basic concepts of Einstein's General Relativity, Dark Matter, Dark Energy, String Theory, Quantum Gravity and Extended Theories of Gravity. The core of this research is based on selecting a class of f(R) theories of gravity, which exhibits scale factor duality transformations. The starting point of this theory is the effective theory of gravity derived from Bosonic String Theory, which is called tree level effective theory of gravity. It is shown that this theory can be cast in a class of f(R) theories of gravity (modified theories of Einstein's General Relativity). It is imposed that FLRW metric be solution of this class of $f(R)$ theories, and, using the Noether symmetry approach, it is found that the cosmological model has scale factor duality like the Pre-Big Bang cosmology of Gasperini and Veneziano.
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.
Gauge Theory and Langlands Duality
Frenkel, Edward
2009-01-01
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves on moduli spaces of (flat) bundles on algebraic curves. Three years ago, in a groundbreaking advance, Kapustin and Witten have linked the geometric Langlands correspondence to the S-duality of 4D supersymmetric gauge theories. This and subsequent works have already led to striking new insights into the geometric Langlands Program, which in particular involve the Homological Mirror Symmetry of the Hitchin moduli spaces of Higgs bundles on algebraic curves associated to two Langlands dual Lie groups.
Hewson, S F
1996-01-01
We investigate non-abelian gaugings of WZNW models. When the gauged group is semisimple we are able to present exact formulae for the dual conformal field theory, for all values of the level k. The results are then applied to non-abelian target space duality in string theory, showing that the standard formulae are quantum mechanically well defined in the low energy limit if the gauged group is semisimple.
Awodey, Steve
2010-01-01
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this case $2$. In the present work, we generalize the entire arrangement from propositional to first-order logic. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed first in the form of a contravariant adjunction, is established by homming into a common dualizing object, now $\\Sets$, regarded once as a boolean category, and...
Classical Geometry and Target Space Duality
1995-01-01
This is the written version of lectures presented at Cargese 95. A new formulation for a ``restricted'' type of target space duality in classical two dimensional nonlinear sigma models is presented. The main idea is summarized by the analogy: euclidean geometry is to riemannian geometry as toroidal target space duality is to ``restricted'' target space duality. The target space is not required to possess symmetry. These lectures only discuss the local theory. The restricted target space duali...
Duality Theorems on Multi-objective Programming of Generalized Functions
Institute of Scientific and Technical Information of China (English)
Li-ping Pang; Wei Wang; Zun-quan Xia
2006-01-01
The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven.
T-Duality in $\\sigma$ Models with Kaluza-Klein Metric as Electric-Magnetic Duality
Jafarizadeh, M A
1999-01-01
It is shown that the T-duality in \\sigma-model with Kaluza-Klein metric, without or with a torsion term, can be interpreted as electric-magnetic duality for some of their solitonic solutions. Actually Buscher's duality transformation interchanges the topological and Noether charges.
The Electromagnetic Duality Formulation of Geometric Phases
Zhang, Yuchao; Li, Kang
2015-06-01
This paper focuses on the electromagnetic(EM) duality formulation of geometric phases of Aharonov-Bohm(A-B) effect and Aharonov-Casher(A-C) effect. Through the two four-vector potential formulation of electromagnetic theory, we construct a EM duality formulation for both A-B effect and A-C effect. The He-McKellar-Wilkens(HMW) effect is included as a EM duality counterpart of the A-C effect, and also the EM duality counterpart of the A-B effect is also predicted.
Space-time duality and superduality
Burgess, C P; Kamela, M; Knutt-Wehlau, M E; Page, P; Quevedo, Fernando; Zebarjad, M
1999-01-01
We introduce a new class of duality symmetries amongst quantum field theories. The new class is based upon global space-time symmetries, such as Poincare invariance and supersymmetry, in the same way as the existing duality transformations are based on global internal symmetries. We illustrate these new duality transformations by dualizing several scalar and spin-half field theories in 1 + 1 space-time dimensions, involving non-supersymmetric as well as (1, 1) and (2, 2) supersymmetric models. For (2, 2) models the new duality transformations can interchange chiral and twisted chiral multiplets.
Prime Factorization in the Duality Computer
Institute of Scientific and Technical Information of China (English)
WANG Wan-Ying; SHANG Bin; WANG Chuan; LONG Gui-Lu
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.
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.
Mirror Symmetry and Polar Duality of Polytopes
Directory of Open Access Journals (Sweden)
David A. Cox
2015-09-01
Full Text Available This expository article explores the connection between the polar duality from polyhedral geometry and mirror symmetry from mathematical physics and algebraic geometry. Topics discussed include duality of polytopes and cones as well as the famous quintic threefold and the toric variety of a reflexive polytope.
Managing Dualities in Planned Change Initiatives
Barge, J. Kevin; Lee, Michael; Maddux, Kristy; Nabring, Richard; Townsend, Bryan
2008-01-01
Dualities play an important role in creating the conditions for change and managing planned change initiatives. Building on Seo, Putnam, and Bartunek's (2003) work, this study focuses on the dualities associated with managing change processes. A case study of a planned change process called the Circle of Prosperity Initiative, a multi-stakeholder…
A Vademecum on Quark-Hadron Duality
Bigi, Ikaros I; Bigi, Ikaros; Uraltsev, Nikolai
2001-01-01
We present an elementary introduction to the problem of quark-hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the Small Velocity expansion. A new potentially significant mechanism for violation of local duality in \\Gamma_sl(B) is analyzed. Yet we conclude that the amount of duality violation in \\Gamma_sl(B) must be safely below the half percent level, with realistic estimates being actually much smaller. Violation of local duality in \\Gamma_sl(B) is thus far below the level relevant to pheno...
Abelian Duality and Abelian Wilson Loops
Zucchini, R
2003-01-01
We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one.
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.
A Vademecum on Quark-Hadron Duality
Bigi, Ikaros; Uraltsev, Nikolai
We present an elementary introduction to the problem of quark-hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the small velocity expansion. A new potentially significant mechanism for the violation of local duality in Γsl(B) is analyzed. Yet we conclude that the amount of duality violation in Γsl(B) must be safely below the half percent level, with realistic estimates being actually much smaller. The violation of local duality in Γsl(B) is thus far below the level relevant to phenomenology. We also present a cautionary note on the B-->D* decay amplitude at zero recoil and show that it is much more vulnerable to violations of quark-hadron duality than Γsl(B). A critical review of some recent literature is given. We point out that the presently limiting factor in genuinely model-independent extraction of Vcb is the precise value of the short-distance charm quark mass. We suggest a direct and precise experimental check of local quark-hadron duality in semileptonic B--> Xclν decays.
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.
Local duality in Loewner equations
Contreras, Manuel D; Gumenyuk, Pavel
2012-01-01
Among diversity of frameworks and constructions introduced in Loewner Theory by different authors, one can distinguish two closely related but still different ways of reasoning, which colloquially may be described as "increasing" and "decreasing". In this paper we review in short the main types of (deterministic) Loewner evolution discussed in the literature and describe in detail the local duality between "increasing" and "decreasing" cases within the general unifying approach in Loewner Theory proposed recently in [Bracci et al. to appear in J Reine Angew Math; arXiv:0807.1594v1], [Bracci et al. in Math Ann 344:947-962, 2009; arXiv:0807.1715v1], [Contreras et al. in Revista Matem\\'atica Iberoamericana 26:975-1012, 2010; arXiv:0902.3116v1]. In particular, we extend several results of R.O.Bauer [in J Math Anal Appl 302:484-501, 2005; arXiv:math/0306130v1], which deal with the chordal Loewner evolution, to this general setting. Although the duality is given by a simple change of the parameter, not all the resu...
Ring wormholes via duality rotations
Gibbons, Gary W
2016-01-01
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 $-c^4/4G$. 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 whole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes...
African Journals Online (AJOL)
agreements on the Nile waters: the 1929 Nile Water Agreement and the 1959 Nile ...... Nile Basin Regional Power Trade; Efficient Water Use for Agricultural Production .... respect to existing bilateral and multilateral agreements on international.
Quark Hadron Duality - Recent Jefferson Lab Results
Energy Technology Data Exchange (ETDEWEB)
Niculescu, Maria Ioana [James Madison Univ., Harrisonburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-08-01
The duality between the partonic and hadronic descriptions of electron--nucleon scattering is a remarkable feature of nuclear interactions. When averaged over appropriate energy intervals the cross section at low energy which is dominated by nucleon resonances resembles the smooth behavior expected from perturbative QCD. Recent Jefferson Lab results indicate that quark-hadron duality is present in a variety of observables, not just the proton F2 structure function. An overview of recent results, especially local quark-hadron duality on the neutron, are presented here.
Wilson Loop Form Factors: A New Duality
Chicherin, Dmitry; Heslop, Paul; Korchemsky, Gregory P.; Sokatchev, Emery
2016-01-01
We find a new duality for form factors of lightlike Wilson loops in planar $\\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality....
Duality Symmetry and Soldering in Different Dimensions
Banerjee, R
1997-01-01
We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in four dimensions. In all cases there are two such distinct actions. Furthermore, by soldering these distinct actions in any dimension a master action is obtained which is duality invariant under a much bigger set of symmetries than is usually envisaged. The concept of swapping duality is introduced and its implications are discussed. The effects of coupling to gravity are also elaborated. Finally, the extension of the analysis for arbitrary dimensions is indicated.
Quark Hadron Duality - Recent Jefferson Lab Results
Niculescu, Ioana
2015-01-01
The duality between the partonic and hadronic descriptions of electron--nucleon scattering is a remarkable feature of nuclear interactions. When averaged over appropriate energy intervals the cross section at low energy which is dominated by nucleon resonances resembles the smooth behavior expected from perturbative QCD. Recent Jefferson Lab results indicate that quark-hadron duality is present in a variety of observables, not just the proton F2 structure function. An overview of recent results, especially local quark-hadron duality on the neutron, are presented here.
A physics perspective on geometric Langlands duality
Schlesinger, Karl-Georg
2009-01-01
We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N=4 supersymmetric four dimensional gauge theory, initiated by Kapustin and Witten in 2006. We sketch some of the central further developments. Placing this four dimensional gauge theory into a six dimensional framework, as advocated by Witten, holds the promise to lead to a formulation which makes geometric Langlands duality a manifest symmetry (like coavariance in differential geometry). Furthermore, it leads to an approach toward geometric Langlands duality for algebraic surfaces, reproducing and extending the recent results of Braverman and Finkelberg.
Understanding strongly coupling magnetism from holographic duality
Cai, Rong-Gen
2016-01-01
The unusual magnetic materials are significant in both science and technology. However, because of the strongly correlated effects, it is difficult to understand their novel properties from theoretical aspects. Holographic duality offers a new approach to understanding such systems from gravity side. This paper will give a brief review of our recent works on the applications of holographic duality in understanding unusual magnetic materials. Some quantitative compare between holographic results and experimental data will be shown and some predictions from holographic duality models will be discussed.
Fermionic T-duality: A snapshot review
Colgáin, Eoin Ó
2012-01-01
Through a self-dual mapping of the geometry AdS5 x S5, fermionic T-duality provides a beautiful geometric interpretation of hidden symmetries for scattering amplitudes in N=4 super-Yang-Mills. Starting with Green-Schwarz sigma-models, we consolidate developments in this area into this small review. In particular, we discuss the translation of fermionic T-duality into the supergravity fields via pure spinor formalism and show that a general class of fermionic transformations can be identified directly in the supergravity. In addition to discussing fermionic T-duality for the geometry AdS4 x CP3, dual to N=6 ABJM theory, we review work on other self-dual geometries. Finally, we present a short round-up of studies with a formal interest in fermionic T-duality.
Generalized complex geometry and T-duality
Cavalcanti, Gil R
2011-01-01
We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically distinct torus bundles, and prescribes a method for transporting geometrical structures between them. We describe how this relation may be understood as a Courant algebroid isomorphism between the spaces in question. This then allows us to transport Dirac structures, generalized Riemannian metrics, generalized complex and generalized Kahler structures, extending the "Buscher rules" well-known to physicists. Finally, we re-interpret T-duality as a Courant reduction, and explain that T-duality between generalized complex manifolds may be viewed as a generalized complex submanifold (D-brane) of the product, in a way that establishes a direct analogy with the Fourier-Mukai transform.
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.
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)
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.
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)
Duality, Entropy and ADM Mass in Supergravity
Energy Technology Data Exchange (ETDEWEB)
Cerchiai, Bianca L.; Ferrara, Sergio; Marrani, Alessio; Zumino, Bruno
2009-02-23
We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both"large" and"small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.
Searching for S-duality in Gravitation
García-Compéan, H; Ramírez, C
2000-01-01
We overview some attempts to find S-duality analogues of non-supersymmetric Yang-Mills theory, in the context of gravity theories. The case of MacDowell-Mansouri gauge theory of gravity is discussed. Three-dimensional dimensional reductions from the topological gravitational sector in four dimensions, enable to recuperate the 2+1 Chern-Simons gravity and the corresponding S-dual theory, from the notion of self-duality in the four-dimensional theory.
Seiberg Duality is an Exceptional Mutation
Herzog, C P
2004-01-01
The low energy gauge theory living on D-branes probing a del Pezzo singularity of a non-compact Calabi-Yau manifold is not unique. In fact there is a large equivalence class of such gauge theories related by Seiberg duality. As a step toward characterizing this class, we show that Seiberg duality can be defined consistently as an admissible mutation of a strongly exceptional collection of coherent sheaves.
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.
Gaugino condensation, duality and supersymmetry breaking
Quevedo, Fernando
1995-01-01
The status of gaugino condensation in low-energy string theory is reviewed. Emphasis is given to the determination of the efective action below condensation scale in terms of the 2PI and Wilson actions. We illustrate how the different perturbative duality symmetries survive this simple nonperturbative phenomenon, providing evidence for the believe that these are exact nonperturbative symmetries of string theory. Consistency with T duality lifts the moduli degeneracy. The B_{\\mu\
Duality and helicity: A symplectic viewpoint
Elbistan, M.; Duval, C.; Horváthy, P. A.; Zhang, P.-M.
2016-10-01
The theorem which says that helicity is the conserved quantity associated with the duality symmetry of the vacuum Maxwell equations is proved by viewing electromagnetism as an infinite dimensional symplectic system. In fact, it is shown that helicity is the moment map of duality acting as an SO (2) group of canonical transformations on the symplectic space of all solutions of the vacuum Maxwell equations.
T-Duality and Topological Insulators
Mathai, Varghese
2015-01-01
It is well known that topological insulators are classified by a family of groups, which coincidentally also classifies D-brane charges on orientifolds in string theory. In this letter, we extend this correlation via a geometric analog of the real Fourier transform to obtain a novel duality of topological insulators that can be viewed as a condensed matter analog of T-duality in string theory.
On local duality invariance in electromagnetism
Tiwari, S C
2011-01-01
Duality is one of the oldest known symmetries of Maxwell equations. In recent years the significance of duality symmetry has been recognized in superstrings and high energy physics and there has been a renewed interest on the question of local duality rotation invariance. In the present paper we re-visit global duality symmetry in the Maxwell action and delineate the ambiguous role of gauge invariance and time locality. We have recently demonstrated that local duality invariance in a Lorentz covariant form can be carried out in the Maxwell equations. In this paper it is shown that in the four-pseudo vector Lagrangian theory of Sudbery a local duality generalization can be naturally and unambiguously implemented and the Euler-Lagrange equations of motion are consistent with the generalized Maxwell field equations. It is pointed out that the extension of Noether theorem in full genrality for a vector action is an important open problem in mathematical physics. Physical consequences of this theory for polarized ...
Conformal Aspects of Spinor-Vector Duality
Faraggi, Alon E; Mohaupt, Thomas; Tsulaia, Mirian
2011-01-01
We present a detailed study of various aspects of Spinor-Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the duality map by using simple toroidal orbifolds preserving N_4 = 1 and N_4 = 2 spacetime supersymmetries in four dimensions. We explain how the duality map arises in this context by turning on special values of the Wilson lines around the compact cycles of the manifold. We argue that in models with N_4 = 2 spacetime supersymmetry, the interpolation between the Spinor-Vector dual vacua can be continuously realized. We trace the origin of the Spinor-Vector duality map to the presence of underlying N = (2, 2) and N = (4, 4) SCFTs, and explicitly show that the induced spectral-flow in the twisted sectors is responsible for the observed duality. The isomorphism between current algebra representations gives rise to a number of chiral character identities, reminiscent of the recently-di...
General Quantum Interference Principle and Duality Computer
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu
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 thesub-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.
Bergshoeff, Eric A
2011-01-01
We construct for arbitrary dimensions a universal T-duality covariant expression for the Wess-Zumino terms of supersymmetric String Solitons in toroidally compactified string theories with 32 supercharges. The worldvolume fields occurring in the effective action of these String Solitons form either a vector or a tensor multiplet with 16 supercharges. We determine the dimensions of the conjugacy classes under T-duality to which these String Solitons belong. We do this in two steps. First, we determine the T-duality representations of the $p$-forms of maximal supergravities that contain the potentials that couple to these String Solitons. We find that these are p-forms, with D-4\\le p\\le 6 if D \\ge 6 and with D-4\\le p\\le D if D < 6, transforming in the antisymmetric representation of rank m=p+4-D\\le 4 of the T-duality symmetry SO(10-D,10-D). All branes support vector multiplets except when m=10-D. In that case the T-duality representation splits, for D<10, into a selfdual and anti-selfdual part, correspond...
Large N Dualities In Topological String Theory
Okuda, T
2005-01-01
We investigate the phenomenon of large N duality in topological string theory from three different perspectives: worldsheets, matrix models, and melting crystals. In the first part, we utilize the technique of mirror symmetry to generalize the worldsheet derivation of the duality, originally given by Ooguri and Vafa for the A- model on the conifold, to the A-model on more general geometries. We also explain how the Landau-Ginzburg models can be used to perform the worldsheet derivation of the B-model large N dualities. In the second part, we consider a class of A-model large N dualities where the open string theory reduces through the Chern-Simons theory on a lens space to a matrix model. We compute and compare the matrix model spectral curve and the Calabi-Yau geometry mirror to the closed string geometry, confirming the predictions of the duality. Finally in the third part, we propose a crystal model that describes the A-model on the resolved conifold. This is a generalization of the crystal for C3. We also...
Issues on 3D Noncommutative Electromagnetic Duality
Rodrigues, D C; Rodrigues, Davi C.; Wotzasek, Clovis
2006-01-01
We extend the ordinary 3D electromagnetic duality to the noncommutative (NC) space-time through a Seiberg-Witten map to second order in the noncommutativity parameter $\\theta$, defining a new scalar field model. There are similarities with the 4D NC duality, these are exploited to clarify properties of both cases. Up to second order in $\\theta$, we find duality interchanges the 2-form $\\theta$ with its 1-form Hodge dual ${^\\star} \\theta $ times the gauge coupling constant, i.e., $ \\theta \\to {^\\star} \\theta g^2$ (similar to the 4D NC electromagnetic duality). We prove that this property is false in the third order expansion in both 3D and 4D space-times. Starting from the third order expansion, $\\theta$ cannot be rescaled to attain an S-duality; on the other hand, to any order in $\\theta$, it is possible to rescale the fields to obtain the same coupling constants in both dual descriptions. In addition to possible applications on effective models, the 3D space-time is useful for studying general properties of ...
Gravitational duality in General Relativity and Supergravity theories
Energy Technology Data Exchange (ETDEWEB)
Dehouck, F. [Service de physique mathematique et interactions fondamentales. Universite Libre de Bruxelles, Campus Plaine CP-231, 1050 Bruxelles (Belgium)
2011-07-15
We quickly review the current status of gravitational duality in General Relativity. We summarize and comment some recent work on constructing dual (topological) charges and understanding how this duality acts in supergravity theories.
Grothendieck-Verdier duality patterns in quantum algebra
Manin, Yu I.
2017-08-01
After a brief survey of the basic definitions of Grothendieck-Verdier categories and dualities, I consider in this context dualities introduced earlier in the categories of quadratic algebras and operads, largely motivated by the theory of quantum groups. Finally, I argue that Dubrovin's `almost duality' in the theory of Frobenius manifolds and quantum cohomology must also fit a (possibly extended) version of Grothendieck-Verdier duality.
The FZZ-Duality Conjecture - A Proof
Hikida, Yasuaki
2009-01-01
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.
Duality theories for Boolean algebras with operators
Givant, Steven
2014-01-01
In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.
Electromagnetic-Magnetoelectric Duality for Waveguides
Sang-Nourpour, Nafiseh; Kheradmand, R; Rezaei, M; Sanders, Barry C
2015-01-01
We develop a theory for waveguides that respects the duality of electromagnetism, namely the symmetry of the equations arising through inclusion of magnetic monopoles in addition to including electrons (electric monopoles). The term magnetoelectric potential is sometimes used to signify the magnetic-monopole induced dual to the usual electromagnetic potential. To this end, we introduce a general theory for describing modes and characteristics of waveguides based on mixed-monopole materials, with both electric and magnetic responses. Our theory accommodates exotic media such as double-negative, near-zero and zero-index materials, and we demonstrate that our general theory exhibits the electromagnetic duality that would arise if we were to incorporate magnetic monopoles into the media. We consider linear, homogeneous, isotropic waveguide materials with slab and cylindrical geometries. To ensure manifest electromagnetic duality, we construct generic electromagnetic susceptibilities that are dual in both electric...
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
Energy Technology Data Exchange (ETDEWEB)
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.
Particle-Vortex Duality from 3d Bosonization
Karch, Andreas
2016-01-01
We provide a simple derivation of particle-vortex duality in d=2+1 dimensions. Our starting point is a relativistic form of flux attachment, designed to transmute the statistics of particles. From this seed, we derive a web of new dualities. These include particle-vortex duality for bosons as well as the recently discovered counterpart for fermions.
A Horizontal Categorification of Gelfand Duality
Bertozzini, Paolo; Lewkeeratiyutkul, Wicharn
2008-01-01
In the setting of C*-categories, we provide a definition of "spectrum" of a commutative full C*-category as a one-dimensional unital saturated Fell bundle over a suitable groupoid (equivalence relation) and prove a categorical Gelfand duality theorem generalizing the usual Gelfand duality between the categories of commutative unital C*-algebras and compact Hausdorff spaces. Although many of the individual ingredients that appear along the way are well-known, the somehow unconventional way we "glue" them together seems to shed some new light on the subject.
Duality of boiling systems and uncertainty phenomena
Institute of Scientific and Technical Information of China (English)
柴立合; 彭晓峰; 王补宣
2000-01-01
Interactions among dry patches at high heat flux are theoretically analyzed. The high heat flux boiling experiments on metal plate wall with different materials and thickness are correspondingly conducted. The duality of boiling system, i.e. hydrodynamic performance and self-organized performance is identified. A unified explanation of hydrodynamic models and dry patches models is given. The scatter and uncertainty in boiling data can be mainly attributed to the intrinsic duality, but not the sole surface effects. The present experimental results explain why the deviation point at high flux boiling is seen only on occasion and why the self-organization of dry patches is often ignored in available literature.
U-Duality and the Leech Lattice
Rios, Michael
2013-01-01
It has recently been shown that the full automorphism group of the Leech lattice, Conway's group Co_0, can be generated by 3 x 3 matrices over the octonions. We show such matrices are of type F_4 in E_{6(-26)}, the U-duality group for N=2, D=5 exceptional magic supergravity. By mapping points of the Leech lattice to black hole charge vectors, it is seen Conway's group Co_0 is generated by U-duality transformations acting as rotations in the charge space for BPS black holes.
Duality between random trap and barrier models
Energy Technology Data Exchange (ETDEWEB)
Jack, Robert L [Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720 (United States); Sollich, Peter [Department of Mathematics, King' s College London, London WC2R 2LS (United Kingdom)
2008-08-15
We discuss the physical consequences of a duality between two models with quenched disorder, in which particles propagate in one dimension among random traps or across random barriers. We derive an exact relation between their diffusion fronts at fixed disorder and deduce from this that their disorder-averaged diffusion fronts are exactly equal. We use effective dynamics schemes to isolate the different physical processes by which particles propagate in the models and discuss how the duality arises from a correspondence between the rates for these different processes.
Noether symmetries and duality transformations in cosmology
Paliathanasis, Andronikos
2016-01-01
We discuss the relation between local transformations generated by Noether (point) symmetries and discrete transformations for a class of minisuperspace cosmological models. Moreover as far as concerns the scale-factor duality of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations. In particular, the same point symmetry exists for the Brans-Dicke- scalar field with linear potential for $\\omega_{BD}=1$ . Furthermore, in the context of the O'Hanlon theory for $f\\left( R\\right) $-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Level/rank Duality and Chern-Simons-Matter Theories
Hsin, Po-Shen
2016-01-01
We discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories. We couple the dual Lagrangians to appropriate background fields (including gauge fields, spin$_c$ connections and the metric). The non-trivial maps between the currents and the line operators in the dual theories is accounted for by mixing of these fields. In order for the duality to be valid we must add finite counterterms depending on these background fields. This analysis allows us to resolve a number of puzzles with these dualities, to provide derivations of some of them, and to find new consistency conditions and relations between them. In addition, we find new level/rank dualities of topological Chern-Simons theories and new dualities of Chern-Simons-matter theories, including new boson/boson and fermion/fermion dualities.
On the dimensional dependence of the electromagnetic duality groups
Wotzasek, C
1998-01-01
We study the two-fold dimensional dependence of the electromagnetic duality groups. We introduce the dual projection operation that systematically discloses the presence of an internal space of potentials where the group operation is defined. A two-fold property of the kernel in the projection is shown to define the dimensional dependence of the duality groups. The dual projection is then generalized to reveal another hidden two-dimensional structure. The new unifying concept of the external duality space remove the dimensional dependence of the kernel, allowing the presence of both $Z_2$ and SO(2) duality groups in all even dimensions. This result, ultimately unifies the notion of selfduality to all D=2k+2 dimensions. Finally, we show the presence of an unexpected duality between the internal and external spaces leading to a duality of the duality groups.
Local Duality for 2-Dimensional Local Ring
Indian Academy of Sciences (India)
Belgacem Draouil
2008-11-01
We prove a local duality for some schemes associated to a 2-dimensional complete local ring whose residue field is an -dimensional local field in the sense of Kato–Parshin. Our results generalize the Saito works in the case =0 and are applied to study the Bloch–Ogus complex for such rings in various cases.
Refined large N duality for torus knots
DEFF Research Database (Denmark)
Nawata, Satoshi; Kameyama, Masaya
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...
New duality Transformations in Orbifold Theory
J. de Boer; J. Evslin; M. Halpern; J.E. Wang
2000-01-01
We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold $A(H)/H$, where $A(H)$ is the set of all current-algebraic conformal field theories with a finite symmetry group $H \\subset Aut(g)$. The permutation orbifolds with $H = Z_\\la
Noether symmetries and duality transformations in cosmology
Paliathanasis, Andronikos; Capozziello, Salvatore
2016-09-01
We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Two Point Pade Approximants and Duality
Banks, Tom
2013-01-01
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a strong/weak duality, when the symmetries do not determine exact expressions for some quantity.
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.
Two-component Duality and Strings
Freund, Peter G O
2007-01-01
A phenomenologically successful two-component hadronic duality picture led to Veneziano's amplitude, the fundamental first step to string theory. This picture is briefly recalled and its two components are identified as the open strings (mesons and baryons) and closed strings (Pomeron).
Gauss decomposition for quantum groups and duality
Damaskinsky, E V; Lyakhovsky, V D; Sokolov, M A
1995-01-01
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality aspects of the Gauss decomposition are also touched. For clarity of exposition a few simple examples are considered in some details.
Dualities for Logics of Transition Systems
Bonsangue, M.M.; Kurz, A.
2005-01-01
We present a general framework for logics of transition systems based on Stone duality. Transition systems are modelled as coalgebras for a functor T on a category X. The propositional logic used to reason about state spaces from X is modelled by the Stone dual A of X (e.g. if X is Stone spaces then
The Higher Spin/Vector Model Duality
Giombi, Simone; Yin, Xi
2012-01-01
This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.
Refined large N duality for torus knots
DEFF Research Database (Denmark)
Nawata, Satoshi; Kameyama, Masaya
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...
Intergenerational equity and dynamic duality principles
Directory of Open Access Journals (Sweden)
Hirofumi Uzawa
2002-01-01
Full Text Available The concept of intergenerational equity concerning intertemporal paths of consumption and capital accumulation is introduced and the analysis of the dynamic processes of capital accumulation and changes in environmental quality that are intergenerationally equitable is developed. The analysis is based upon the dynamic duality principles, as originally developed by Koopmans and Uzawa, and later extended to the case involving environmental quality.
An alternative formulation of classical electromagnetic duality
Li, K; Li, Kang; Naón, Carlos M.
2001-01-01
By introducing a doublet of electromagnetic four dimensional vector potentials, we set up a manifestly Lorentz covariant and SO(2) duality invariant classical field theory of electric and magnetic charges. In our formulation one does not need to introduce the concept of Dirac string.
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.
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.
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...
A duality web of linear quivers
Brünner, Frederic
2016-01-01
We show that applying the Bailey lemma to elliptic hypergeometric integrals on the $A_n$ root system leads to a large web of dualities for $\\mathcal{N} = 1$ supersymmetric linear quiver theories. The superconformal index of Seiberg's SQCD with $SU(N_c)$ gauge group and $SU(N_f)\\times SU(N_f)\\times U(1)$ global symmetry is equal to that of $N_f-N_c-1$ distinct linear quivers. Seiberg duality further enlarges this web by adding new quivers. In particular, both interacting electric and magnetic theories with arbitrary $N_c$ and $N_f$ can be constructed by quivering an $s$-confining theory with $N_f=N_c+1$.
Abelian Duality on Globally Hyperbolic Spacetimes
Becker, Christian; Benini, Marco; Schenkel, Alexander; Szabo, Richard J.
2017-01-01
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.
Off-shell Color-Kinematics Duality
Mastrolia, Pierpaolo; Schubert, Ulrich; Bobadilla, William J Torres
2015-01-01
We elaborate on the color-kinematics duality for off-shell diagrams in gauge theories coupled to matter, by investigating the scattering process $gg\\to ss, q\\bar q, gg$, and show that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduces to a color-kinematics violating term due to the contributions of sub-graphs only. Such anomaly vanishes when the four particles connected by the Jacobi relation are on their mass shell with vanishing squared momenta, being either external or cut particles, where the validity of the color-kinematics duality is recovered. We discuss the role of this off-shell decomposition in the direct construction of higher-multiplicity numerators satisfying color-kinematics identity, providing an explicit example for the QCD process $gg\\to q\\bar{q}g$.
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).
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...
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...
Duality Covariant Solutions in Extended Field Theories
Rudolph, Felix J
2016-01-01
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to winding modes of the fundamental objects. This geometrically unifies the spacetime metric and the gauge fields (and their local symmetries) in a generalized geometry. Solutions to these extended field theories take the simple form of waves and monopoles in the extended space. From a supergravity point of view they appear as 1/2 BPS objects such as the string, the membrane and the fivebrane in ordinary spacetime. In this thesis double field theory and exceptional field theory are introduced, solutions to their equations of motion are constructed and their properties are analyzed. Further it is established how isometries in the extended space give rise to duality relations between the supergravity solutions. Extensions to these core ideas include studying Goldstone modes, probing s...
Duality orbits of non-geometric fluxes
Energy Technology Data Exchange (ETDEWEB)
Dibitetto, G.; Roest, D. [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Fernandez-Melgarejo, J.J. [Grupo de Fisica Teorica y Cosmologia, Dept. de Fisica, University of Murcia, Campus de Espinardo, 30100-Murcia (Spain); Marques, D. [Institut de Physique Theorique, CEA/ Saclay, 91191 Gif-sur-Yvette Cedex (France)
2012-11-15
Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T- and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometric orbits in the half-maximal case. We show how the latter are obtained from compactifications of double field theory. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Natsuume, Makoto
2014-01-01
This is the draft version of a textbook on "real-world" applications of the AdS/CFT duality for beginning graduate students in particle physics and for researchers in the other fields. The aim of this book is to provide background materials such as string theory, general relativity, nuclear physics, nonequilibrium physics, and condensed-matter physics as well as some key applications of the AdS/CFT duality in a single textbook. Contents: (1) Introduction, (2) General relativity and black holes, (3) Black holes and thermodynamics, (4) Strong interaction and gauge theories, (5) The road to AdS/CFT, (6) The AdS spacetime, (7) AdS/CFT - equilibrium, (8) AdS/CFT - adding probes, (9) Basics of nonequilibrium physics, (10) AdS/CFT - nonequilibrium, (11) Other AdS spacetimes, (12) Applications to quark-gluon plasma, (13) Basics of phase transition, (14) AdS/CFT - phase transition.
Hadamard states for quantum Abelian duality
Benini, Marco; Dappiaggi, Claudio
2016-01-01
Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C$^*$-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states to such algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three C$^*$-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors we obtain a state for the full theory, providing ultimately a unitary implementation of Abelian duality.
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...
Grassmann Duality and the Particle Spectrum
Delbourgo, Robert
2016-01-01
Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the {\\em classification} group SU(3)$\\times$SU(2)$_L\\times$SU(2)$_R$, which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge -4/3 and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain $4\\sin^2\\theta_w = 1 - 2\\alpha/3\\alpha_s$ which is not far from the experimental value around the $M_Z$ mass.
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, the equat......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......, the equation of state of the dark energy can be related to the apparent cutoff in the CMB spectrum. The present limits on the equation of state of dark energy are shown to imply an IR cutoff in the CMB multipole interval of 9>l>8.5....
Conceptual Aspects of Gauge/Gravity Duality
de Haro, Sebastian; Butterfield, Jeremy
2015-01-01
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Section 5, the central and original example: Maldacena's AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to de Sitter spacetime and to black holes. Section 10 discusses the bearing of gauge/gravity duality on two philosophical topics: the equivalence of physical theories, and the idea that spacetime, or some features of it, are emergent.
Conceptual Aspects of Gauge/Gravity Duality
De Haro, Sebastian; Mayerson, Daniel R.; Butterfield, Jeremy N.
2016-11-01
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Sect. 5, the central and original example: Maldacena's AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to de Sitter spacetime and to black holes. Section 10 discusses the bearing of gauge/gravity duality on two philosophical topics: the equivalence of physical theories, and the idea that spacetime, or some features of it, are emergent.
Distributive lattice orderings and Priestley duality
Krebs, Michel
2007-01-01
The ordering relation of a bounded distributive lattice L is a (distributive) (0, 1)-sublattice of L \\times L. This construction gives rise to a functor \\Phi from the category of bounded distributive lattices to itself. We examine the interaction of \\Phi with Priestley duality and characterise those bounded distributive lattices L such that there is a bounded distributive lattice K such that \\Phi(K) is (isomorphic to) L.
Nash equilibria via duality and homological selection
Indian Academy of Sciences (India)
Arnab Basu; Samik Basu; Mahan MJ
2014-11-01
Given a multifunction from to the -fold symmetric product Sym$_{k}(X)$, we use the Dold–Thom theorem to establish a homological selection theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré duality in addition to the Dold–Thom theorem.
Capturing consumer engagement: duality, dimensionality and measurement
Dessart, Laurence; Veloutsou, Cleopatra; Morgan-Thomas, Anna
2016-01-01
This study advances the conceptualisation and operationalisation of consumer engagement in the context of online brand communities (OBCs). Past scholarship has only partially addressed the dimensionality of engagement and the different engagement foci, and these oversights have important theoretical and empirical consequences. This study contributes to the nascent stream of research that aims to theoretically refine and operationalise engagement by espousing the duality of engagement with two...
Electromagnetic duality anomaly in curved spacetimes
Agullo, I; Navarro-Salas, J
2016-01-01
The source-free Maxwell action is invariant under electric-magnetic duality rotations in arbitrary spacetimes. This leads to a conserved classical Noether charge. We show that this conservation law is broken at the quantum level in presence of a background classical gravitational field with a non-trivial Chern-Pontryagin invariant, in a parallel way to the chiral anomaly for massless Dirac fermions. Among the physical consequences, the net polarization of the quantum electromagnetic field is not conserved.
Duality without constraint qualification in nonsmooth optimization
S. Nobakhtian
2006-01-01
We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualification. Then we formulate the dual problem corresponding to the primal problem, and some duality res...
Maxwell Duality, Lorentz Invariance, and Topological Phase
Dowling, J P; Franson, J D; Dowling, Jonathan P.; Williams, Colin P.
1999-01-01
We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena. We also elucidate Lorentz transformations that allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose a realistic set up for measuring and interpreting the He-McKellar-Wilkens phase directly in an experiment.
Duality properties between spectra and tilings
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Spectra and tilings play an important role in analysis and geometry respectively.The relations between spectra and tilings have bafied the mathematicians for a long time.Many conjectures,such as the Fuglede conjecture,are placed on the establishment of relations between spectra and tilings,although there are no desired results.In the present paper we derive some characteristic properties of spectra and tilings which highlight certain duality properties between them.
Duality properties of Gorringe-Leach equations
Grandati, Yves; Berard, Alain; Mohrbach, Herve
2004-01-01
International audience; In the category of motions preserving the angular momentum's 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 one of the other
Duality properties of Gorringe-Leach equations
Grandati, Yves; Mohrbach, Herve
2007-01-01
In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they're 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 one of the other.
Higher-Spin Gauge Fields and Duality
Francia, D
2006-01-01
We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravity in $D$ dimensions and its dual realisations in detail.
Real weights, bound states and duality orbits
Marrani, Alessio; Romano, Luca
2015-01-01
We show that the duality orbits of extremal black holes in supergravity theories with symmetric scalar manifolds can be derived by studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the duality symmetry group. The weight vectors always correspond to weights that are real, where the reality properties are derived from the Tits-Satake diagram that identifies the real form of the Lie algebra of the duality symmetry group. Both N=2 magic Maxwell-Einstein supergravities and the semisimple infinite sequences of N=2 and N=4 theories in D=4 and 5 are considered, and various results, obtained over the years in the literature using different methods, are retrieved. In particular, we show that the stratification of the orbits of these theories occurs because of very specific properties of the representations: in the case of the theory based on the real numbers, whose symmetry group is maximally non-compact and there...
Aspects of duality in gravitational theories
Troessaert, Cedric
2013-01-01
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an action manifestly invariant under duality rotations in presence of both electric and magnetic external sources. It is also shown how, in the reduced phase-space, all higher spin gauge fields can be written as bi-hamiltonian systems. The role of the second hamiltonian is played by the electromagnetic duality generator. The second part is devoted to the study of asymptotic symmetries and their applications to holography. After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In particular, it is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of su...
Duality quantum algorithm efficiently simulates open quantum systems
Shi-Jie Wei; Dong Ruan; Gui-Lu Long
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 op...
Proton Spin Structure Functions and Quark-Hadron Duality
Institute of Scientific and Technical Information of China (English)
DONG Yu-Bing
2006-01-01
@@ Quark-hadron duality of three proton spin structure functions g1, g2 and gT are discussed simultaneously. It is found that the onsets of the quark-hadron dualities of g1p, g2p and g3p are similar and they are expected to be at about Q2 ～ 2 GeV2. In addition, our results show that the elastic peak remarkably breaks local quark-hadron duality.
Topological duality twist and brane instantons in F-theory
Energy Technology Data Exchange (ETDEWEB)
Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei”, Università di Padova andINFN - Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy)
2014-06-30
A variant of the topological twist, involving SL(2,ℤ) dualities and hence named topological duality twist, is introduced and explicitly applied to describe a U(1) N=4 super Yang-Mills theory on a Kähler space with holomorphically space-dependent coupling. Three-dimensional duality walls and two-dimensional chiral theories naturally enter the formulation of the duality twisted theory. Appropriately generalized, this theory is relevant for the study of Euclidean D3-brane instantons in F-theory compactifications. Some of its properties and implications are discussed.
Particle-vortex duality in topological insulators and superconductors
Murugan, Jeff
2016-01-01
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.
Type Ii/heterotic Duality And Mirror Symmetry (bundle Deformation, String Duality)
Perevalov, E V
1998-01-01
Toric geometry is used to systematically construct Type II compactifications dual to Heterotic models in six dimensions involving singular K3 surfaces as well as vector bundles. Reflexive polyhedra are shown to encode the spectra of the resulting low-energy theories. Finally, the connection between mirror symmetry and deformation of bundles on K3 surfaces is exhibited via string duality.
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
Casalderrey-Solana, Jorge; Liu, Hong; Mateos, David; Rajagopal, Krishna; Wiedemann, Urs Achim
2014-06-01
1. Opening remarks; 2. A heavy ion phenomenology primer; 3. Results from lattice QCD at nonzero temperature; 4. Introducing the gauge/string duality; 5. A duality toolbox; 6. Bulk properties of strongly coupled plasma; 7. From hydrodynamics for far-from-equilibrium dynamics; 8. Probing strongly coupled plasma; 9. Quarkonium mesons in strongly coupled plasma; 10. Concluding remarks and outlook; Appendixes; References; Index.
Dualities in M-theory and Born-Infeld Theory
Energy Technology Data Exchange (ETDEWEB)
Brace, Daniel M. [Univ. of California, Berkeley, CA (United States)
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.
T-duality trivializes bulk-boundary correspondence
Mathai, Varghese
2015-01-01
Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that T-duality trivializes the bulk-boundary correspondence.
Duality symmetries and the type II string effective action
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
S-duality in N=4 Yang-Mills theories
Girardello, L; Porrati, Massimo; Zaffaroni, A
1995-01-01
Evidence in favor of SL(2,Z) S-duality in N=4 supersymmetric Yang-Mills theories in four dimensions and with general compact, simple gauge groups is presented. (Contribution to the Proceedings of the Strings '95 conference, March 13-18, 1995, USC, and the Proceedings of the Trieste Conference on S-Duality and Mirror Symmetry June 5-9, 1995.)
Quantum Poisson-Lie T-duality and WZNW model
Alekseev, A Yu; Tseytlin, Arkady A
1996-01-01
A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space. The quantum equivalence of the models is established by using a path integral argument.
Dualities in M-theory and Born-Infeld Theory
Energy Technology Data Exchange (ETDEWEB)
Brace, Daniel, M
2001-08-01
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 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...
Duality symmetric string and M-theory
Berman, David S.; Thompson, Daniel C.
2015-03-01
We review recent developments in duality symmetric string theory. We begin with the world-sheet doubled formalism which describes strings in an extended spacetime with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk-Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an En(n) U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extended space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk-Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.
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.
A CMB/Dark Energy Cosmic Duality
Enqvist, K; Enqvist, Kari; Sloth, Martin S.
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, the equation of state of the dark energy can be related to the apparent cutoff in the CMB spectrum. The present limits on the equation of state of dark energy are shown to imply an IR cutoff in the CMB multipole interval of 9>l>8.5.
Exact Chern-Simons / Topological String duality
Krefl, Daniel
2015-01-01
We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N as well. In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extend to refined Chern-Simons with orthogonal groups.
Poincare duality angles for Riemannian manifolds with boundary
Shonkwiler, Clayton
2009-01-01
On a compact Riemannian manifold with boundary, the absolute and relative cohomology groups appear as certain subspaces of harmonic forms. DeTurck and Gluck showed that these concrete realizations of the cohomology groups decompose into orthogonal subspaces corresponding to cohomology coming from the interior and boundary of the manifold. The principal angles between these interior subspaces are all acute and are called Poincare duality angles. This paper determines the Poincare duality angles of a collection of interesting manifolds with boundary derived from complex projective spaces and from Grassmannians, providing evidence that the Poincare duality angles measure, in some sense, how "close" a manifold is to being closed. This paper also elucidates a connection between the Poincare duality angles and the Dirichlet-to-Neumann operator for differential forms, which generalizes the classical Dirichlet-to-Neumann map arising in the problem of Electrical Impedance Tomography. Specifically, the Poincare duality...
Spectral Duality in Integrable Systems from AGT Conjecture
Mironov, A; Zenkevich, Y; Zotov, A
2012-01-01
We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrodinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2x2 and NxN representations of the Toda chain and the famous AHH duality.
Extending dualities to trialities deepens the foundations of dynamics
Smolin, Lee
2015-01-01
Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, and show how breaking its natural triality symmetry by imposing different compactifications yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.
Baryons, monopoles and dualities in Chern-Simons-matter theories
Energy Technology Data Exchange (ETDEWEB)
Aharony, Ofer [Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot, 7610001 (Israel)
2016-02-15
There is significant evidence for a duality between (non-supersymmetric) U(N) Chern-Simons theories at level k coupled to fermions, and U(k) Chern-Simons theories at level N coupled to scalars. Most of the evidence comes from the large N ’t Hooft limit, where many details of the duality (such as whether the gauge group is U(N) or SU(N), the precise level of the U(1) factor, and order one shifts in the level) are not important. The main evidence for the validity of the duality at finite N comes from adding masses and flowing to pure Chern-Simons theories related by level-rank duality, and from flowing to the non-supersymmetric duality from supersymmetric dualities, whose finite N validity is well-established. In this note we clarify the implications of these flows for the precise form of the duality; in particular we argue that in its simplest form the duality maps SU(N) theories to U(k) theories, though there is also another version relating U(N) to U(k). This precise form strongly affects the mapping under the duality of baryon and monopole operators, and we show, following arguments by Radičević, that their mapping is consistent with our claims. We also discuss the implications of our results for the additional duality between these Chern-Simons matter theories and (the UV completion of) high-spin gravity theories on AdS{sub 4}. The latter theories should contain heavy particles carrying electric and/or magnetic charges under their U(1) gauge symmetry.
Liouville mode in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Moskalets, Tatiana [Karazin Kharkov National University, Department of Physics and Technology, Kharkov (Ukraine); Nurmagambetov, Alexei [Karazin Kharkov National University, Department of Physics and Technology, Kharkov (Ukraine); Akhiezer Institute for Theoretical Physics of NSC KIPT, Kharkov (Ukraine)
2015-11-15
We establish solutions corresponding to AdS{sub 4} static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry. We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range. The solutions obtained are also extended to higher-dimensional AdS space. We observe two different DC conductivities in 4D and higher-dimensional effective strongly coupled dual media and formulate conditions under which the appropriate ratio of different conductivities is qualitatively the same as that observed in an anisotropic strongly coupled fluid. We briefly discuss ways of how the Liouville field could appear in condensed matter physics and outline prospects of further employing the gauge/gravity duality in CMP problems. (orig.)
Liouville mode in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Moskalets, Tatiana, E-mail: tatyana.moskalets@gmail.com [Department of Physics and Technology, Karazin Kharkov National University, 4 Svobody Sq., 61022, Kharkov, UA (Ukraine); Nurmagambetov, Alexei, E-mail: ajn@kipt.kharkov.ua [Department of Physics and Technology, Karazin Kharkov National University, 4 Svobody Sq., 61022, Kharkov, UA (Ukraine); Akhiezer Institute for Theoretical Physics of NSC KIPT, 1 Akademicheskaya St., 61108, Kharkov, UA (Ukraine)
2015-11-25
We establish solutions corresponding to AdS{sub 4} static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry. We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range. The solutions obtained are also extended to higher-dimensional AdS space. We observe two different DC conductivities in 4D and higher-dimensional effective strongly coupled dual media and formulate conditions under which the appropriate ratio of different conductivities is qualitatively the same as that observed in an anisotropic strongly coupled fluid. We briefly discuss ways of how the Liouville field could appear in condensed matter physics and outline prospects of further employing the gauge/gravity duality in CMP problems.
Scale Factor Duality for Conformal Cyclic Cosmologies
dS, U Camara; 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 K\\"ahler 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 ...
Scale factor duality for conformal cyclic cosmologies
Camara da Silva, U.; Alves Lima, A. L.; Sotkov, G. M.
2016-11-01
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.
Wave-particle duality in classical mechanics
Davydov, Alexander Y.
2012-05-01
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in a strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propel via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, an observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may emerge as approximation from a more profound theory on a deeper level.
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.
Fricke S-duality in CHL models
Energy Technology Data Exchange (ETDEWEB)
Persson, Daniel [Fundamental Physics, Chalmers University of Technology,412 96, Gothenburg (Sweden); Volpato, Roberto [Theory Group, SLAC National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025 (United States); Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305 (United States)
2015-12-23
We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3×T{sup 2} by a ℤ{sub N} symmetry acting (possibly) non-geometrically on K3. We show that most of these models (in particular, for geometric symmetries) are self-dual under a weak-strong duality acting on the heterotic axio-dilaton modulus S by a “Fricke involution” S→−1/NS. This is a novel symmetry of CHL models that lies outside of the standard SL(2,ℤ)-symmetry of the parent theory, heterotic strings on T{sup 6}. For self-dual models this implies that the lattice of purely electric charges is N-modular, i.e. isometric to its dual up to a rescaling of its quadratic form by N. We verify this prediction by determining the lattices of electric and magnetic charges in all relevant examples. We also calculate certain BPS-saturated couplings and verify that they are invariant under the Fricke S-duality. For CHL models that are not self-dual, the strong coupling limit is dual to type IIA compactified on T{sup 6}/ℤ{sub N}, for some ℤ{sub N}-symmetry preserving half of the spacetime supersymmetries.
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
On T-duality transformations for the three-sphere
Directory of Open Access Journals (Sweden)
Erik Plauschinn
2015-04-01
Full Text Available We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting backgrounds turn out to be geometric in nature. To perform the duality transformations, we develop a novel procedure for non-abelian T-duality, which follows a route different compared to the known literature, and which highlights the underlying structure from an alternative point of view.
On T-duality transformations for the three-sphere
Energy Technology Data Exchange (ETDEWEB)
Plauschinn, Erik, E-mail: erik.plauschinn@pd.infn.it [Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova (Italy)
2015-04-15
We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting backgrounds turn out to be geometric in nature. To perform the duality transformations, we develop a novel procedure for non-abelian T-duality, which follows a route different compared to the known literature, and which highlights the underlying structure from an alternative point of view.
On Various R-duals and the Duality Principle
DEFF Research Database (Denmark)
Stoeva, Diana T.; Christensen, Ole
2016-01-01
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...... 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...
Duality as a gauge symmetry and topology change
Giveon, Amit
1993-01-01
Duality groups as (spontaneously broken) gauge symmetries for toroidal backgrounds, and their role in ($\\infty$-dimensional) underlying string gauge algebras are reviewed. For curved backgrounds, it is shown that there is a duality in the moduli space of WZNW sigma-models, that can be interpreted as a broken gauge symmetry. In particular, this duality relates the backgrounds corresponding to axially gauged abelian cosets $G/U(1)_a$, to vectorially gauged abelian cosets, $G/U(1)_v$. Finally, topology change in the moduli space of WZNW sigma-models is discussed.
Review of lattice supersymmetry and gauge-gravity duality
Energy Technology Data Exchange (ETDEWEB)
Joseph, Anosh [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics (DAMTP)
2015-12-15
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.
APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES
Institute of Scientific and Technical Information of China (English)
Amir KHOSRAVI; Morteza MIRZAEE AZANDARYANI
2014-01-01
In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.
Kim, Jungmin; Lee, Kimyeong
2015-01-01
We study the 2d N = 4 gauge theory descriptions of little strings on type II NS5- branes. The IIB strings on N NS5-branes are described by the N = (4,4) gauge theories, whose Higgs branch CFTs on U(N) instanton moduli spaces are relevant. The IIA strings are described by N = (4,4) circular A_{N-1} quiver theories, whose Coulomb branch CFTs are relevant. We study new N = (0,4) quiver gauge theories for the IIA strings, which make it easier to study some infrared observables. In particular, we show that the elliptic genera of the IIA / IIB strings precisely map to each other by T-duality.
Liouville mode in Gauge/Gravity Duality
Moskalets, Tatiana
2014-01-01
We establish solutions corresponding to AdS4 static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of 2D constant curvature space, the metric potential of internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of Gauge/Gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in presence of inhomogeneity on black hole horizons with planar, spherical and hyperbolic geometry. We discuss subtleties of the developed approach for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling into the experimentally relevant range. The obtained solutions are also extended to higher-dime...
Constructing Dualities from Quantum State Manifolds
van Zyl, H J R
2015-01-01
The thesis develops a systematic procedure to construct semi-classical gravitational duals from quantum state manifolds. Though the systems investigated are simple quantum mechanical systems without gauge symmetry many familiar concepts from the conventional gauge/gravity duality come about in a very natural way. The investigation of the low-dimensional manifolds link existing results in the $AdS_2/CFT_1$ literature. We are able to extend these in various ways and provide an explicit dictionary. The higher dimensional investigation is also concluded with a simple dictionary, but this dictionary requires the inclusion of many bulk coordinates. Consequently further work is needed to relate these results to existing literature. Possible ways to achieve this are discussed.
The duality of computation under focus
Curien, Pierre-Louis
2010-01-01
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the duality of computation. We use this kit to provide a term language for a presentation of LK (with conjunction, disjunction, and negation), and to transcribe cut elimination as (non confluent) rewriting. A key slogan here, which may appear here in print for the first time, is that commutative cut elimination rules are explicit substitution propagation rules. We then describe the focalised proof search discipline (in the classical setting), and narrow down the language and the rewriting rules to a confluent calculus (a variant of the second author's focalising system L). We then define a game of patterns and counterpatterns, leading us to a fully focalised finitary syntax for a synthetic presentation of classical logic, that provides a quotient on (focalised) proofs, abstracting ou...
Some Generalizations of Fedorchuk Duality Theorem -- II
Dimov, Georgi Dobromirov
2007-01-01
As it was shown in the first part of this paper, there exists a duality between the category DSkeLC (introduced there) and the category SkeLC of locally compact Hausdorff spaces and continuous skeletal maps. We describe here the subcategories of the category DSkeLC which are dually equivalent to the following eight categories: all of them have as objects the locally compact Hausdorff spaces and their morphisms are, respectively, the injective (respectively, surjective) continuous skeletal maps, the injective (resp., surjective) open maps, the injective (resp., surjective) skeletal perfect maps, the injective (resp., surjective) open perfect maps. The particular cases of these theorems for the full subcategories of the last four categories having as objects all compact Hausdorff spaces are formulated and proved. The DSkeLC-morphisms which are LCA-embeddings and the dense homeomorphic embeddings are characterized through their dual morphisms. For any locally compact space X, a description of the frame of all op...
Duality of Maximum Entropy and Minimum Divergence
Directory of Open Access Journals (Sweden)
Shinto Eguchi
2014-06-01
Full Text Available We discuss a special class of generalized divergence measures by the use of generator functions. Any divergence measure in the class is separated into the difference between cross and diagonal entropy. The diagonal entropy measure in the class associates with a model of maximum entropy distributions; the divergence measure leads to statistical estimation via minimization, for arbitrarily giving a statistical model. The dualistic relationship between the maximum entropy model and the minimum divergence estimation is explored in the framework of information geometry. The model of maximum entropy distributions is characterized to be totally geodesic with respect to the linear connection associated with the divergence. A natural extension for the classical theory for the maximum likelihood method under the maximum entropy model in terms of the Boltzmann-Gibbs-Shannon entropy is given. We discuss the duality in detail for Tsallis entropy as a typical example.
Distance Duality Relation from Strong Gravitational Lensing
Liao, Kai; Cao, Shuo; Biesiada, Marek; Zheng, Xiaogang; Zhu, Zong-Hong
2015-01-01
Under very general assumptions of metric theory of spacetime, photons traveling along null geodesics and photon number conservation, two observable concepts of cosmic distance, i.e. the angular diameter and the luminosity distances are related to each other by the so called distance duality relation (DDR) $D^L=D^A(1+z)^2$. Observational validation of this relation is quite important because any evidence of its violation could be a signal of new physics. In this letter we introduce a new method to test DDR based on strong gravitational lensing systems and supernovae Ia. Using a new compilation of strong lensing systems and JLA compilation of SNe Ia we found no evidence of DDR violation. However, not so much the final result but the method itself is worth attention, because unlike previously proposed techniques, it does not depend on prior assumptions concerning the details of cosmological model and galaxy cluster modelling.
Schur-Weyl Duality for Heisenberg Cosets
Creutzig, Thomas; Linshaw, Andrew R; Ridout, David
2016-01-01
Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C=\\text{Com}\\left( {H}, {V}\\right)$ be the coset of ${H}$ in ${V}$. Assuming that the representation categories of interest are vertex tensor categories in the sense of Huang, Lepowsky and Zhang, a Schur-Weyl type duality for both simple and indecomposable but reducible modules is proven. Families of vertex algebra extensions of ${C}$ are found and every simple ${C}$-module is shown to be contained in at least one ${V}$-module. A corollary of this is that if ${V}$ is rational and $C_2$-cofinite and CFT-type, and $\\text{Com}\\left( {C}, {V}\\right)$ is a rational lattice vertex operator algebra, then so is ${C}$. These results are illustrated with many examples and the $C_1$-cofiniteness of certain interesting classes of modules is established.
Duality of Health Promotion and Sustainable Development
DEFF Research Database (Denmark)
Pedersen, Kirsten Bransholm; Land, Birgit; Kjærgård, Bente
2015-01-01
sustainability and, vice versa, sustainability conditions health. Thus, to avoid unintended, negative effects the strategies directed towards sustainable development must be correlated with strategies for health promotion. The conceptual model is used to take a closer look at the complexities of food waste......A In this article we introduce the concept of duality of structures as our starting point for understanding the linkages between sustainability and health. We argue that the two concepts cannot be separated but must be understood as mutually dependent in the sense that health conditions...... reduction and how these strategies affect the prospects for promoting health and sustainable food production and consumption. Danish food waste reduction strategies are used as examples with references to selected policy documents on food waste reduction strategies launched by international organisations...
Duality in deformed coset fermionic models
Cabra, D C
1996-01-01
We study the SU(2)_k/U(1)-parafermion model perturbed by its first thermal operator. By formulating the theory in terms of a (perturbed) fermionic coset model we show that the model is equivalent to interacting WZW fields modulo free fields. In this scheme, the order and disorder operators of the Z_k parafermion theory are constructed as gauge invariant composites. We find that the theory presents a duality symmetry that interchanges the roles of the spin and dual spin operators. For two particular values of the coupling constant we find that the theory recovers conformal invariance and the gauge symmetry is enlarged. We also find a novel self-dual point.
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 ...
T-duality and $\\alpha'$-corrections
Marques, Diego
2015-01-01
We construct an $O(d,d)$ invariant universal formulation of the first-order $\\alpha'$-corrections of the string effective actions involving the dilaton, metric and two-form fields. Two free parameters interpolate between four-derivative terms that are even and odd with respect to a $Z_2$-parity transformation that changes the sign of the two-form field. The $Z_2$-symmetric model reproduces the closed bosonic string, and the heterotic string effective action is obtained through a $Z_2$-parity-breaking choice of parameters. The theory is an extension of the generalized frame formulation of Double Field Theory, in which the gauge transformations are deformed by a first-order generalized Green-Schwarz transformation. This deformation defines a duality covariant gauge principle that requires and fixes the four-derivative terms. We discuss the $O(d,d)$ structure of the theory and the (non-)covariance of the required field redefinitions.
Ketov, S V
1996-01-01
The (2,2) world-sheet supersymmetric string theory is discussed from the viewpoint of string/membrane unification. The effective field theory in the closed string target space is known to be the 2+2 dimensional (integrable) theory of self-dual gravity (SDG). A world-volume supersymmetrization of the Pleba'nski action for SDG naturally implies the maximal N=8 world-volume supersymmetry, while the maximal supersymmetrization of the dual covariant K"ahler-Lorentz-Chern-Simons action for SDG implies gauging a self-dual part of the super-Lorentz symmetry in 2+10 dimensions. The proposed OSp(32|1) supersymmetric action for the M-brane may be useful for a fundamental formulation of uncompactified F theory, with the self-duality being playing the central role both in the world-volume and in the target space of the M-brane.
Quark-hadron duality: pinched kernel approch
Dominguez, C A; Schilcher, K; Spiesberger, H
2016-01-01
Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark-hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to $s = 10\\; {\\mbox{GeV}^2}$ by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using $e^+ e^-$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.
Duality properties of indicatrices of knots
Adams, Colin; Hawkins, Katherine; Sia, Charmaine; Silversmith, Robert; Tshishiku, Bena
2012-01-01
The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.
Wave-Particle Duality in Classical Mechanics
Davydov, Alexander Y
2012-01-01
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after surprising discovery of "walkers" - droplets that bounce on a vertically vibrating bath of the same fluid and can form wave-particle symbiotic structures with the surface waves they generate. Macroscopic walkers were shown experimentally to exhibit particle and wave properties simultaneously. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to walkers, no constant inflow of energy is required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show that such quantum phenomena as p...
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.)
Gauge/String Duality in Confining Theories
Edelstein, J D; Edelstein, Jose D.; Portugues, Ruben
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, held in 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.
Wronskians, dualities and FZZT-Cardy branes
Chan, Chuan-Tsung; Niedner, Benjamin; Yeh, Chi-Hsien
2016-01-01
The resolvent operator plays a central role in matrix models. For instance, with utilizing the loop equation, all of the perturbative amplitudes including correlators, the free-energy and those of instanton corrections can be obtained from the spectral curve of the resolvent operator. However, at the level of non-perturbative completion, the resolvent operator is generally not sufficient to recover all the information from the loop equations. Therefore it is necessary to find a sufficient set of operators which provide the missing non-perturbative information. In this paper, we study generalized Wronskians of the Baker-Akhiezer systems as a manifestation of these new degrees of freedom. In particular, we derive their isomonodromy systems and then extend several spectral dualities to these systems. In addition, we discuss how these Wronskian operators are naturally aligned on the Kac table. Since they are consistent with the Seiberg-Shih relation, we propose that these new degrees of freedom can be identified ...
Holographic duality from random tensor networks
Hayden, Patrick; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao
2016-01-01
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit simple 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 obey the Ryu-Takayanagi entropy formula for all boundary regions, whether connected or not, a fact closely related to known properties of the multipartite entanglement of assistance. Moreover, we find that all boundary regions faithfully encode the physics of their entire bulk entanglement wedges, not just their smaller causal wedges. 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 bu...
Lefschetz-Pontrjagin duality for differential characters
Directory of Open Access Journals (Sweden)
REESE HARVEY
2001-06-01
Full Text Available A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a Lefschetz-Pontrjagin Duality Theorem, which asserts that the pairing given by (alpha, beta (alpha * beta [X] induces isomorphisms onto the smooth Pontrjagin duals. In particular, and are injective with dense range in the group of all continuous homomorphisms into the circle. A coboundary map is introduced which yields a long sequence for the character groups associated to the pair (X, X. The relation of the sequence to the duality mappings is analyzed.Uma teoria de caracteres diferenciais é aqui desenvolvida para variedades com bordo. Isto é feito tanto do ponto de vista de Cheeger-Simons como do deRham-Federer. O resultado central deste artigo é a formulação e a prova de um teorema da dualidade de Lefschetz-Pontrjagin, que afirma que o pareamento dado por (alfa,beta (alfa * beta [X] induz isomorfismos sobre os duais diferenciáveis de Pontrjagin. Em particular, e são injetivos com domínios densos no grupo de todos os homeomorfismos contínuos no círculo. Uma aplicação de cobordo é introduzida, a qual fornece uma sequência longa para os grupos de caracteres associados ao par ( X, X. A relação desta sequência com as aplicações de dualidade é analisada.
New Evidence for (0,2) Target Space Duality
Anderson, Lara B
2016-01-01
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.
New evidence for (0,2) target space duality
Anderson, Lara B.; Feng, He
2017-02-01
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.
A duality theorem of crossed coproduct for Hopf algebras
Institute of Scientific and Technical Information of China (English)
王栓宏
1995-01-01
A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).
Spinor-vector duality in heterotic SUSY vacua
Energy Technology Data Exchange (ETDEWEB)
Catelin-Jullien, Tristan [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231 Paris cedex 05 (France)], E-mail: catelin@lpt.ens.fr; Faraggi, Alon E. [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom)], E-mail: alon.faraggi@liv.ac.uk; Kounnas, Costas [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231 Paris cedex 05 (France)], E-mail: costas.kounnas@lpt.ens.fr; Rizos, John [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece)], E-mail: irizos@uoi.gr
2009-05-01
We elaborate on the recently discovered spinor-vector duality in realistic free fermionic heterotic vacua. We emphasize the interpretation of the freely-acting orbifolds carried out on the six internal dimensions as coordinate-dependent compactifications; they play a central role in the duality, especially because of their ability to break the right-moving superconformal algebra of the space-time supersymmetric heterotic vacua. These considerations lead to a simple and intuitive proof of the spinor-vector duality, and to the formulation of explicit rules to find the dual of a given model. We discuss the interest of such a duality, notably concerning the structure of the space of vacua of superstring theory.
Bosonisation and Duality Symmetry in the Soldering Formalism
Banerjee, R
1998-01-01
We develop a technique that solders the dual aspects of some symmetry. Using this technique it is possible to combine two theories with such symmetries to yield a new effective theory. Some applications in two and three dimensional bosonisation are discussed. In particular, it is shown that two apparently independent three dimensional massive Thirring models with same coupling but opposite mass signatures, in the long wavelegth limit, combine by the process of bosonisation and soldering to yield an effective massive Maxwell theory. Similar features also hold for quantum electrodynamics in three dimensions. We also provide a systematic derivation of duality symmetric actions and show that the soldering mechanism leads to a master action which is duality invariant under a bigger set of symmetries than is usually envisaged. The concept of duality swapping is introduced and its implications are analysed. The example of electromagnetic duality is discussed in details.
On Duality Symmetry in Charged P-Form Theories
Menezes, R; Menezes, Roberto; Wotzasek, Clovis
2004-01-01
We study duality transformation and duality symmetry in the the electromagnetic-like charged p-form theories. It is shown that the dichotomic characterization of duality groups as $Z_2$ or SO(2) remains as the only possibilities but are now present in all dimensions even and odd. This is a property defined in the symplectic sector of the theory both for massive and massless tensors. It is shown that the duality groups depend, in general, both on the ranks of the fields and on the dimension of the spacetime. We search for the physical origin of this two-fold property and show that it is traceable to the dimensional and rank dependence of the parity of certain operator (a generalized-curl) that naturally decomposes the symplectic sector of the action. These operators are only slightly different in the massive and in the massless cases but their physical origin are quite distinct.
A "fair sampling" perspective on an apparent violation of duality
Bolduc, Eliot; Miatto, Filippo M; Leuchs, Gerd; Boyd, Robert W
2014-01-01
In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited". [M. O. Scully, B.-G. Englert, and H. Walther. Nature, 351:111-116, 1991.] emphasized the importance of additional degrees of freedom in the context of complementarity. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work contributes to the explanation of previous experimental apparent violations of duality [R. Menzel, D. Puhlmann, A. Heuer, and W. P. Schleich. Proc. Natl. Acad. Sci., 109(24):9314-9319, 2012.] and opens up the way for novel experimental tests of duality.
Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function
Zhou, Da; He, Yang-Hui
2015-01-01
We study Ihara zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara zeta function to be the generating function for the generic superpotential of the gauge theory.
Matrix-model dualities in the collective field formulation
Andric, I
2005-01-01
We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field formulation, the duality is displayed in terms of the generators of the conformal group. The conformally invariant master Hamiltonian is constructed and we conjecture that the master Hamiltonian corresponds to the hermitian matrix model.
Duality quantum algorithm efficiently simulates open quantum systems.
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-28
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(d(3)) in contrast to O(d(4)) 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.
Duality quantum algorithm efficiently simulates open quantum systems
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-01
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.
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
Reggeon exchange from gauge/gravity duality
Giordano, M
2011-01-01
We perform the analysis of quark-antiquark Reggeon exchange in meson-meson scattering, in the framework of the gauge/gravity correspondence in a confining background. On the gauge theory side, Reggeon exchange is described as quark-antiquark exchange in the t channel between fast projectiles. The corresponding amplitude is represented in terms of Wilson loops running along the trajectories of the constituent quarks and antiquarks. The paths of the exchanged fermions are integrated over, while the "spectator" fermions are dealt with in an eikonal approximation. On the gravity side, we follow a previously proposed approach, and we evaluate the Wilson-loop expectation value by making use of gauge/gravity duality for a generic confining gauge theory. The amplitude is obtained in a saddle-point approximation through the determination near the confining horizon of a Euclidean "minimal surface with floating boundaries", i.e., by fixing the trajectories of the exchanged quark and antiquark by means of a minimisation ...
Seiberg duality versus hidden local symmetry
Abel, Steven
2012-01-01
It is widely believed that the emergent magnetic gauge symmetry of SQCD is analogous to a hidden local symmetry (HLS). We explore this idea in detail, deriving the entire (spontaneously broken) magnetic theory by applying the HLS formalism to spontaneously broken SU(N) SQCD. We deduce the K\\"ahler potential in the HLS description, and show that gauge and flavour symmetry are smoothly restored along certain scaling directions in moduli space. We propose that it is these symmetry restoring directions, associated with the R-symmetry of the theory, that allow full Seiberg duality. Reconsidering the origin of the magnetic gauge bosons as the rho-mesons of the electric theory, colour-flavour locking allows a simple determination of the parameter "a". Its value continuously interpolates between a=2 on the baryonic branch of moduli space - corresponding to "vector meson dominance" - and a=1 on the mesonic branch. Both limiting values are consistent with previous results in the literature. The HLS formalism is further...
A test for cosmic distance duality
Energy Technology Data Exchange (ETDEWEB)
Holanda, R.F.L.; Gonçalves, R.S.; Alcaniz, J.S., E-mail: holanda@on.br, E-mail: rsousa@on.br, E-mail: alcaniz@on.br [Departamento de Astronomia, Observatório Nacional, 20921-400, Rio de Janeiro - RJ (Brazil)
2012-06-01
Testing the cosmic distance duality relation (CDDR) constitutes an important task for cosmology and fundamental physics since any violation of it would be a clear evidence of new physics. In this paper, we propose a new test for the CDDR using only current measurements of the gas mass fraction of galaxy clusters from Sunyaev-Zeldovich (f{sub SZE}) and X-ray surface brightness (f{sub X−ray}) observations. We show that the relation between f{sub X−ray} and f{sub SZE} observations is given by f{sub SZE} = ηf{sub X−ray}, where η quantifies deviations from the CDDR. Since this latter expression is valid for the same object in a given galaxy cluster sample, the method proposed removes possible contaminations from different systematics error sources and redshift differences involved in luminosity and angular diameter distance measurements. We apply this cosmological model-independent methodology to the most recent f{sub X−ray} and f{sub SZE} data and show that no significant violation of the CDDR is found.
A test for cosmic distance duality
Holanda, R F L; Alcaniz, J S
2012-01-01
Testing the cosmic distance duality relation (CDDR) constitutes an important task for cosmology and fundamental physics since any violation of it would be a clear evidence of new physics. In this {\\it Letter}, we propose a new test for the CDDR using only measurements of the gas mass fraction of galaxy clusters from Sunyaev-Zeldovich ($f_{SZE}$) and X-ray surface brightness ($f_{X-ray}$) observations. We show that the relation between current $f_{X-ray}$ and $f_{SZE}$ observations is given by $f_{SZE}=\\eta f_{X-ray}$, where $\\eta$ quantifies deviations from the CDDR. Since this latter expression is valid for the same object in a given galaxy cluster sample, the method proposed removes possible contaminations from different systematics error sources and redshift differences involved in luminosity and angular diameter distance measurements. We apply this cosmological model-independent methodology to the most recent $f_{X-ray}$ and $f_{SZE}$ data and show that no significant violation of the CDDR is found.
Residues and duality for Cousin complexes
Lipman, J; Lipman, Joseph; Sastry, Pramathanath
1996-01-01
We construct a canonical pseudofunctor ^# on the category of finite-type maps of (say) connected noetherian universally catenary finite-dimensional separated schemes, taking values in the category of Cousin complexes. This pseudofunctor is a concrete approximation to the restriction of the Grothendieck Duality pseudofunctor ^! to the full subcategory of the derived category having Cohen-Macaulay complexes as objects (a subcategory equivalent to the category of Cousin complexes, once a codimension function has been fixed). Specifically, for Cousin complexes M and any scheme map f:X -> Y as above, there is a functorial derived-category map \\gamma: f^# M -> f^! M inducing a functorial isomorphism in the category of Cousin complexes f^# M \\iso E(f^! M) (where E is the Cousin functor). \\gamma itself is an isomorphism if the complex f^! M is Cohen-Macaulay--which will be so whenever the map f is Cohen-Macaulay or whenever the complex M is injective. Also, f^# takes residual (resp. injective) complexes on Y to resid...
Disentangling the $f(R)$ Duality
Broy, Benedict J; Westphal, Alexander
2015-01-01
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 $R^{n}$ with $1
Yang-Baxter deformations and string dualities
Energy Technology Data Exchange (ETDEWEB)
Matsumoto, Takuya [Institute for Advanced Research and Department of Mathematics, Nagoya University,Nagoya 464-8602 (Japan); Yoshida, Kentaroh [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan)
2015-03-25
We further study integrable deformations of the AdS{sub 5}×S{sup 5} superstring by following the Yang-Baxter sigma model approach with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). Deformed string backgrounds specified by r-matrices are considered as solutions of type IIB supergravity, and therefore the relation between gravitational solutions and r-matrices may be called the gravity/CYBE correspondence. In this paper, we present a family of string backgrounds associated with a classical r-matrices carrying two parameters and its three-parameter generalization. The two-parameter case leads to the metric and NS-NS two-form of a solution found by Hubeny-Rangamani-Ross [hep-th/0504034] and another solution in [arXiv:1402.6147]. For all of the backgrounds associated with the three-parameter case, the metric and NS-NS two-form are reproduced by performing TsT transformations and S-dualities for the undeformed AdS{sub 5}×S{sup 5} background. As a result, one can anticipate the R-R sector that should be reproduced via a supercoset construction.
Stringy horizons and generalized FZZ duality in perturbation theory
Giribet, Gaston
2017-02-01
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 [1]. 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.
Spinor-vector duality in N=2 heterotic string vacua
Energy Technology Data Exchange (ETDEWEB)
Faraggi, Alon E. [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom)], E-mail: faraggi@amtp.liv.ac.uk; Kounnas, Costas [Laboratoire Physique Theorique, Ecole Normale Superieure, F-75231 Paris 05 (France); Rizos, John [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece)
2008-08-11
Classification of the N=1 space-time supersymmetric fermionic Z{sub 2}xZ{sub 2} heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S{sub t}{r_reversible}V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z{sub 2} heterotic string models, which preserve N=2 space-time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S{sub t}{r_reversible}V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.
Extending Dualities to Trialities Deepens the Foundations of Dynamics
Smolin, Lee
2016-11-01
Dualities are often supposed to be foundational, but they may come into conflict with a strong form of background independence, which is the principle that the dynamical equations of a theory not depend on arbitrary, fixed, non-dynamical structures. This is because a hidden fixed structures is needed to define the duality transformation. Examples include a fixed, absolute notion of time, a fixed non-dynamical background geometry, or the metric of Hilbert space. We show that this conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, which have a natural triality symmetry. We show how breaking this triality symmetry by imposing different compactifications, which are expansions around fixed classical solutions, yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.
Spin duality in the nucleon: Measurements at Jefferson Lab Hall A
Energy Technology Data Exchange (ETDEWEB)
Nilanga Liyanage
2005-02-01
The current experimental status of quark-hadron duality is discussed with particular emphasis on separated longitudinal and transverse structure functions. In addition, current and future experiments, which could help elucidate the nature of duality, are briefly discussed.
4D/3D reduction of dualities: mirrors on the circle
Energy Technology Data Exchange (ETDEWEB)
Amariti, Antonio [LPTENS - UMR CNRS 8549,24, rue Lhomond, 75231 Paris (France); Forcella, Davide [Physique Théorique et Mathématique and International Solvay Institutes, ULB,C.P. 231, 1050 Bruxelles (Belgium); Klare, Claudius [IPHT, CEA/Saclay,91191 Gif-sur-Yvette (France); IHES,35, Route de Chartres, 91440 Bures-sur-Yvette (France); Orlando, Domenico [LPTENS - UMR CNRS 8549,24, rue Lhomond, 75231 Paris (France); IPT Ph. Meyer,24, rue Lhomond, 75231 Paris (France); Reffert, Susanne [ITP - AEC, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-10-08
We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a sector of interacting singlets, giving a unified mechanism for the brane reduction of dualities.
Kramers-Wannier duality applied to the boolean satifiability problem
Mitchell, Joe; Hsu, Benjamin; Galitski, Victor
2014-03-01
Kramers-Wannier duality, first considered in 1941, is an exact technique used in statistical mechanics to relate two models together through an order-disorder transformation, and thereby study their structure and critical phenomena. The boolean satisfiability problem is one of the most important problems in computer science, specifically complexity theory; it is the first proven NP-complete problem. Using a mapping to a multi-spin Ising model in the limit of zero temperature, we present an application of Kramers-Wannier duality to this problem. This results in a novel relationship between solving the boolean satisfiability counting problem and a different computational problem: listing the non-negative solutions to a particular system of linear integer equations. This mapping relates the complexity of the two problems. We discuss the generality of Kramers-Wannier duality and its possible application to other computational problems. This research was supported by NSF-CAREER award No. DMR-0847224 and Simons Foundation.
Spectral Duality Between Heisenberg Chain and Gaudin Model
Mironov, A; Runov, B; Zenkevich, Y; Zotov, A
2012-01-01
In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.
Duality and Topological Mass Generation in Diverse Dimensions
Wotzasek, C
2004-01-01
We shall discuss issues of duality and topological mass generation in diverse dimensions. Particular emphasis will be given to the mass generation mechanism from interference between self and anti self-dual components, as disclosed by the soldering formalism. This is a gauge embedding procedure derived from an old algorithm of second-class constraint conversion used by the author to approach anomalous gauge theories. The problem of classification of the electromagnetic duality groups, both massless and massive, that is closely related will be discussed. Particular attention will be paid to a new approach to duality based on the soldering embedding to tackle the problem of mass generation by topological mechanisms in arbitrary dimensions including the couplings to dynamical matter, nonlinear cases and nonabelian symmetries.
Trigonometric version of quantum-classical duality in integrable systems
Beketov, M; Zabrodin, A; Zotov, A
2015-01-01
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 correspondin...
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.
New localization mechanism and Hodge duality for q -form field
Fu, Chun-E.; Liu, Yu-Xiao; Guo, Heng; Zhang, Sheng-Li
2016-03-01
In this paper, we investigate the problem of localization and the Hodge duality for a q -form field on a p -brane with codimension one. By a general Kaluza-Klein (KK) decomposition without gauge fixing, we obtain two Schrödinger-like equations for two types of KK modes of the bulk q -form field, which determine the localization and mass spectra of these KK modes. It is found that there are two types of zero modes (the 0-level modes): a q -form zero mode and a (q -1 )-form one, which cannot be localized on the brane at the same time. For the n -level KK modes, there are two interacting KK modes, a massive q -form KK mode and a massless (q -1 )-form one. By analyzing gauge invariance of the effective action and choosing a gauge condition, the n -level massive q -form KK mode decouples from the n -level massless (q -1 )-form one. It is also found that the Hodge duality in the bulk naturally becomes two dualities on the brane. The first one is the Hodge duality between a q -form zero mode and a (p -q -1 )-form one, or between a (q -1 )-form zero mode and a (p -q )-form one. The second duality is between two group KK modes: one is an n -level massive q -form KK mode with mass mn and an n -level massless (q -1 )-form mode; another is an n -level (p -q )-form one with the same mass mn and an n -level massless (p -q -1 )-form mode. Because of the dualities, the effective field theories on the brane for the KK modes of the two dual bulk form fields are physically equivalent.
A Remark on Gelfand Duality for Spectral Triples
Bertozzini, Paolo; Lewkeeratiyutkul, Wicharn
2008-01-01
We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-C*-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in arXiv:math/0502583v1 into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.
Non-abelian T-duality, generalised geometry and holography
Macpherson, Niall T
2013-01-01
Recent progress which relates non-abelian T-duality of $\\mathcal{N}=1$ SuGra solutions to the powerful techniques of Generalised geometry is reviewed. It is shown that SU(3) structure solutions are mapped to SU(2) structures and the transformation rule of the corresponding pure spinors is presented. This constitutes an important step on the road towards the utility of the duality within holography, showing for example, how smeared sources must transform and so how to add flavour to the T-duals.
New Correlation Duality Relations for the Planar Potts Model
King, C.; Wu, F. Y.
2002-05-01
We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. We show that generally it is linear combinations of correlation functions, not the individual correlations, that are related by dualities. The method is illustrated in several non-trivial cases, and the relation to earlier results is explained. A graph-theoretical formulation of our results in terms of rooted dichromatic, or Tutte, polynomials is also given.
Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
Bjerrum-Bohr, N E J; Damgaard, Poul H; Feng, Bo
2016-01-01
We prove that the scattering equation formalism for Yang-Mills amplitudes can be used to make manifest the theory's color-kinematics duality. This is achieved through a concrete reduction algorithm which renders this duality manifest term-by-term. The reduction follows from the recently derived set of identities for amplitudes expressed in the scattering equation formalism that are analogous to monodromy relations in string theory. A byproduct of our algorithm is a generalization of the identities among gravity and Yang-Mills amplitudes.
Wave-particle duality in a Raman atom interferometer
Jia, Ai-Ai; Yang, Jun; Yan, Shu-Hua; Hu, Qing-Qing; Luo, Yu-Kun; Zhu, Shi-Yao
2015-08-01
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, P2 + V2 ≤ 1. Project supported by the National Natural Science Foundation of China (Grant No. 51275523) and the Special Research Found for the Doctoral Program of Higher Education, China (Grant No. 20134307110009).
Higher Derivative Brane Couplings from T-Duality
Becker, Katrin; Robbins, Daniel
2010-01-01
The Wess-Zumino coupling on D-branes in string theory is known to receive higher derivative corrections which couple the Ramond-Ramond potential to terms involving the square of the spacetime curvature tensor. Consistency with T-duality implies that the branes should also have four-derivative couplings that involve the NS-NS B-field. We use T-duality to predict some of these couplings. We then confirm these results with string worldsheet computations by evaluating disc amplitudes with insertions of one R-R and two NS-NS vertex operators.
A duality theorem by means of Riemann Stieltjes integral
Directory of Open Access Journals (Sweden)
Ottavio Caligaris
1993-05-01
Full Text Available Duality between the space of continuous functions and the space of bounded variations functions can be easily characterized by means of Riemann-Stieltjes integrals when we consider real valued functions defined, e.g., on [0,1]; here we give a self-contained exposition of Riemann-Stieltjes integration theory for functions which assumes values in infinite dimensional vector spaces and we show as the duality between the space of continuous functions and the space of bounded variation functions can be represented by means of such theory.
Vector optimization and monotone operators via convex duality recent advances
Grad, Sorin-Mihai
2014-01-01
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
Duality and conformal twisted boundaries in the Ising model
Grimm, U
2002-01-01
There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper symmetry of the model at criticality. Thus, at criticality, the duality-twisted Ising model is translationally invariant, similar to the more familiar cases of periodic and antiperiodic boundary conditions. The complete finite-size spectrum of the Ising quantum chain with this peculiar boundary condition is obtained.
Duality and Dimensional Reduction of 5D BF Theory
Amoretti, Andrea; Caruso, Giacomo; Maggiore, Nicola; Magnoli, Nicodemo
2013-01-01
A planar boundary introduced \\`a la Symanzik in the 5D topological BF theory, with the only requirement of locality and power counting, allows to uniquely determine a gauge invariant, non topological 4D Lagrangian. The boundary condition on the bulk fields is interpreted as a duality relation for the boundary fields, in analogy with the fermionization duality which holds in the 3D case. This suggests that the 4D degrees of freedom might be fermionic, although starting from a bosonic bulk theory. The method we propose to dimensionally reduce a Quantum Field Theory and to identify the resulting degrees of freedom can be applied to a generic spacetime dimension.
Duality invariance of s≥32 fermions in AdS
Directory of Open Access Journals (Sweden)
S. Deser
2014-11-01
Full Text Available We show that in D=4 AdS, s≥3/2 partially massless (PM fermions retain the duality invariances of their flat space massless counterparts. They have tuned ratios m2/M2≠0 that turn them into sums of effectively massless unconstrained helicity ±(s,⋯,32 excitations, shorn of the lowest (non-dual helicity ±12-rung and — more generally — of succeeding higher rung as well. Each helicity mode is separately duality invariant, like its flat space counterpart.
Geometric Constraints from Subregion Duality Beyond the Classical Regime
Akers, Chris; Leichenauer, Stefan; Levine, Adam
2016-01-01
Subregion duality in AdS/CFT implies certain constraints on the geometry: entanglement wedges must contain causal wedges, and nested boundary regions must have nested entanglement wedges. We elucidate the logical connections between these statements and the Quantum Focussing Conjecture, Quantum Null Energy Condition, Boundary Causality Condition, and Averaged Null Energy Condition. Our analysis does not rely on the classical limit of bulk physics, but instead works to all orders in \\(G\\hbar \\sim 1/N\\). This constitutes a nontrivial check on the consistency of subregion duality, entanglement wedge reconstruction, and holographic entanglement entropy beyond the classical regime.
Black hole thermodynamics, stringy dualities and double field theory
Arvanitakis, Alex S.; Blair, Chris D. A.
2017-03-01
We discuss black hole thermodynamics in the manifestly duality invariant formalism of double field theory (DFT). We reformulate and prove the first law of black hole thermodynamics in DFT, using the covariant phase space approach. After splitting the full O(D, D) invariant DFT into a Kaluza–Klein-inspired form where only n coordinates are doubled, our results provide explicit duality invariant mass and entropy formulas. We illustrate how this works by discussing the black string solution and its T-duals.
Black hole thermodynamics, stringy dualities and double field theory
Arvanitakis, Alex S
2016-01-01
We discuss black hole thermodynamics in the manifestly duality invariant formalism of double field theory (DFT). We reformulate and prove the first law of black hole thermodynamics in DFT, using the covariant phase space approach. After splitting the full O(D, D) invariant DFT into a Kaluza-Klein-inspired form where only n coordinates are doubled, our results provide explicit duality invariant mass and entropy formulas. We illustrate how this works by discussing the black fundamental string solution and its T-duals.
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.
Color-kinematic duality in ABJM theory without amplitude relations
Sivaramakrishnan, Allic
2017-01-01
We explicitly show that the Bern-Carrasco-Johansson color-kinematic duality holds at tree level through at least eight points in Aharony-Bergman-Jafferis-Maldacena theory with gauge group SU(N) × SU(N). At six points we give the explicit form of numerators in terms of amplitudes, displaying the generalized gauge freedom that leads to amplitude relations. However, at eight points no amplitude relations follow from the duality, so the diagram numerators are fixed unique functions of partial amplitudes. We provide the explicit amplitude-numerator decomposition and the numerator relations for eight-point amplitudes.
Lee, Taejin
2016-09-01
We study the dissipative Hofstadter model on a triangular lattice, making use of the O(2, 2; R) T-dual transformation of string theory. The O(2, 2; R) dual transformation transcribes the model in a commutative basis into the model in a noncommutative basis. In the zero-temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two-dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence relation, which identifies the points on the two-dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.
Pro-Torus Actions on Poincaré Duality Spaces
Indian Academy of Sciences (India)
Ali Özkurt; Doğan Dönmez
2006-08-01
In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if `torus’ is replaced by `pro-torus’.
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.
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...
Finite Temperature Maps in Vector/Higher Spin Duality
Jevicki, Antal; Suzuki, Kenta; Yoon, Junggi
We discuss the question of reconstructing higher spin bulk fields from finite temperature N-component vector models. This is done in the framework of thermofield quantum theory at Large N. A bi-local construction of connected dual space-times is accomplished, and issues related to the implementation of domain duality are discussed.
Piezoelectricity and Piezomagnetism: Duality in two-dimensional checkerboards
Fel, Leonid G.
2002-05-01
The duality approach in two-dimensional two-component regular checkerboards is extended to piezoelectricity and piezomagnetism. The relation between the effective piezoelectric and piezomagnetic moduli is found for a checkerboard with the p6'mm'-plane symmetry group (dichromatic triangle).
Non-uniform horizons in Gauge/Gravity Duality
Moskalets, T M
2015-01-01
In this communication, based on our paper http://arxiv.org/abs/1409.4186, we discuss a way of enhancing Gauge/Gravity Duality and response of a dual strongly coupled medium on placing the inhomogeneity on the gravity side.
Stringy horizons and generalized FZZ duality in perturbation theory
Giribet, Gaston
2016-01-01
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 ...
New Insights into Quantum Gravity from Gauge/gravity Duality
Engelhardt, Netta
2016-01-01
Using gauge/gravity duality, we deduce several nontrivial consequences of quantum gravity from simple properties of the dual field theory. These include: (1) a version of cosmic censorship, (2) restrictions on evolution through black hole singularities, and (3) the exclusion of certain cosmological bounces. In the classical limit, the latter implies a new singularity theorem.
New insights into quantum gravity from gauge/gravity duality
Engelhardt, Netta; Horowitz, Gary T.
2016-06-01
Using gauge/gravity duality, we deduce several nontrivial consequences of quantum gravity from simple properties of the dual field theory. These include: (1) a version of cosmic censorship, (2) restrictions on evolution through black hole singularities, and (3) the exclusion of certain cosmological bounces. In the classical limit, the latter implies a new singularity theorem.
Some Duality Results for Fuzzy Nonlinear Programming Problem
Sangeeta Jaiswal; Geetanjali Panda
2012-01-01
The concept of duality plays an important role in optimization theory. This paper discusses some relations between primal and dual nonlinear programming problems in fuzzy environment. Here, fuzzy feasible region for a general fuzzy nonlinear programming is formed and the concept of fuzzy feasible solution is defined. First order dual relation for fuzzy nonlinear programming problem is studied.
On Duality in the Born-Infeld Theory
Khoudeir, Adel; Parra, Yoan
1997-01-01
The $SL(2,R)$ duality symmetric action for the Born-Infeld theory in terms of two potentials, coupled with non-trivial backgroud fields in four dimensions is established. This construction is carried out in detail by analysing the hamiltonian structure of the Born-Infeld theory. The equivalence with the usual Born-Infeld theory is shown.
On domain-wall/QFT dualities in various dimensions
Behrndt, Klaus; Bergshoeff, Eric; Halbersma, Rein; Schaar, Jan Pieter van der
1999-01-01
We investigate domain-wall/quantum field-theory correspondences in various dimensions. Our general analysis covers not only the well studied cases in 10 and 11 dimensions, but also enables us to discuss new cases like a type I/heterotic 6-brane in 10 dimensions and domain-wall dualities in lower
Geometric Langlands Program and Dualities in Quantum Physics
2009-04-30
systems, such as the KdV hier- archy, to an affine analogue of the Langlands duality. We have conjectured that common eigenvalues of the mutually...the spectra of the quantum KdV Hamiltonians. (5) In the joint papers [2, 3] with B. Feigin and L. Rybnikov, we have studied the spectra of the
Softer Hard Scattering and Noncommutative Gauge-String Duality
Rey, S J; Rey, Soo-Jong; Yee, Jung-Tay
2003-01-01
We study exclusive scattering of `hadrons' at high energy and fixed angle in (nonconformal) noncommutative gauge theories. Via gauge-string duality, we show that the noncommutativity renders the scattering soft, leading to exponential suppression. The result fits with the picture that, in noncommutative gauge theory, fundamental parton contents constitute wee-partons only and `hadrons' are made out of open Wilson lines.
Spinor-Vector Duality in N=2 Heterotic String Vacua
Faraggi, Alon E; Rizos, John
2007-01-01
Classification of the N=1 space-time supersymmetric fermionic Z2XZ2 heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor--vector duality exists also in fermionic Z2 heterotic string models, which preserve N=2 space-time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t V duality map. We present a novel basis to generate the free fermionic models in which the ten dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non--trivial sectors, and due to the triality property of the SO(...
Resummation and S-duality in N=4 SYM
Beem, Christopher; Sen, Ashoke; van Rees, Balt C
2013-01-01
We consider the problem of resumming the perturbative expansions for anomalous dimensions of low twist, non-BPS operators in four dimensional N=4 supersymmetric Yang-Mills theories. The requirement of S-duality invariance imposes considerable restrictions on any such resummation. We introduce several prescriptions that produce interpolating functions on the upper half plane that are compatible with a subgroup of the full duality group. These lead to predictions for the anomalous dimensions at all points in the fundamental domain of the complex gauge coupling, and in particular at the duality-invariant values \\tau=i and \\tau=exp(i\\pi/3). For low-rank gauge groups, the predictions are compatible with the bounds derived by conformal bootstrap methods for these anomalous dimensions; within numerical errors, they are in good agreement with the conjecture that said bounds are saturated at a duality-invariant point. We also find that the anomalous dimensions of the lowest twist operators lie within an extremely narr...
Dualities in 3D large N vector models
Muteeb, Nouman; Zayas, Leopoldo A. Pando; Quevedo, Fernando
2016-05-01
Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large N limit. We first consider a fermionic U( N) vector model coupled to level k Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength F μν to vanish introducing a Lagrange multiplier Λ. Exchanging the order of integrations we obtain the bosonized theory with Λ as the propagating field using the large N rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar U ( N) vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large N limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large N limit. We also present a partial analysis at subleading order in large N and find that the duality does not generically hold at this level.
Dualities in 3D large N vector models
Energy Technology Data Exchange (ETDEWEB)
Muteeb, Nouman [The Abdus Salam International Centre for Theoretical Physics, ICTP,Strada Costiera 11, 34014 Trieste (Italy); SISSA,Via Bonomea 265, 34136 Trieste (Italy); Zayas, Leopoldo A. Pando [The Abdus Salam International Centre for Theoretical Physics, ICTP,Strada Costiera 11, 34014 Trieste (Italy); Michigan Center for Theoretical Physics, Department of Physics,University of Michigan, Ann Arbor, MI 48109 (United States); Quevedo, Fernando [The Abdus Salam International Centre for Theoretical Physics, ICTP,Strada Costiera 11, 34014 Trieste (Italy); DAMTP, CMS, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2016-05-09
Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large N limit. We first consider a fermionic U(N) vector model coupled to level k Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength F{sub μν} to vanish introducing a Lagrange multiplier Λ. Exchanging the order of integrations we obtain the bosonized theory with Λ as the propagating field using the large N rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar U(N) vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large N limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large N limit. We also present a partial analysis at subleading order in large N and find that the duality does not generically hold at this level.
Algebra of Observables and States for Quantum Abelian Duality
Capoferri, Matteo
2016-01-01
The study of dualities is a central issue in several modern approaches to quantum field theory, as they have broad consequences on the structure and on the properties of the theory itself. We call Abelian duality the generalisation to arbitrary spacetime dimension of the duality between electric and magnetic field in Maxwell theory. In the present thesis, in the framework of algebraic quantum field theory, the Abelian duality for quantum field theory on globally hyperbolic spacetime with compact Cauchy surface is tackled. Fistly, the algebra of observables is constructed. It is shown that it can be presented as the direct sum of three pre-symplectic Abelian groups, each corresponding to a different sector of the theory. As a consequence, it is possible to provide quantum states for the theory by building separate states on each direct summand. In particular, explicit examples in two and four dimensions are discussed thoroughly; a ground Hadamard state in a suitable sense is proved to exist for both of them. L...
Puzzles on the duality between heterotic and type IIA strings
Abe, M; Abe, Mitsuko; Sato, Masamichi
1999-01-01
We discuss the possibility of the extension of the duality between the webs of heterotic string and the type IIA string to Calabi-Yau 3-folds with another K3 fiber by comparing the dual polyhedron of Calabi-Yau 3-folds given by Candelas, Perevalov and Rajesh.
S-duality invariant dilaton couplings at order $\\alpha'^3$
Garousi, Mohammad R
2013-01-01
The Riemann curvature correction to the type II supergravity at eight-derivative level is given schematically as $(t_8t_8+{1}{8}\\eps_{10}\\eps_{10})R^4$ at tree-level. The replacement of the generalized Riemann curvature in $t_8t_8R^4$, proposed by Gross and Sloan, produces various NS-NS couplings which are invariant under T-duality. Recently, using the combination of S-duality and T-duality transformations on these couplings, we have found groups of couplings which are invariant under the S-duality transformation. In this paper, we have examined the couplings involving the dilaton with direct scattering amplitude calculations of four NS-NS vertex operators in the superstring theory and found exact agreement. The coupling $\\eps_{10}\\eps_{10}R^4$ is a total derivative term at four-field level. The $\\sigma$-model beta function approach implies the presence of this term at the tree-level. By examining the sphere-level scattering amplitude of five gravitons, we have also confirmed the presence of this term in the ...
On the Duality Mapping Sets in Orlicz Sequence Spaces
Institute of Scientific and Technical Information of China (English)
Bao Xiang WANG
2001-01-01
The criteria for the weak compactness of duality mapping sets J(x) = {f ∈ X*:
Topics On Ads/cft Duality And Holography
Lin, F
2000-01-01
This dissertation presents our study on various aspects of Maldacena's AdS/CFT duality and on a generalization of it from the point of view of holography. The AdS/CFT duality states that supergravity on anti-de Sitter (AdS) background is equivalent to a local conformal field theory (CFT) on the boundary at infinity of AdS space. One way to generalize the AdS/CFT duality is to turn on more background fields of supergravity such as the r-form fields. The bulk geometry is no longer AdS, and one finds that in the spirit of AdS/CFT duality, it corresponds to a nonconformal field theory with the radial position of the boundary as the energy scale and with the boundary at infinity as the ultraviolet fixed point. Moreover, one can derive the holographic renormalization group (RG) flows of the field theory from its gravity dual. A specific case of interest is the Neveu-Schwarz 2-form potential on the world volume of a D-brane, the resulting open-string low energy effective field theory has been shown to be a Yang-Mill...
Renormalization group flows in gauge-gravity duality
Murugan, Arvind
2016-01-01
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated with the breaking of supersymmetry. Chapter 5 contains new unpublished material on various instabilities of the weakly curved non-supersymmetric $AdS_4$ backgrounds of M-theory.
A D-induced duality and its applications
J. Brinkhuis (Jan); S. Zhang (Shuzhong)
2002-01-01
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
M-theory duality and BPS-extended supergravity
de Wit, Bernard
2001-01-01
We discuss toroidal compactifications of maximal supergravity coupled to an extended configuration of BPS states which transform consistently under the U-duality group. Under certain conditions this leads to theories that live in more than eleven spacetime dimensions, with maximal supersymmetry but only partial Lorentz invariance. We demonstrate certain features of this construction for the case of nine-dimensional N=2 supergravity.
Some remarks on defects and T-duality
DEFF Research Database (Denmark)
Sarkissian, Gor; Schweigert, Christoph
2009-01-01
conditions. We also exhibit a class of diagonal defects that induce a shift of the B-field. We finally study T-dualities for S1 -fibrations in the example of the Wess–Zumino–Witten model on SU(2) and lens spaces. Using standard techniques from D-branes, we derive from algebraic data in rational conformal...
Observables in the Guarino-Jafferis-Varela/CS-SYM duality
Araujo, Thiago R.; Nastase, Horatiu
2017-07-01
We study various semiclassical observables in the duality proposed by Guarino, Jafferis and Varela, between a warped AdS 4× squashed S 6 gravitational solution and a 3 dimensional N=2 SYM-{CS}_k conformal gauge theory, deformed from the maximal SU( N) N=8SYM . Baryonverticescorrespondingtoparticle-likebraneshaveunusualbehaviour with N and k and present strong evidence for a certain level-rank duality. Wilson loops and the anomalous dimensions of operators of high spin scale like ( N/k)3/2. The entanglement entropy behaves like in a usual CFT. Giant magnon operators obey the same law as in 4 dimensional N=4 SYM , and giant gravitons are also sub-determinant operators.
Duality and Superconvergence Relation in Supersymmetric Gauge Theories
Tachibana, M
1998-01-01
We investigate the phase structures of various N=1 supersymmetric gauge theories including even the exceptional gauge group from the viewpoint of superconvergence of the gauge field propagator. Especially we analyze in detail whether a new type of duality recently discovered by Oehme in $SU(N_c)$ gauge theory coupled to fundamental matter fields can be found in more general gauge theories with more general matter representations or not. The result is that in the cases of theories including matter fields in only the fundamental representation, Oehme's duality holds but otherwise it does not. In the former case, superconvergence relation might give good criterion to describe the interacting non-Abelian Coulomb phase without using some information from dual magnetic theory.
Forecasting constraints on the cosmic duality relation with galaxy clusters
Gonçalves, R. S.; Alcaniz, J. S.; Carvalho, J. C.; Holanda, R. F. L.
2015-01-01
One of the fundamental hypotheses in observational cosmology is the validity of the so-called cosmic distance-duality relation. In this paper, we perform Monte Carlo simulations based on the method developed in Holanda, Gonçalves, and Alcaniz [J. Cosmol. Astropart. Phys. 06 (2012) 022] to answer the following question: what is the number of galaxy clusters observations Ncrit needed to check the validity of this relation at a given confidence level? At 2 σ , we find that Ncrit should be increased at least by a factor of 5 relative to the current sample size if we assume the current observational uncertainty σobs . Reducing this latter quantity by a factor of 2, we show that the present amount of data would be already close to the required number to check the validity of the cosmic distance-duality relation at 2 σ .
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.
Generalized entropies and logarithms and their duality relations.
Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray
2012-11-20
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with these generalized entropies, making them useful for understanding distribution functions of non-Markovian or nonergodic complex systems. For such systems where the composability axiom is violated there exist only two ways to implement the maximum entropy principle, one using escort probabilities, the other not. The two ways are connected through a duality. Here we show that this duality fixes a unique escort probability, which allows us to derive a complete theory of the generalized logarithms that naturally arise from the violation of this axiom. We then show how the functional forms of these generalized logarithms are related to the asymptotic scaling behavior of the entropy.
Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
Mogull, Gustav
2015-01-01
The discovery of colour-kinematics duality has allowed great progress in our understanding of the UV structure of gravity. However, it has proven difficult to find numerators which satisfy colour-kinematics duality in certain cases. We discuss obstacles to building a set of such numerators in the context of the five-gluon amplitude with all helicities positive at two loops. We are able to overcome the obstacles by adding more loop momentum to our numerator to accommodate tension between the values of certain cuts and the symmetries of certain diagrams. At the same time, we maintain control over the size of our ansatz by identifying a highly constraining but desirable symmetry property of our master numerator. The resulting numerators have twelve powers of loop momenta rather than the seven one would expect from the Feynman rules.
Non-isometric T-duality from gauged sigma models
Chatzistavrakidis, Athanasios
2016-01-01
Local symmetries is one of the most successful themes in modern theoretical physics. Although they are usually associated to Lie algebras, a gradual increase of interest in more general situations where local symmetries are associated to groupoids and algebroids has taken place in recent years. On the other hand, dualities is another persistently interesting theme in modern physics. One of the most prominent examples is provided by target space duality in string theory. The latter, Abelian or not, is usually associated to the presence of isometries, which is however a very restrictive assumption. In this contribution we discuss some recent advances located at the intersection of the above two themes. Focusing on bosonic string sigma models we discuss certain gauged versions where (a) the invariance conditions on the background fields are much milder than the isometric case and (b) the gauge symmetry is generically associated to a Lie algebroid instead of just a Lie algebra. Furthermore we utilize such gauged ...
Quark-Hadron Duality in Neutron (3He) Spin Structure
Energy Technology Data Exchange (ETDEWEB)
Solvignon, Patricia; Liyanage, Nilanga; Chen, Jian-Ping; Choi, Seonho; Aniol, Konrad; Averett, Todd; Boeglin, Werner; Camsonne, Alexandre; Cates, Gordon; Chang, C.; Chang, C.C.; Chang, C.; Chang, C.C.; Chudakov, Eugene; Craver, Brandon; Cusanno, Francesco; Deur, Alexandre; Dutta, Dipangkar; Ent, Rolf; Feuerbach, Robert; Frullani, Salvatore; Gao, Haiyan; Garibaldi, Franco; Gilman, Ronald; Glashausser, Charles; Gorbenko, Viktor; Hansen, Jens-Ole; Higinbotham, Douglas; Ibrahim, Hassan; Jiang, Xiaodong; Jones, Mark; Kelleher, Aidan; Kelly, J.; Keppel, Cynthia; Kim, Wooyoung; Korsch, Wolfgang; Kramer, Kevin; Kumbartzki, Gerfried; LeRose, John; Lindgren, Richard; Ma, Bin; Margaziotis, Demetrius; Markowitz, Pete; McCormick, Kathy; Meziani, Zein-Eddine; Michaels, Robert; Moffit, Bryan; Monaghan, Peter; Munoz-Camacho, Carlos; Paschke, Kent; Reitz, Bodo; Saha, Arunava; Sheyor, Ran; Singh, Jaideep; Slifer, Karl; Sulkosky, Vince; Sulkosky, Vincent; Sulkosky, Vince; Sulkosky, Vincent; Tobias, William; Urciuoli, Guido; Wang, Kebin; Wijesooriya, Krishni; Wojtsekhowski, Bogdan; Woo, Seungtae; Yang, Jae-Choon; Zheng, Xiaochao; Zhu, Lingyan
2008-10-01
We present experimental results of the first high-precision test of quark-hadron duality in the spin-structure function g_1 of the neutron and $^3$He using a polarized 3He target in the four-momentum-transfer-squared range from 0.7 to 4.0 (GeV/c)^2. Global duality is observed for the spin-structure function g_1 down to at least Q^2 = 1.8 (GeV/c)^2 in both targets. We have also formed the photon-nucleon asymmetry A_1 in the resonance region for 3He and found no strong Q^2-dependence above 2.2 (GeV/c)^2.
String organization of field theories duality and gauge invariance
Feng, Y J; Feng, Y J; Lam, C S
1994-01-01
String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invari...
Quark-Hadron Duality in Neutron (3He) Spin Structure
Solvignon, P; Chen, J -P; Choi, Seonho; Aniol, K; Averett, T; Boeglin, W; Camsonne, A; Cates, G D; Chang, G; Chudakov, E; Craver, B; Cusanno, F; Deur, A; Dutta, D; Ent, R; Feuerbach, R; Frullani, S; Gao, H; Garibaldi, F; Gilman, R; Glashausser, C; Gorbenko, V; Hansen, O; Higinbotham, D W; Ibrahim, H; Jiang, X; Jones, M; Kelleher, A; Kelly, J; Keppel, C; Kim, W; Korsch, W; Krämer, K; Kumbartzki, G; LeRose, J J; Lindgren, R; Ma, B; Margaziotis, D J; Markowitz, P; McCormick, K; Meziani, Z -E; Michaels, R; Moffit, B; Monaghan, P; Camacho, C Munoz; Paschke, K; Reitz, B; Saha, A; Sheyor, R; Singh, J; Slifer, K; Sulkosky, V; Tobias, A; Urciuoli, G M; Wang, K; Wijesooriya, K; Wojtsekhowski, B; Woo, S; Yang, J -C; Zheng, X; Zhu, L
2008-01-01
We present experimental results of the first high-precision test of quark-hadron duality in the spin-structure function g_1 of the neutron and $^3$He using a polarized 3He target in the four-momentum-transfer-squared range from 0.7 to 4.0 (GeV/c)^2. Global duality is observed for the spin-structure function g_1 down to at least Q^2 = 1.8 (GeV/c)^2 in both targets. We have also formed the photon-nucleon asymmetry A_1 in the resonance region for 3He and found no strong Q^2-dependence above 2.2 (GeV/c)^2.
Background Independence and Duality Invariance in String Theory.
Hohm, Olaf
2017-03-31
Closed string theory exhibits an O(D,D) duality symmetry on tori, which in double field theory is manifest before compactification. I prove that to first order in α^{'} there is no manifestly background independent and duality invariant formulation of bosonic string theory in terms of a metric, b field, and dilaton. To this end I use O(D,D) invariant second order perturbation theory around flat space to show that the unique background independent candidate expression for the gauge algebra at order α^{'} is inconsistent with the Jacobi identity. A background independent formulation exists instead for frame variables subject to α^{'}-deformed frame transformations (generalized Green-Schwarz transformations). Potential applications for curved backgrounds, as in cosmology, are discussed.
Spectrum of a duality-twisted Ising quantum chain
Grimm, U
2002-01-01
The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.
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.)
Gauge Symmetry, T-Duality and Doubled Geometry
Hull, C M
2008-01-01
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.
Generalized entropies and logarithms and their duality relations
Hanel, Rudolf; Gell-Mann, Murray; 10.1073/pnas.1216885109
2012-01-01
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with these generalized entropies, making them useful for understanding distribution functions of non-Markovian or non-ergodic complex systems. For such systems where the composability axiom is violated there exist only two ways to implement the maximum entropy principle, one using escort probabilities, the other not. The two ways are connected through a duality. Here we show that this duality fixes a unique escort probability, which allows us to derive a complete theory of the generalized logarithms that naturally arise from the violation of this axiom. We then show how the functional forms of these generalized logarithms are related to the asymptotic scaling behavior of the entropy.
Observables in the Guarino-Jafferis-Varela/CS-SYM duality
Araujo, Thiago R
2016-01-01
We study various semiclassical observables in the duality proposed by Guarino, Jafferis and Varela, between a warped $AdS_4\\times$ squashed $S^6$ gravitational solution and a 3 dimensional ${\\cal N}=2$ SYM-CS$_k$ conformal gauge theory, deformed from the maximal $SU(N)$ ${\\cal N}=8$ SYM. Baryon vertices corresponding to particle-like branes have unusual behaviour with $N$ and $k$ and present strong evidence for a certain level-rank duality. Wilson loops and the anomalous dimensions of operators of high spin scale like $(N/k)^{3/2}$. The entanglement entropy behaves like in a usual CFT. Giant magnon operators obey the same law as in 4 dimensional ${\\cal N}=4$ SYM, and giant gravitons are also sub-determinant operators.
Pure gravities via color-kinematics duality for fundamental matter
Energy Technology Data Exchange (ETDEWEB)
Johansson, Henrik [Theory Division, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Ochirov, Alexander [Institut de Physique Théorique, CEA-Saclay, F-91191 Gif-sur-Yvette cedex (France)
2015-11-06
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 the supergravity theories. 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.
Les Houches Lectures on Fields, Strings and Duality
Dijkgraaf, R.
1997-01-01
Notes of my 14 `lectures on everything' given at the 1995 Les Houches school. An introductory course in topological and conformal field theory, strings, gauge fields, supersymmetry and more. The presentation is more mathematical then usual and takes a modern point of view stressing moduli spaces, duality and the interconnectedness of the subject. An apocryphal lecture on BPS states and D-branes is added.
Duality Theorem and Drinfeld Double in Braided Tensor Categories
Institute of Scientific and Technical Information of China (English)
Shouchuan Zhang
2003-01-01
Let (C, ( ), I, C) be a braided tensor category. For a finite Hopf algebra H in c with CH, H = C-1 H,H, the duality theorem is shown, i.e.,(R#H)#H^* ≌ R( ) (H-( )H^*)as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in c.
Superspace with manifest T-duality from type II superstring
Hatsuda, Machiko; Siegel, Warren
2014-01-01
A superspace formulation of type II superstring background with manifest T-duality symmetry is presented. This manifestly T-dual formulation is constructed in a space spanned by two sets of nondegenerate super-Poincare algebra. Supertorsion constraints are obtained from consistency of the kappa-symmetric Virasoro constraints. All superconnections and vielbein fields are solved in terms of a prepotential which is one of the vielbein components. AdS5xS5 background is explained in this formulation.
Gravitational Duality in MacDowell-Mansouri Gauge Theory
García-Compéan, H; Ramírez, C
1998-01-01
Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show that an analogous procedure allows to find the dual action to the gauge theory of gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\\Theta$ term.
Complementary variational principle and duality in mathematical programming.
Chan, W. L.; Leininger, G. G.; Farison, J. B.
1973-01-01
The relationship between the complementary variational principle and duality in mathematical programming is demonstrated through a geometric approach in a Hilbert space setting. A necessary and sufficient condition for the existence of such a principle is given in the case of a convex functional constrained by linear dynamics. Its relationship to the Kuhn-Tucker saddle point theory is indicated. Applications to various programming and control problems are discussed.
The Onset of Quark-Hadron Duality in Pion Electroproduction
Navasardyan, T; Ahmidouch, A; Angelescu, T; Arrington, J; Asaturyan, R; Baker, O K; Benmouna, N; Bertoncini, C; Blok, H P; Bosted, P E; Breuer, H; Böglin, W; Christy, M E; Connell, S H; Cui, Y; Dalton, M M; Danagulyan, S; Day, D; Dodario, T; Dunne, J A; Dutta, D; Ent, R; Fenker, H C; Frolov, V V; Gan, L; Gaskell, D; Hafidi, K; Hinton, W; Holt, R J; Horn, T; Huber, G M; Hungerford, E; Jiang, X; Jones, M; Joo, K; Kalantarians, N; Kelly, J J; Keppel, C E; Khayari, N E; Kinney, E R; Kubarovski, V; Li, Y; Liang, Y; Malace, S; Markowitz, P; McGrath, E; McKee, P; Meekins, D G; Mkrtchyan, H; Moziak, B; Niculescu, G; Niculescu, I; Opper, A K; Ostapenko, T; Reimer, P; Reinhold, J; Roche, J; Rock, S E; Schulte, E; Segbefia, E; Smith, C; Smith, G R; Stoler, P; Tadevosyan, V; Tang, L; Ungaro, M; Uzzle, A; Vidakovic, S; Villano, A; Vulcan, W F; Wang, M; Warren, G; Wesselmann, F; Wojtsekhowski, B; Wood, S A; Xu, C; Yuan, L; Zheng, X; Zhu, H
2007-01-01
A large data set of charged-pion electroproduction from both hydrogen and deuterium targets has been obtained spanning the low-energy residual-mass region. These data conclusively show the onset of the quark-hadron duality phenomenon, as predicted for high-energy hadron electroproduction. We construct several ratios from these data to exhibit the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark-to- pion production mechanisms.
Lightcone dualities for curves in the lightcone unit 3-sphere
2013-01-01
In this paper, we consider the curves in the unit 3-sphere in the lightcone. The unit 3-sphere can be canonically embedded in the lightcone and de Sitter 4-space in Lorentz-Minkowski 5-space. We investigate these curves in the framework of the theory of Legendrian dualities between pseudo-spheres in Lorentz-Minkowski 5-space. (C) 2013 AIP Publishing LLC.
Topological partition function and string-string duality
Curio, G
1995-01-01
The evidence for string/string-duality can be extended from the matching of the vector couplings to gravitational couplings. In this note this is shown in the rank three example, the closest stringy analog of the Seiberg/Witten-setup, which is related to the Calabi-Yau WP^4_{1,1,2,2,6}(12). I provide an exact analytical verification of a relation checked by coefficient comparison to fourth order by Kaplunovsky, Louis and Theisen.
An introduction to the gauge/gravity duality
Maldacena, Juan M
2015-01-01
This chapter is a short introduction to the gauge/gravity duality or AdS/CFT correspondence. After reviewing some basic facts about anti-de-Sitter space, the author describes some of the basic elements of the dictionary between the two sides. The author relates fields in the interior to operators in the boundary. The author also relates the thermodynamics of the field theory to properties of black holes in the gravity solution.
Non-differentiable multiobjective mixed symmetric duality under generalized convexity
Directory of Open Access Journals (Sweden)
Li Jueyou
2011-01-01
Full Text Available Abstract The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions. Weak, strong and converse duality theorems are established for the model under some suitable assumptions of generalized convexity. Several special cases are also obtained. MS Classification: 90C32; 90C46.
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-d...
Duality between webs of heterotic and type II vacua
Candelas, Philip; Candelas, Philip; Font, Anamaria
1996-01-01
We discuss how transitions in the space of heterotic K3\\times T^2 compactifications are mapped by duality into transitions in the space of Type II compactifications on Calabi-Yau manifolds. We observe that perturbative symmetry restoration, as well as non-perturbative processes such as changes in the number of tensor multiplets, have at least in some cases a simple description in terms of the reflexive polyhedra of the Calabi-Yau manifolds.
Rowlands' Duality Principle: A Generalization of Noether's Theorem?
Karam, Sabah E.
This paper will examine a physical principle that has been used in making valid predictions and generalizes established conservation laws. In a previous paper it was shown how Rowlands' zero-totality condition could be viewed as a generalization of Newton's third law of motion. In this paper it will be argued that Rowlands' Duality Principle is a generalization of Noether's Theorem and that the two principles taken together are truly foundational principles that have tamed Metaphysics.
One-dimensional contact process: duality and renormalization.
Hooyberghs, J; Vanderzande, C
2001-04-01
We study the one-dimensional contact process in its quantum version using a recently proposed real-space renormalization technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates that are comparable in accuracy with the best known in the literature.
Quadratic 0-1 programming: Geometric methods and duality analysis
Liu, Chunli
The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems.
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...
U-duality transformation of membrane on Tn revisited
Hu, Shan; Li, Tianjun
2016-08-01
The problem with the U-duality transformation of membrane on T n is recently addressed in [arXiv:1509.02915]. We will consider the U-duality transformation rule of membrane on T n × R. It turns out that winding modes on T n should be taken into account, since the duality transformation may bring the membrane configuration without winding modes into the one with winding modes. With the winding modes added, the membrane worldvolume theory in lightcone gauge is equivalent to the n + 1 dimensional super-Yang-Mills (SYM) theory in {tilde{T}}^n , which has SL(2 , Z) × SL(3 , Z) and SL(5 , Z) symmetries for n = 3 and n = 4, respectively. The SL(2 , Z) × SL(3 , Z) transformation can be realized classically, making the on-shell field configurations transformed into each other. However, the SL(5 , Z) symmetry may only be realized at the quantum level, since the classical 5 d SYM field configurations cannot form the representation of SL(5 , Z).
Fermionic T-duality in fermionic double space
Nikolic, Bojan
2016-01-01
In this article we offer the interpretation of the fermionic T-duality of the type II superstring theory in double space. We generalize the idea of double space doubling the fermionic sector of the superspace. In such doubled space fermionic T-duality is repersented as permutation of the fermionic coordinates $\\theta^\\alpha$ and $\\bar\\theta^\\alpha$ with the corresponding fermionic T-dual ones, $\\vartheta_\\alpha$ and $\\bar\\vartheta_\\alpha$, respectively. Demanding that T-dual transformation law has the same form as inital one, we obtain the known form of the fermionic T-dual NS-R i R-R background fields. Fermionic T-dual NS-NS background fields are obtained under some assumptions. We conclude that only symmetric part of R-R field strength and symmetric part of its fermionic T-dual contribute to the fermionic T-duality transformation of dilaton field and analyze the dilaton field in fermionic double space. As a model we use the ghost free action of type II superstring in pure spinor formulation in approximation...
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.
Fermionic T-duality in fermionic double space
Nikolić, B.; Sazdović, B.
2017-04-01
In this article we offer the interpretation of the fermionic T-duality of the type II superstring theory in double space. We generalize the idea of double space doubling the fermionic sector of the superspace. In such doubled space fermionic T-duality is represented as permutation of the fermionic coordinates θα and θbarα with the corresponding fermionic T-dual ones, ϑα and ϑbarα, respectively. Demanding that T-dual transformation law has the same form as initial one, we obtain the known form of the fermionic T-dual NS-R and R-R background fields. Fermionic T-dual NS-NS background fields are obtained under some assumptions. We conclude that only symmetric part of R-R field strength and symmetric part of its fermionic T-dual contribute to the fermionic T-duality transformation of dilaton field and analyze the dilaton field in fermionic double space. As a model we use the ghost free action of type II superstring in pure spinor formulation in approximation of constant background fields up to the quadratic terms.
BPS States in the Duality Web of the Omega deformation
Hellerman, Simeon; Reffert, Susanne
2013-01-01
In this note, we study different limits of an Omega-deformed (2,0) six-dimensional gauge theory realized in a M-theory fluxtrap background. Via a chain of dualities, we connect the Omega-deformed SYM to a new four-dimensional gauge theory which we refer to as the reciprocal gauge theory. This theory has several properties in common with Liouville field theory, such as its gauge coupling b^2 =\\epsilon_2 / \\epsilon_1, and its behavior under S-duality. Finally, we realize the BPS states on the SYM side of the AGT correspondence and follow them along the chain of dualities. In the fluxtrap frame, we are dealing with two distinct types of states localized in different radial positions, while in the reciprocal frame, we find single states carrying both charges localized in one place which appear to be perturbatively stable. Our microscopic picture of the small-b limit exhibits semiclassically BPS bound states, which are not visible at the level of the partition function.
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...
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.
Trigonometric version of quantum-classical duality in integrable systems
Beketov, M.; Liashyk, A.; Zabrodin, A.; Zotov, A.
2016-02-01
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.
Higher S-dualities and Shephard-Todd groups
Cecotti, Sergio
2015-01-01
Seiberg and Witten have shown that in N=2 SQCD with $N_f=2N_c=4$ the S-duality group PSL(2,Z) acts on the flavor charges, which are weights of Spin(8), by triality. There are other N=2 SCFTs in which SU(2) SYM is coupled to strongly-interacting non-Lagrangian matter: their matter charges are weights of $E_6$, $E_7$ and $E_8$ instead of Spin(8). The S-duality group PSL(2,Z) acts on these weights: what replaces Spin(8) triality for the $E_6,E_7,E_8$ root lattices? In this paper we answer the question. The action on the matter charges of (a finite central extension of) PSL(2,Z) factorizes trough the action of the exceptional Shephard--Todd groups $G_4$ and $G_8$ which should be seen as complex analogs of the usual triality group $\\mathfrak{S}_3\\simeq \\mathrm{Weyl}(A_2)$. Our analysis is based on the identification of S-duality for SU(2) gauge SCFTs with the group of automorphisms of the cluster category of weighted projective lines of tubular type.
Fair sampling perspective on an apparent violation of duality
Bolduc, Eliot; Leach, Jonathan; Miatto, Filippo M.; Leuchs, Gerd; Boyd, Robert W.
2014-01-01
In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that “the simultaneous observation of wave and particle behavior is prohibited” [Scully MO, Englert B-G, Walther H (1991) Nature 351:111–116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior generally corresponds to the acquisition of which-path information by means of coupling the paths to a measuring device or part of their environment. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work gives insight into a possible mechanism for obtaining simultaneous high which-path information and high-visibility fringes in a single experiment. Further, our results introduce previously unidentified avenues for experimental tests of duality. PMID:25114237
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
New dualities from orientifold transitions Part II: string theory
García-Etxebarria, Iñaki; Heidenreich, Ben; Wrase, Timm
2013-10-01
We present a string theoretical description, given in terms of branes and orientifolds wrapping vanishing cycles, of the dual pairs of gauge theories analyzed in [1]. Based on the resulting construction we argue that the duality that we observe in field theory is inherited from S-duality of type IIB string theory. We analyze in detail the complex cone over the zeroth del Pezzo surface and discuss an infinite family of orbifolds of flat space. For the del Pezzo case we describe the system in terms of large volume objects, and show that in this language the duality can be understood from the strongly coupled behavior of the O7+ plane, which we analyze using simple F-theory considerations. For all cases we also give a different argument based on the existence of appropriate torsional components of the 3-form flux lattice. Along the way we clarify some aspects of the description of orientifolds in the derived category of coherent sheaves, and in particular we discuss the important role played by exotic orientifolds — ordinary orientifolds composed with auto-equivalences of the category — when describing orientifolds of ordinary quiver gauge theories.
半群分次环上的Morita对偶%Morita Duality of Semigroup Graded Rings
Institute of Scientific and Technical Information of China (English)
张子龙; 侯波; 李艳梅
2008-01-01
This paper studies Morita duality of semigroup-graded rings,and discusses an equivalence between duality functors of graded module category and bigraded himodules.An important result is obtained:A semigroup bigraded R-A-bimodule Q defines a semigroup graded Morita duality if and only if Q is gr-faithfully balanced and Ref(RQ),Ref(QA) is closed under graded submodules and graded quotients.
$L^2$ Serre Duality on Domains in Complex Manifolds and Applications
Chakrabarti, Debraj
2010-01-01
An $L^2$ version of the Serre duality on domains in complex manifolds involving duality of Hilbert space realizations of the $\\overline{\\partial}$-operator is established. This duality is used to study the solution of the $\\overline{\\partial}$-equation with prescribed support. Applications are given to $\\overline{\\partial}$-closed extension of forms, as well to Bochner-Hartogs type extension of CR functions.
Spectral dualities in XXZ spin chains and five dimensional gauge theories
Mironov, A; Runov, B; Zenkevich, Y; Zotov, A
2013-01-01
Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for q-->1, i.e. when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.
Supersymmetry and non-Abelian T-duality in type II supergravity
Kelekci, Özgür; Macpherson, Niall T; Colgáin, Eoin Ó
2014-01-01
We study the effect of T-duality on supersymmetry in the context of type II supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we demonstrate that the Killing spinor equations before and after T-duality can be mapped up to the Kosmann spinorial Lie derivative, which guarantees supersymmetry is preserved upon vanishing. As a byproduct, we give closed expressions for SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and comment on specific examples of T-dual geometries, including a novel AdS3 geometry with large N = (4,4) superconformal symmetry.
On powercounting in perturbative quantum gravity theories through color-kinematic duality
Boels, Rutger H.; Isermann, Reinke Sven
2013-06-01
The standard argument why gravity is not renormalisable relies on direct powercounting of Feynman graphs to estimate the degree of UV divergence. In several (highly) supersymmetric examples the actual divergences have been shown to be considerably better. In these examples the improvement follows from a conjectured duality between color and kinematics. In this paper we initiate the systematic study of quite general powercounting under the assumption that color-kinematic duality exists. The main technical tool is a reformulation of the duality in terms of linear maps, modulo subtleties at loop level mostly inherent to the duality. This tool may have wider applications in both gauge and gravity theories, up to resolution of the subtleties. Here it is first applied to the large Britto-Cachazo-Feng-Witten (BCFW) shift behavior of gravity integrands constructed through the duality. Assuming color-kinematic duality and reasonable technical requirements hold these shifts are shown to be independent of loop order. This is a new quantitative measure for massive cancellations with respect to the Feynman graph expression. More speculatively, the same approach is then applied to provide estimates of the overall degree of UV divergence in quite general gravity theories, assuming the duality exists. The manifest cancellations obtained in these estimates depends on the exact implementation of the duality at loop level, especially on graph topology. The developed arguments apply to all multiplicity. Finally, some evidence for the duality to all loop orders is provided from an analysis of BCFW shifts of gauge theory integrands through Feynman graphs.
Dualities and Curved Space Partition Functions of Supersymmetric Theories
Agarwal, Prarit
In this dissertation we discuss some conjectured dualities in supersymmetric field theories and provide non-trivial checks for these conjectures. A quick review of supersymmetry and related topics is provided in chapter 1. In chapter 2, we develop a method to identify the so called BPS states in the Hilbert space of a supersymmetric field theory (that preserves at least two real supercharges) on a generic curved space. As an application we obtain the superconformal index (SCI) of 4d theories. The large N SCI of quiver gauge theories has been previously noticed to factorize over the set of extremal BPS mesonic operators. In chapter 3, we reformulate this factorization in terms of the zigzag paths in the dimer model associated to the quiver and extend the factorization theorem of the index to include theories obtained from D-branes probing orbifold singularities. In chapter 4, we consider the dualities in two classes of 3 dimensional theories. The first class consist of dualities of certain necklace type Chern-Simons (CS) quiver gauge theories. A non trivial check of these dualities is provided by matching their squashed sphere partition functions. The second class consists of theories whose duals are described by a collection of free fields. In such cases, due to mixing between the superconformal R-symmetry and accidental symmetries, the matching of electric and magnetic partition functions is not straightforward. We provide a prescription to rectify this mismatch. In chapter 5, we consider some the N = 1 4d theories with orthogonal and symplectic gauge groups, arising from N = 1 preserving reduction of 6d theories on a Riemann surface. This construction allows us to dual descriptions of 4d theories. Some of the dual frames have no known Lagrangian description. We check the dualities by computing the anomaly coefficients and the superconformal indices. We also give a prescription to write the index of the theory obtained by reduction of 6d theories on a three
String theory and the 4D/3D reduction of Seiberg duality. A Review
Amariti, Antonio; Reffert, Susanne
2016-01-01
We review the reduction of four-dimensional N=1 Seiberg duality to three dimensions focusing on the D brane engineering approach. We start with an overview of four-dimensional Seiberg duality for theories with various types of gauge groups and matter content both from a field-theoretic and a brane engineering point of view. Then we describe two families of N=2 three-dimensional dualities, namely Giveon-Kutasov-like and Aharony-like dualities. The last part of our discussion is devoted to the 4D/3D reduction of the dualities studied above. We discuss both the analysis at finite radius, crucial for preserving the duality in the dimensional reduction, and the zero-size limit that must be supported by a real mass flow and a Higgsing, which can differ case by case. We show that this mechanism is reproduced in the brane description by T-duality, supplying a unified picture for all the different cases. As a bonus we show that this analysis provides a brane description for Aharony-like dualities.
On S-duality in (2+1)-Chern-Simons Supergravity
García-Compéan, H; Ramírez, C; Sabido, M
2001-01-01
Strong/weak coupling duality in Chern-Simons supergravity is studied. It is argued that this duality can be regarded as an example of superduality. The use of supergroup techniques for the description of Chern-Simons supergravity greatly facilitates the analysis.
Duality for Ext-groups and extensions of discrete series for graded Hecke algebras
Chan, K.Y.
2016-01-01
In this paper, we study extensions of graded affine Hecke algebra modules. In particular, based on an explicit projective resolution on graded affine Hecke algebra modules, we prove a duality result for Ext-groups. This duality result with an Ind-Res resolution gives an algebraic proof of the fact t
T-duality and actions for non-BPS D-branes
Bergshoeff, EA; de Roo, M; de Wit, TC; Eyras, E; Panda, S; Wit, Tim C. de
2000-01-01
We employ T-duality to restrict the tachyon dependence of effective actions for non-BPS D-branes. For the Born-Infeld part the criteria of T-duality and supersymmetry are satisfied by a simple extension of the D-brane Born-Infeld action.
In search of balance – managing the dualities of HRM: an overview of the issues
Boselie, J.P.P.E.F.; 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.
An N/4 fixed-point duality quantum search algorithm
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops automatically.This algorithm uses a constant non-unitary operator,and requires N/4 steps on average(N is the number of data from the database) to locate the marked state.The implementation of this algorithm in a usual quantum computer is also demonstrated.
Fracton topological order, generalized lattice gauge theory, and duality
Vijay, Sagar; Haah, Jeongwan; Fu, Liang
2016-12-01
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, pointlike topological excitations, and subextensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical tool set for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.
Integrability from 2d N=(2,2) Dualities
Yamazaki, Masahito
2015-01-01
We study integrable models in the context of the recently discovered Gauge/YBE correspondence, where the Yang-Baxter equation is promoted to a duality between two supersymmetric gauge theories. We study flavored elliptic genus of 2d $\\mathcal{N}=(2,2)$ quiver gauge theories, which theories are defined from statistical lattices regarded as quiver diagrams. Our R-matrices are written in terms of theta functions, and simplifies considerably when the gauge groups at the quiver nodes are Abelian. We also discuss the modularity properties of the R-matrix, reduction of 2d index to 1d Witten index, and string theory realizations of our theories.
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...
Holographic duality and the resistivity of strange metals
Davison, Richard A; Zaanen, Jan
2013-01-01
We present a strange metal, described by a holographic duality, which reproduces the famous linear resistivity of the normal state of the copper oxides, in addition to the linear specific heat. This holographic metal reveals a simple and general mechanism for producing such a resistivity, which requires only quenched disorder and a strongly interacting quantum critical state. The key is the minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and therefore is important for the electrical transport. This mechanism produces a resistivity proportional to the electronic entropy.
Modular Schrödinger equation and dynamical duality.
Garbaczewski, Piotr
2008-09-01
We discuss quite surprising properties of the one-parameter family of modular nonlinear Schrödinger equations [G. Auberson and P. G. Sabatier, J. Math. Phys. 35, 4028 (1994)]. We develop a unified theoretical framework for this family. Special attention is paid to the emergent dual time evolution scenarios which, albeit running in the real time parameter of the pertinent nonlinear equation, in each considered case may be mapped among each other by means of a suitable analytic continuation-in-time procedure. This dynamical duality is characteristic for nondissipative quantum motions and their dissipative (diffusion-type processes) partners, and naturally extends to classical motions in confining and scattering potentials.
A Vector Non-abelian Chern-Simons Duality
García-Compéan, H; Ramírez, C
2002-01-01
Abelian Chern-Simons gauge theory it is known to possess a `S-self-dual' action where its coupling constant k is inverted i.e. k goes to 1/k. Here a vector non-abelian duality it is found in the pure non-abelian Chern-Simons action at the classical level. The procedure is given explicitly for the gauge group SU(2), but it is valid for any compact Lie group. The dimensional reduction of the dual Chern-Simons action to two-dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature.
Takesaki-Takai Duality Theorem in Hilbert C*-Modules
Institute of Scientific and Technical Information of China (English)
Mao Zheng GUO; Xiao Xia ZHANG
2004-01-01
In this paper, we generalize the Takesaki-Takai duality theorem in Hilbert C*-modules;that is to say, if (H, V, U) is a Kac-system, where H is a Hilbert space, V is a multiplicative unitary operator on H (×) H and U is a unitary operator on H, and if E is an (j)-compatible Hilbert (A)-module,then E × (j∧) × (j) (≌) E (×) K(H), where K(H) is the set of all compact operators on H, and (j) and (j) are Hopf C*-algebras corresponding to the Kac-system (H, V, U).
S-duality in N = 1 orientifold SCFTs
Energy Technology Data Exchange (ETDEWEB)
Garcia-Etxebarria, Inaki [Max Planck Institute for Physics, Munich (Germany); Heidenreich, Ben [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2017-03-15
We present a general solution to the problem of determining all S-dual descriptions for a specific (but very rich) class of N = 1 SCFTs. These SCFTs are indexed by decorated toric diagrams, and can be engineered in string theory by probing orientifolds of isolated toric singularities with D3 branes. The S-dual phases are described by quiver gauge theories coupled to specific types of conformal matter which we describe explicitly. We illustrate our construction with many examples, including S-dualities in previously unknown SCFTs. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Error bound results for convex inequality systems via conjugate duality
Bot, Radu Ioan
2010-01-01
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via one convex inequality and extend the achieved results, by making use of a celebrated scalarization function, to convex inequality systems expressed by means of a general vector function. We also propose a second approach for guaranteeing the existence of global error bounds of the latter, which meanwhile sharpens the classical result of Robinson.
On the concept of local parton-hadron duality
Energy Technology Data Exchange (ETDEWEB)
Dokshitzer, Yu.L.; Khoze, V.A.; Troyan, S.I. (Lund Univ. (Sweden). Dept. of Theoretical Physics AN SSSR, Leningrad (USSR). Inst. Yadernoj Fiziki)
1991-10-01
In the last decade jet physics has been intensively studied at both e{sup +}e{sup -} and hadronic colliders. With the start of LEP activity a wealth of new data has become available. They show that the global features of hadronic jets systems (multiplicities, angular patterns of particle flows, inclusive energy spectra etc), calculated at the parton level, agree very well with the measured ones. This convincingly demonstrates the dominant role of the perturbative phase of jet evolution and strongly supports the hypothesis of local parton-hadron duality. (author).
Ergodic theory and the duality principle on homogeneous spaces
Gorodnik, Alexander
2012-01-01
We prove mean and pointwise ergodic theorems for the action of a discrete lattice subgroup in a connected algebraic Lie group, on infinite volume homogeneous algebraic varieties. Under suitable necessary conditions, our results are quantitative, namely we establish rates of convergence in the mean and pointwise ergodic theorems, which can be estimated explicitly. Our results give a precise and in most cases optimal quantitative form to the duality principle governing dynamics on homogeneous spaces. We illustrate their scope in a variety of equidistribution problems.
Dualities in all-order finite N=1 gauge theories
Energy Technology Data Exchange (ETDEWEB)
Karch, A.; Luest, D.; Zoupanos, G. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
1998-09-28
We search for dual gauge theories of all-loop finite, N=1 supersymmetric gauge theories. It is shown how to find explicitly the dual gauge theories of almost all chiral, N=1, all-loop finite gauge theories, while several models have been discussed in detail, including a realistic finite SU(5) unified theory. Out of our search only one all-loop, N=1 finite SO(10) theory emerges, so far, as a candidate for exhibiting also S-duality. (orig.) 60 refs.
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.)
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....
Duality, Monodromy and Integrability of Two Dimensional String Effective Action
Das, A; Melikyan, A; Das, Ashok
2002-01-01
The monodromy matrix, ${\\hat{\\cal M}}$, is constructed for two dimensional tree level string effective action. The pole structure of ${\\hat{\\cal M}}$ is derived using its factorizability property. It is found that the monodromy matrix transforms non-trivially under the non-compact T-duality group, which leaves the effective action invariant and this can be used to construct the monodromy matrix for more complicated backgrounds starting from simpler ones. We construct, explicitly, ${\\hat{\\cal M}}$ for the exactly solvable Nappi-Witten model, both when B=0 and $B\
First Numerical Implementation of the Loop-Tree Duality Method
Buchta, Sebastian
2015-01-01
The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level amplitudes, which gives rise to the idea of treating them simultaneously in a common Monte Carlo. Initially introduced for one-loop scalar integrals, the applicability of the LTD has been expanded to higher order loops and Feynman graphs beyond simple poles. For the first time, a numerical implementation relying on the LTD was realized in the form of a computer program that calculates one-loop scattering amplitudes. We present details on the employed contour deformation as well as results for scalar and tensor integrals.
Numerical implementation of the Loop-Tree Duality method
Buchta, Sebastian; Draggiotis, Petros; Rodrigo, German
2015-01-01
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 present explicit results for scalar integrals with up to five external legs (pentagons) and tensor integrals with up to six legs (hexagons). The LTD method features an excellent performance independently of the number of external legs.
Quark-Hadron Duality for the Pion: a Phenomenological Study
Energy Technology Data Exchange (ETDEWEB)
Wally Melnitchouk
2002-08-01
We explore the relationship between exclusive and inclusive electromagnetic scattering from the pion, focusing on the transition region at intermediate Q{sup 2}. Combining Drell-Yan data on the leading twist quark distribution in the pion with a model for the resonance region at large x, we calculate QCD moments of the pion structure function over a range of Q{sup 2}, and quantify the role of higher twist corrections. Using a parameterization of the pion elastic form factor and phenomenological models for the pi --> p transition form factor, we test the extent to which local duality may be valid for the pion.
S^3/Z_n partition function and dualities
Imamura, Yosuke
2012-01-01
We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle points with different holonomies. An appropriate choice of the phase of each contribution is essential to obtain the partition function. We determine the relative phases in the holonomy sum in a few examples by using duality to non-gauge theories. In the case of odd n the phase factors can be absorbed by modifying a single function appearing in the partition function.
Duality and helicity: the photon wave function approach
Elbistan, M.; Horváthy, P. A.; Zhang, P.-M.
2017-08-01
The photon wave equation proposed in terms of the Riemann-Silberstein vector is derived from a first-order Dirac/Weyl-type action principle. It is symmetric w.r.t. duality transformations, but the associated Noether quantity vanishes. Replacing the fields by potentials and using instead a quadratic Klein-Gordon-type Lagrangian allows us to recover the double-Chern-Simons expression of conserved helicity and is shown to be equivalent to recently proposed alternative frameworks. Applied to the potential-modified theory the Dirac/Weyl-type approach yields again zero conserved charge, whereas the Klein-Gordon-type approach applied to the original setting yields Lipkin's ;zilch;.
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.
Arthur Wigan and The Duality of the Mind.
Clarke, B
1987-01-01
It is not easy to see a simple outline in the progress of the idea of duality, because it did not develop evenly or reach the stage of general acceptance. From the seventeenth century there were shifts in some of the basic assumptions about how the brain and mind functioned, and there are some useful markers along the way to an era of more systematic studies. Descartes is the most convenient base. He had earlier firmly separated mind and matter in his philosophy, and is still chiefly known for that. But at the end of his life (1649) he tried to reconcile them by the device of a specific 'seat of the soul' in the brain through which information passed between brain and mind. Symmetry of the operation of the hemispheres was assumed. This theory had currency into the eighteenth century. At the end of that century Franz Gall of Austria and France was assigning discrete faculties to numerous parts of the brain on no strong evidence, and nothing the double form of the brain, without claiming independent action of the hemispheres. Hewett Watson in 1836 discussed duality more directly than had been the case before, and Arthur Wigan in 1844 asserted the duality of the mind roundly and treated the two hemispheres, not consistently, as two independent brains. He was not satisfied with independence, however, and tried various ways of allowing for joint action by the two sides of the brain, as well as for substitution, with one side having the power to act on behalf of both in cases of disease or injury. He also considered that one hemisphere, usually the left, was generally dominant; but he did not see the two hemispheres as differently constituted. Recognition of differentiation of function between the two sides came chiefly out of the largely French discussions, in the 1820s and after, about the location--frontal or not--of 'language', and out of the work and arguments of the middle of the century. Broca's left frontal language centre became widely known, though its
A Geometric Approach to Massive p-form Duality
Arias, P J; Pérez-Mosquera, J C; Arias, Pio J.; Leal, Lorenzo; Perez-Mosquera, Jean Carlos
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 non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables. For the Proca model its geometric representation is constructed from two Self-Dual representations by direct product.
Concepts in Gauge Theory Leading to Electric--Magnetic Duality
2000-01-01
Gauge theory, which is the basis of all particle physics, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. In this short lecture course I shall try to give an introduction to these concepts, both from the physical and mathematical points of view. Then I shall show how these considerations lead to a nonabelian generalization of the well-known electric--magnetic duality in electromagnetism. I shall end by sketching some of the man...
Symmetries of the Schrodinger Equation and Algebra/Superalgebra Duality
Energy Technology Data Exchange (ETDEWEB)
Toppan, Francesco
2014-12-15
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)
Impact of Duality Violations on Spectral Sum Rule Analyses
Cata, O
2007-01-01
Recent sum rule analyses on the two-point correlator have led to significant discrepancies in the values found for the OPE condensates, most dramatically in the dimension eight condensate and to a lesser extent in the dimension six one. Precise knowledge of these condensates is of relevance in kaon decays and therefore it seems mandatory to assess the actual impact of what is commonly neglected in spectral sum rules, most prominently the issue of duality violations. We will explicitly compute them in a toy model and show that they are a priori non-negligible.
Host defense peptides and their antimicrobial-immunomodulatory duality.
Steinstraesser, Lars; Kraneburg, Ursula; Jacobsen, Frank; Al-Benna, Sammy
2011-03-01
Host defence peptides (HDPs) are short cationic molecules produced by the immune systems of most multicellular organisms and play a central role as effector molecules of innate immunity. Host defence peptides have a wide range of biological activities from direct killing of invading pathogens to modulation of immunity and other biological responses of the host. HDPs have important functions in multiple, clinically relevant disease processes and their imbalanced expression is associated with pathology in different organ systems and cell types. Furthermore, HDPs are now evaluated as model molecules for the development of novel natural antibiotics and immunoregulatory compounds. This review provides an overview of HDPs focused on their antimicrobial-immunomodulatory duality.
T-duality transformation of gauged linear sigma model with F-term
Directory of Open Access Journals (Sweden)
Tetsuji Kimura
2014-10-01
Full Text Available We develop the duality transformation rules in two-dimensional theories in the superfield formalism. Even if the chiral superfield which we dualize involves an F-term, we can dualize it by virtue of the property of chiral superfields. We apply the duality transformation rule of the neutral chiral superfield to the N=(4,4 gauged linear sigma model for five-branes. We also investigate the duality transformation rule of the charged chiral superfield in the N=(4,4 gauged linear sigma model for the A1-type ALE space. In both cases we obtain the dual Lagrangians in the superfield formalism. In the low energy limit we find that their duality transformations are interpreted as T-duality transformations consistent with the Buscher rule.
T-duality Transformation of Gauged Linear Sigma Model with F-term
Kimura, Tetsuji
2014-01-01
We develop the duality transformation rules in two-dimensional theories in the superfield formalism. Even if the chiral superfield which we dualize is involved in F-term, we can convert the F-term to D-terms by virtue of the property of chiral superfields. We apply the duality transformation rule of the neutral chiral superfield to the ${\\cal N}=(4,4)$ gauged linear sigma model for five-branes. We also investigate the duality transformation rule of the charged chiral superfield in the ${\\cal N} = (4,4)$ gauged linear sigma model for the $A_1$-type ALE space. In both cases we obtain the dual Lagrangians in the superfield formalism. In the low energy limit we find that their duality transformations are interpreted as the T-duality transformations consistent with the Buscher rule.
A General Rate Duality of the MIMO Multiple Access Channel and the MIMO Broadcast Channel
Hunger, Raphael
2008-01-01
We present a general rate duality between the multiple access channel (MAC) and the broadcast channel (BC) which is applicable to systems with and without nonlinear interference cancellation. Different to the state-of-the-art rate duality with interference subtraction from Vishwanath et al., the proposed duality is filter-based instead of covariance-based and exploits the arising unitary degree of freedom to decorrelate every point-to-point link. Therefore, it allows for noncooperative stream-wise decoding which reduces complexity and latency. Moreover, the conversion from one domain to the other does not exhibit any dependencies during its computation making it accessible to a parallel implementation instead of a serial one. We additionally derive a rate duality for systems with multi-antenna terminals when linear filtering without interference (pre-)subtraction is applied and the different streams of a single user are not treated as self-interference. Both dualities are based on a framework already applied ...
Mixed type symmetric and self duality for multiobjective variational problems with support functions
Directory of Open Access Journals (Sweden)
Husain I.
2013-01-01
Full Text Available In this paper, a pair of mixed type symmetric dual multiobjective variational problems containing support functions is formulated. This mixed formulation unifies two existing pairs Wolfe and Mond-Weir type symmetric dual multiobjective variational problems containing support functions. For this pair of mixed type nondifferentiable multiobjective variational problems, various duality theorems are established under convexity-concavity and pseudoconvexity-pseudoconcavity of certain combination of functionals appearing in the formulation. A self duality theorem under additional assumptions on the kernel functions that occur in the problems is validated. A pair of mixed type nondifferentiable multiobjective variational problem with natural boundary values is also formulated to investigate various duality theorems. It is also pointed that our duality theorems can be viewed as dynamic generalizations of the corresponding (static symmetric and self duality of multiobjective nonlinear programming with support functions.
6d SCFTs, 5d Dualities and Tao Web Diagrams
Hayashi, Hirotaka; Lee, Kimyeong; Yagi, Futoshi
2015-01-01
We propose 5d descriptions of 6d ${\\cal N}=(1,0)$ superconformal field theories arising from Type IIA brane configurations with an $O8^-$-plane. We T-dualize the brane diagram along a compactification circle and obtain a 5-brane web diagram with two $O7^-$-planes. The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories. There are three sources which lead to the 5d dualities. One type comes from either resolving both or one of the two $O7^-$-planes. The two situations give us two different ways to read off a 5d gauge theory from essentially the same web diagram. The second type originates from different distributions of D5 or D7-branes, shifting the gauge group ranks of the 5d quiver theory. The last one comes from the 90 or 45 degree rotations of the 5-brane web diagram, which is a part of the $SL(2,\\mathbb{Z})$ duality of Type IIB string theory, leading to completely differen...
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Energy Technology Data Exchange (ETDEWEB)
Abłamowicz, Rafał, E-mail: rablamowicz@tntech.edu [Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, Tennessee 38505 (United States); Gonçalves, Icaro, E-mail: icaro.goncalves@ufabc.edu.br [Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP (Brazil); Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy)
2014-10-15
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Momentum dissipation and holographic transport without self-duality
Wu, Jian-Pin
2016-01-01
We implement the momentum dissipation introduced by spatial linear axionic fields in a holographic model without self-duality, broken by Weyl tensor coupling to Maxwell field, and study its response. It is found that for the positive Weyl coupling parameter $\\gamma>0$, the momentum dissipation characterizing by parameter $\\hat{\\alpha}$ drives the conformal field theory (CFT) described by Maxwell-Weyl system into the incoherent metallic phase with a dip, which is away from CFT. While for $\\gamma<0$, an oppositive scenario is found. Our present model provides a route toward the problem that which sign of $\\gamma$ is the correct description of the CFT of boson Hubbard model. In addition, we also investigate the DC conductivity, diffusion constant and susceptibility. We find that there is a specific value of $\\hat{\\alpha}$, for which these quantities are independent of $\\gamma$. But they are different from each other and so are not universal. Finally, the electromagnetic (EM) duality is also studied and we fin...
Duality Fixed Point and Zero Point Theorems and Applications
Directory of Open Access Journals (Sweden)
Qingqing Cheng
2012-01-01
Full Text Available The following main results have been given. (1 Let E be a p-uniformly convex Banach space and let T:E→E* be a (p-1-L-Lipschitz mapping with condition 0<(pL/c21/(p-1<1. Then T has a unique generalized duality fixed point x*∈E and (2 let E be a p-uniformly convex Banach space and let T:E→E* be a q-α-inverse strongly monotone mapping with conditions 1/p+1/q=1, 0<(q/(q-1c2q-1<α. Then T has a unique generalized duality fixed point x*∈E. (3 Let E be a 2-uniformly smooth and uniformly convex Banach space with uniformly convex constant c and uniformly smooth constant b and let T:E→E* be a L-lipschitz mapping with condition 0<2b/c2<1. Then T has a unique zero point x*. These main results can be used for solving the relative variational inequalities and optimal problems and operator equations.
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...
Gauge/String-Gravity Duality and Froissart Bound
Kang, K
2005-01-01
The gauge/string-gravity duality correspondence opened renewed hope and possibility to address some of the fundamental and non-perturbative QCD problems in particle physics, such as hadron spectrum and Regge behavior of the scattering amplitude at high energies. One of the most fundamental and long-standing problem is the high energy behavior of total cross-sections. According to a series of exhaustive tests by the COMPETE group, (1). total cross-sections have a universal Heisenberg behavior in energy corresponding to the maximal energy behavior allowed by the Froissart bound, i.e., $A + B ln^2 (s/s_0)$ with $B \\sim 0.32 mb$ and $s_0 \\sim 34.41 GeV^2$ for all reactions, and (2). the factorization relation among $\\sigma_{pp, even}, \\sigma_{\\gamma p}, and \\sigma_{\\gamma \\gamma}$ is well satisfied by experiments. I discuss the recent interesting application of the gauge/string-gravity duality of $AdS/CFT$ correspondence with a deformed background metric so as to break the conformal symmetry that can lead to the ...
Heterotic/heterotic duality in D=6,4
Aldazabal, G; Ibáñez, L E; Quevedo, Fernando
1996-01-01
We consider E_8\\times E_8 heterotic compactifications on K3 and K3\\times T^2. The idea of heterotic/heterotic duality in D=6 has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both E_8's. We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. Upon further toroidal compactification to D=4, we find that the duals in the DMW case correspond to N=2 models in which the \\beta-function of the different group factors verify {\\beta }_\\alpha=12, whereas the asymmetric solutions that we propose have {\\beta }_\\alpha=24. We check the consistency of these dualities by studying the different large T,S limits of the gauge kinetic function. Dual N...
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.)
The duality principle in the presence of postselection
Leach, Jonathan; Bolduc, Eliot; Miatto, Filippo M.; Piché, Kevin; Leuchs, Gerd; Boyd, Robert W.
2016-01-01
The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility of interference fringes and predictability of paths within a two-alternative system, which are bound by the inequality . However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e. measures that are conditioned on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. This work highlights some of the subtleties that one can encounter while interpreting familiar quantities such as which-alternative information and visibility. While we concentrated on an extreme example, it is of utmost importance to realise that such subtleties might also be present in cases where the results are not obviously violating an algebraic bound, making them harder (but not any less crucial) to detect.
Off-shell currents and color–kinematics duality
Directory of Open Access Journals (Sweden)
Pierpaolo Mastrolia
2016-02-01
Full Text Available We elaborate on the color–kinematics duality for off-shell diagrams in gauge theories coupled to matter, by investigating the scattering process gg→ss,qq¯,gg, and show that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduce to a color–kinematics violating term due to the contributions of sub-graphs only. Such anomaly vanishes when the four particles connected by the Jacobi relation are on their mass shell with vanishing squared momenta, being either external or cut particles, where the validity of the color–kinematics duality is recovered. We discuss the role of the off-shell decomposition in the direct construction of higher-multiplicity numerators satisfying color–kinematics identity in four as well as in d dimensions, for the latter employing the Four Dimensional Formalism variant of the Four Dimensional Helicity scheme. We provide explicit examples for the QCD process gg→qq¯g.
Open/closed string duality and relativistic fluids
Niarchos, Vasilis
2016-07-01
We propose an open/closed string duality in general backgrounds extending previous ideas about open string completeness by Ashoke Sen. Our proposal sets up a general version of holography that works in gravity as a tomographic principle. We argue, in particular, that previous expectations of a supergravity/Dirac-Born-Infeld (DBI) correspondence are naturally embedded in this conjecture and can be tested in a well-defined manner. As an example, we consider the correspondence between open string field theories on extremal D-brane setups in flat space in the large-N , large 't Hooft limit, and asymptotically flat solutions in ten-dimensional type II supergravity. We focus on a convenient long-wavelength regime, where specific effects of higher-spin open string modes can be traced explicitly in the dual supergravity computation. For instance, in this regime we show how the full Abelian DBI action arises from supergravity as a straightforward reformulation of relativistic hydrodynamics. In the example of a (2 +1 )-dimensional open string theory this reformulation involves an Abelian Hodge duality. We also point out how different deformations of the DBI action, related to higher-derivative corrections and non-Abelian effects, can arise in this context as deformations in corresponding relativistic hydrodynamics.
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
A duality web in 2 + 1 dimensions and condensed matter physics
Seiberg, Nathan; Senthil, T.; Wang, Chong; Witten, Edward
2016-11-01
Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in 2 + 1 dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For example, the long distance behavior of the 2 + 1-dimensional analog of QED with a single Dirac fermion (a theory known as U(1)1/2) is identified with the O(2) Wilson-Fisher fixed point. The gauged version of that fixed point with a Chern-Simons coupling at level one is identified as a free Dirac fermion. The latter theory also has a dual version as a fermion interacting with some gauge fields. Assuming some of these dualities, other dualities can be derived. Our analysis resolves a number of confusing issues in the literature including how time reversal is realized in these theories. It also has many applications in condensed matter physics like the theory of topological insulators (and their gapped boundary states) and the problem of electrons in the lowest Landau level at half filling. (Our techniques also clarify some points in the fractional Hall effect and its description using flux attachment.) In addition to presenting several consistency checks, we also present plausible (but not rigorous) derivations of the dualities and relate them to 3 + 1-dimensional S-duality.
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.
Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
Basu-Mallick, B; Hikami, K; Sen, D; Bondyopadhaya, Nilanjan; Hikami, Kazuhiro; Sen, Diptiman
2007-01-01
By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation.
Mross, David F.; Alicea, Jason; Motrunich, Olexei I.
2016-07-01
We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2 +1 ) dimensions (QED3 ) with N =1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED3 scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N =2 QED3 .
Duality in Landau-Zener-Stueckelberg potential curve crossing
Fujikawa, K; Fujikawa, Kazuo; Suzuki, Hiroshi
1997-01-01
It is pointed out that there exists an interesting strong and weak duality in the Landau-Zener-Stueckelberg potential curve crossing. A reliable perturbation theory can thus be formulated in the both limits of weak and strong interactions. It is shown that main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple (time-independent) perturbation theory without referring to Stokes phenomena. A kink-like topological object appears in the ``magnetic'' picture, which is responsible for the absence of the coupling constant in the prefactor of the Landau-Zener formula. It is also shown that quantum coherence in a double well potential is generally suppressed by the effect of potential curve crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.
M5-branes, orientifolds, and S-duality
Hwang, Yoonseok; Kim, Seok
2016-01-01
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 $S^5$ partition functions that correspond to the 6d (2,0) superconformal indices. Our SO(2N) index takes the form of the vacuum character of $\\mathcal{W}_D$ algebra in a special limit, supporting the $\\mathcal{W}$ 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 $S^5$.
Bosonization and Duality in Arbitrary Dimensions New Results
Cantcheff, M B
2003-01-01
A generic massive Thirring Model in three space-time dimensions exhibits a correspondence with a topologically massive bosonized gauge action associated to a self-duality constraint, and we write down a general expression to this relationship. We also generalize this structure to $d$ dimensions by adopting a doublet approach introduced recently. In particular, a non-conventional formulation of the bosonization technique in higher dimensions (in the spirit of $d=3$), is proposed and, as an application, we show how fermionic (Thirring-like) representations for especially interesting bosonic topologically massive models in four dimensions (such as Cremmer-Scherk-Kalb-Ramond and Born-Infeld-Kalb- Ramond) may be built up.
Duality in adiabatic level crossing Quantum coherence and complete reflection
Fujikawa, K; Fujikawa, Kazuo; Suzuki, Hiroshi
1997-01-01
A field dependent su(2) gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) level crossing problem. It is pointed out that weak and strong level crossing interactions are interchanged under this transformation, and thus realizing a naive strong and weak duality. A reliable perturbation theory is thus formulated in the both limits of weak and strong interactions. Main characteristics of the level crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double well potential is generally suppressed by the effect of level crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.
Reconstruct the Comic Distance Duality Relation by Gaussian Process
Zhang, Yi
2014-01-01
In this letter, the cosmic distance duality relation (CDDR) is reconstructed by gaussian process (GP) which is cosmological model independent. We will at least use GP two times to get a continuous $\\eta$ which denotes the deviation of the CDDR. The GP is needed to make the redshifts of the luminosity distance data (LD, $D_{L}$) and the angular diameter distance data (ADD, $D_{A}$) at the same point. Then, it is possible to construct the $\\eta$ sample. And, the GP is needed again to see the shape of the CDDR (or $\\eta$). The spherical sample of galaxy cluster (GC) which gives out the ADD data seems inconsistent with the CDDR. Our reconstructing results from the Union 2.1 and the elliptical sample of galaxy cluster show a nearly constant $\\eta$.
Forecasting constraints on the cosmic duality relation with galaxy clusters
Goncalves, R S; Carvalho, J C; Holanda, R F L
2013-01-01
One of the fundamental hypotheses in observational cosmology is the validity of the so-called cosmic distance-duality relation (CDDR). In this paper, we perform Monte Carlo simulations based on the method developed in Holanda, Goncalves & Alcaniz (2012) [JCAP 1206 (2012) 022] to answer the following question: what is the number of galaxy clusters observations N_{crit} needed to check the validity of this relation at a given confidence level? At 2\\sigma, we find that N_{crit} should be increased at least by a factor of 5 relative to the current sample size if we assume the current observational uncertainty \\sigma_{obs}. Reducing this latter quantity by a factor of 2, we show that the present number of data would be already enough to check the validity of the CDDR at 2\\sigma.
Lectures on Cohomology, T-Duality, and Generalized Geometry
Bouwknegt, P.
These are notes for lectures, originally entitled "Selected Mathematical Aspects of Modern Quantum Field Theory", presented at the Summer School "New Paths Towards Quantum Gravity", Holbæ k, Denmark, 10-16 May 2008. My aim for these lectures was to introduce a mixture of physics and mathematics postgraduate students into a selection of exciting new developments on the interface of mathematics and quantum field theory. This write-up covers three topics: (1) cohomology and differential characters, (2) T-duality, and (3) generalized geometry. The three chapters can be read, more or less, independent of each other, but there is a common central theme, namely the occurrence of a (local) 2-form gauge field in certain quantum fields theories, the so-called B-field, which plays a role analogous to the electromagnetic gauge field.
Penguins with charm and quark-hadron duality
Beneke, M.; Buchalla, G.; Neubert, M.; Sachrajda, C. T.
2009-06-01
The integrated branching fraction of the process B→ X s l + l - is dominated by resonance background from narrow charmonium states, such as B→ X s ψ→ X s l + l -, which exceeds the non-resonant charm-loop contribution by two orders of magnitude. The origin of this fact is discussed in view of the general expectation of quark-hadron duality. The situation in B→ X s l + l - is contrasted with charm-penguin amplitudes in two-body hadronic B decays of the type B→ π π, for which it is demonstrated that resonance effects and the potentially non-perturbative cbar{c} threshold region do not invalidate the standard picture of QCD factorization. This holds irrespective of whether the charm quark is treated as a light or a heavy quark.
Attouch-Th\\'era duality revisited: paramonotonicity and operator splitting
Bauschke, Heinz H; Hare, Warren L; Moursi, Walaa M
2011-01-01
The problem of finding the zeros of the sum of two maximally monotone operators is of fundamental importance in optimization and variational analysis. In this paper, we systematically study Attouch-Th\\'era duality for this problem. We provide new results related to Passty's parallel sum, to Eckstein and Svaiter's extended solution set, and to Combettes' fixed point description of the set of primal solutions. Furthermore, paramonotonicity is revealed to be a key property because it allows for the recovery of all primal solutions given just one arbitrary dual solution. As an application, we generalize the best approximation results by Bauschke, Combettes and Luke [J. Approx. Theory 141 (2006), 63-69] from normal cone operators to paramonotone operators. Our results are illustrated through numerous examples.
Revisiting the Distance Duality Relation using LOESS and SIMEX
Rana, Akshay; Mahajan, Shobhit; Mukherjee, Amitabha
2015-01-01
Interdependence of luminosity distance and angular diameter distance, shown by the distance duality relation (DDR) is very significant in observational Cosmology. Any deviation from this relation highlights the emergence of new physics. Our aim in this work is to check the consistency of this relation using a very efficient non-parametric method, LOESS with SIMEX. This technique avoids dependency on the cosmological model and works with a minimal set of assumptions. We use the Union 2.1 SNe Ia data for luminosity distance while the angular diameter distances are obtained from X-ray surface brightness and Sunyaev-Zeldovich (S-Z) effect measurement of galaxy clusters by assuming elliptical and spherical profiles. We find no evidence of deviation from {\\eta} = 1 and both geometries of galaxy clusters are fairly compatible within 1{\\sigma}.
Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
Bianchi, Marco S; Mauri, Andrea; Penati, Silvia; Santambrogio, Alberto
2011-01-01
For N=6 superconformal Chern-Simons-matter theories in three dimensions, by a direct superspace Feynman diagram approach, we compute the two-loop four-point scatteringa amplitude with external chiral matter fields. We find that the result is in perfect agreement with the two-loop result for a light-like four-polygon Wilson loop. This is a nontrivial evidence of the scattering amplitudes/Wilson loop duality in three dimensions. Moreover, both the IR divergent and the finite parts of our two-loop result agree with a BDS-like ansatz for all-loop amplitudes where the scaling function is given in terms of the N=4 SYM one, according to the conjectured Bethe equations for ABJM. Consequently, we are able to make a prediction for the four-loop correction to the amplitude. We also discuss the dual conformal invariance of the two-loop result.
Duality and hidden symmetries in interacting particle systems
Giardina, Cristian; Redig, Frank; Vafayi, Kiamars
2008-01-01
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. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.
Integrable Structure in SUSY Gauge Theories, and String Duality
Nam, S
1996-01-01
There is a close relation between duality in $N=2$ SUSY gauge theories and integrable models. In particular, the quantum moduli space of vacua of $N=2$ SUSY $SU(3)$ gauge theories coupled to two flavors of massless quarks in the fundamental representation can be related to the spectral curve of the Goryachev-Chaplygin top. Generalizing this to the cases with {\\it massive} quarks, and $N_f = 0,1,2$, we find a corresponding integrable system in seven dimensional phase space where a hyperelliptic curve appears in the Painlevé test. To understand the stringy origin of the integrability of these theories we obtain exact nonperturbative point particle limit of type II string compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of $SU(2)$ QCD with $N_f =1$ hypermultiplet.
Coupling a QFT to a TQFT and duality
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology,Pasadena, CA 91125 (United States); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)
2014-04-01
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On ℝ{sup 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{sup 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.
M5-branes, orientifolds, and S-duality
Hwang, Yoonseok; Kim, Joonho; Kim, Seok
2016-12-01
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 5 partition functions that correspond to the 6d (2 , 0) superconformal indices. Our SO(2 N ) index takes the form of the vacuum character of W_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 5.
Bulk Locality from Entanglement in Gauge/Gravity Duality
Lin, Jennifer
2015-01-01
Gauge/gravity duality posits an equivalence between certain strongly coupled quantum field theories and theories of gravity with negative cosmological constant in a higher number of spacetime dimensions. The map between the degrees of freedom on the two sides is non-local and incompletely understood. I describe recent work towards characterizing this map using entanglement in the QFT, where near the dual AdS boundary, the classical energy density at a point in the bulk is stored in the relative entropies of boundary subregions whose homologous minimal surfaces pass through the bulk point. I also derive bulk classical energy conditions near the AdS boundary from entanglement inequalities in the CFT. This is based on the paper [1] with Matilde Marcolli, Hirosi Ooguri and Bogdan Stoica. More generally, in recent years, there has appeared some evidence that quantum entanglement is responsible for the emergence of spacetime. I review and comment on the state of these developments.
Duality between noise and spatial resolution in linear systems.
Gureyev, Timur E; Nesterets, Yakov I; de Hoog, Frank; Schmalz, Gerd; Mayo, Sheridan C; Mohammadi, Sara; Tromba, Giuliana
2014-04-21
It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of phase-space volume that is invariant with respect to linear scaling of the point-spread function, and it cannot be made smaller than a certain positive absolute lower limit. A corresponding intrinsic "quality" characteristic is introduced and then evaluated for the cases of some popular imaging systems, including computed tomography, generic image convolution and phase-contrast imaging. It is shown that in the latter case the spatial resolution and the noise can sometimes be decoupled, potentially leading to a substantial increase in the imaging quality.
Constraining axionlike particles using the distance-duality relation
Tiwari, Prabhakar
2017-01-01
One of the fundamental results used in observational cosmology is the distance duality relation (DDR), which relates the luminosity distance, DL , with angular diameter distance, DA , at a given redshift z . We employ the observed limits of this relation to constrain the coupling of axionlike particles (ALPs) with photons. With our detailed 3 D ALP-photon mixing simulation in standard Λ CDM universe and latest DDR limits observed in Holanda and Barros [Phys. Rev. D 94, 023524 (2016)]., 10.1103/PhysRevD.94.023524 we limit the coupling constant gϕ≤6 ×10-13 GeV-1(n/G ⟨B ⟩Mpc ) for ALPs of mass ≤10-15 eV . The DDR observations can provide very stringent constraint on ALPs mixing in the future. Also any deviation in DDR can be conventionally explained as photons decaying to axions or vice-versa.
Penguins with Charm and Quark-Hadron Duality
Beneke, M; Neubert, M; Sachrajda, C T
2009-01-01
The integrated branching fraction of the process $B\\to X_s l^+l^-$ is dominated by resonance background from narrow charmonium states, such as $B\\to X_s\\psi\\to X_s l^+l^-$, which exceeds the non-resonant charm-loop contribution by two orders of magnitude. The origin of this fact is discussed in view of the general expectation of quark-hadron duality. The situation in $B\\to X_s l^+l^-$ is contrasted with charm-penguin amplitudes in two-body hadronic B decays of the type $B\\to\\pi\\pi$, for which it is demonstrated that resonance effects and the potentially non-perturbative $c\\bar c$ threshold region do not invalidate the standard picture of QCD factorization. This holds irrespective of whether the charm quark is treated as a light or a heavy quark.
Particle-Hole Duality in the Lowest Landau Level
Nguyen, Dung Xuan; Can, Tankut; Gromov, Andrey
2017-05-01
We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several nontrivial checks of the relations, including for the Jain states and their PH conjugates.
Electrodynamic duality and vortex unbinding in driven-dissipative condensates
Wachtel, G.; Sieberer, L. M.; Diehl, S.; Altman, E.
2016-09-01
We investigate the superfluid properties of two-dimensional driven Bose liquids, such as polariton condensates, using their long-wavelength description in terms of a compact Kardar-Parisi-Zhang (KPZ) equation for the phase dynamics. We account for topological defects (vortices) in the phase field through a duality mapping between the compact KPZ equation and a theory of nonlinear electrodynamics coupled to charges. Using the dual theory, we derive renormalization group equations that describe vortex unbinding in these media. When the nonequilibirum drive is turned off, the KPZ nonlinearity λ vanishes and the RG flow gives the usual Kosterlitz-Thouless (KT) transition. On the other hand, with nonlinearity λ >0 vortices always unbind, even if the same system with λ =0 is superfluid. We predict the finite-size scaling behavior of the superfluid stiffness in the crossover governed by vortex unbinding showing its clear distinction from the scaling associated with the KT transition.
Proving AGT conjecture as HS duality: Extension to five dimensions
Energy Technology Data Exchange (ETDEWEB)
Mironov, A., E-mail: mironov@itep.ru [Lebedev Physics Institute, Moscow (Russian Federation); ITEP, Moscow (Russian Federation); Morozov, A., E-mail: morozov@itep.ru [ITEP, Moscow (Russian Federation); Shakirov, Sh., E-mail: shakirov@math.berkeley.edu [Department of Mathematics, University of California, Berkeley, CA (United States); ITEP, Moscow (Russian Federation); Smirnov, A., E-mail: asmirnov@itep.ru [ITEP, Moscow (Russian Federation); MIPT, Dolgoprudny (Russian Federation)
2012-02-01
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 {beta}=1, i.e. for q=t in MacDonald's notation. For {beta}{ne}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.
Proving AGT conjecture as HS duality: extension to five dimensions
Mironov, A; Shakirov, Sh; Smirnov, A
2011-01-01
We extend the proof from arXiv:1012.3137, 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 trivial: 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 \\beta = 1, i.e. for q=t in MacDonald's notation. For \\beta\
T-Duality for Orientifolds and Twisted KR-Theory
Doran, Charles; Méndez-Diez, Stefan; Rosenberg, Jonathan
2014-08-01
D-brane charges in orientifold string theories are classified by the KR-theory of Atiyah. However, this is assuming that all O-planes have the same sign. When there are O-planes of different signs, physics demands a "KR-theory with a sign choice" which up until now has not been studied by mathematicians (with the unique exception of Moutuou, who did not have a specific application in mind). We give a definition of this theory and compute it for orientifold theories compactified on S 1 and T 2. We also explain how and why additional "twisting" is implemented. We show that our results satisfy all possible T-duality relationships for orientifold string theories on elliptic curves, which will be studied further in subsequent work.
Gluing Branes II: Flavour Physics and String Duality
Donagi, R
2011-01-01
Recently we discussed new aspects of degenerate brane configurations, which can appear in the context of heterotic strings, perturbative type II, or M/F-theory. Here we continue our study of degenerate brane configurations, focussing on two applications. First we show how the notion of gluing can be viewed as a tool to engineer flavour structures in F-theory and type IIb, such as models with bulk matter and with Yukawa textures arising from the holomorphic zero mechanism. We find that there is in principle enough structure to solve some of the major flavour problems without generating exotics. In particular, we show how this addresses the mu-problem, doublet/triplet splitting and proton decay. Secondly, we describe the Fourier-Mukai transform of heterotic monad constructions, which occur in the large volume limit of heterotic linear sigma model vacua. Degenerate structures again often appear. One may use this to explore strong coupling phenomena using heterotic/F-theory duality.
Duality invariance in Fayet-Iliopoulos gauged supergravity
Cacciatori, Sergio L; Rabbiosi, Marco
2016-01-01
We propose a geometric method to study the residual symmetries in $N=2$, $d=4$ $\\text{U}(1)$ Fayet-Iliopoulos (FI) gauged supergravity. It essentially involves the stabilization of the symplectic vector of gauge couplings (FI parameters) under the action of the U-duality symmetry of the ungauged theory. In particular we are interested in those transformations that act non-trivially on the solutions and produce scalar hair and dyonic black holes from a given seed. We illustrate the procedure for finding this group in general and then show how it works in some specific models. For the prepotential $F=-iX^0X^1$, we use our method to add one more parameter to the rotating Chow-Comp\\`ere solution, representing scalar hair.
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...
Exact self-duality in a modified Skyrme model
Ferreira, L. A.
2017-07-01
We propose a modification of the Skyrme model that supports a self-dual sector possessing exact non-trivial finite energy solutions. The action of such a theory possesses the usual quadratic and quartic terms in field derivatives, but the couplings of the components of the Maurer-Cartan form of the Skyrme model is made by a non-constant symmetric matrix, instead of the usual Killing form of the SU(2) Lie algebra. The introduction of such a matrix make the self-duality equations conformally invariant in three space dimensions, even though it may break the global internal symmetries of the original Skyrme model. For the case where that matrix is proportional to the identity we show that the theory possesses exact self-dual Skyrmions of unity topological charges.
De Sitter space in gauge/gravity duality
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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.
De Sitter space in gauge/gravity duality
Anguelova, Lilia; Suranyi, Peter; Wijewardhana, L. C. R.
2015-10-01
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 (A) dS 4 spacetime. Finally, we comment on the implications of our dS4 solutions for building gravity duals of Glueball Inflation.
De Sitter Space in Gauge/Gravity Duality
Anguelova, Lilia; Wijewardhana, L C Rohana
2014-01-01
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 dS_4 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 (A)dS_4 spacetime. Finally, we comment on the implications of our dS_4 solutions for building gravity duals of Glueball Inflation.
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.
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.
String duality transformations in $f(R)$ gravity from Noether symmetry approach
Capozziello, Salvatore; Vernieri, Daniele
2015-01-01
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 effective one-loop bosonic string theory of gravity 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.
O(d,d) duality transformations in F(R) theories of gravity
Gionti, Gabriele
2016-01-01
The argument of Hodge duality symmetry is introduced starting from the electromagnetic field. Introducing bosonic string theory, O(d,d) duality symmetry can be implemented when there exist d-symmetries, which allows one to write Hodge-dual fields. A tree-level effective gravitational action of bosonic string theory coupled with the dilaton field is considered. This theory inherits the Busher's duality of its parent string theory. The dilaton field can be recast into the Weyl's mode of the metric tensor in the Jordan frame. This maps the effective one-loop bosonic string theory of gravity into a Lagrangian of a f(R) function. Constraining this f(R)-Lagrangian on a FLRW metric and using Noether symmetries approach for extended theory of gravity, it is possible to show that the Lagrangian exibits a Gasperini-Veneziano duality symmetry.
Duality for Multitime Multiobjective Ratio Variational Problems on First Order Jet Bundle
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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.
Real Baum-Connes assembly and T-duality for torus orientifolds
Rosenberg, Jonathan
2015-03-01
We show that the real Baum-Connes conjecture for abelian groups, possibly twisted by a cocycle, explains the isomorphisms of (twisted) KR-groups that underlie all T-dualities of torus orientifold string theories.
Seiberg duality, quiver gauge theories, and Ihara’s zeta function
Zhou, Da; Xiao, Yan; He, Yang-Hui
2015-07-01
We study Ihara’s zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara’s zeta function to be the generating function for the generic superpotential of the gauge theory.
Hecke Operator and S-Duality of N=4 ADE Gauge Theory on K3
Sasaki, T
2003-01-01
We determine ${\\cal N}=4$ partition functions on K3 for some ADE gauge groups, on the assumption that they are holomorphic. Our partition functions satisfy the gap condition and Montonen-Olive duality at the same time, like the SU(N) partition functions of Vafa and Witten. As a result, we reveal a close relation between Hecke operator and S-duality of ${\\cal N}=4 ADE$ gauge theory on K3.
Marginal and non-commutative deformations via non-abelian T-duality
Hoare, Ben; Thompson, Daniel C.
2017-02-01
In this short article we develop recent proposals to relate Yang-Baxter sigmamodels and non-abelian T-duality. We demonstrate explicitly that the holographic spacetimes 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.
Marginal and non-commutative deformations via non-abelian T-duality
Hoare, Ben
2016-01-01
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)-$\\beta$-deformations and non-commutative deformations of ${\\cal N}=4$ super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
String Cosmological Solutions with O(d, d) Duality Symmetry and Matter Coupling
Institute of Scientific and Technical Information of China (English)
LI Bao-Lin; YAN Jun
2013-01-01
The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D =d + 1dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.
From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
Wu, Hong-Tu; Guo, Han-Ying
2008-01-01
By means of Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the de Sitter special relativity and their UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a complete Yang model at both classical and quantum level can be presented and there really exist Snyder's model, the dS special relativity and the duality.
Local Quark-Hadron Duality and Magnetic Form Factors of Bound Proton
Institute of Scientific and Technical Information of China (English)
WANG Hong-Min; ZHANG Ben-Ai
2005-01-01
We discuss the consequence of local duality for elastic scattering, and derive a model-independent equation between structure functions at x ～ 1 and elastic electromagnetic form factors. Then the electromagnetic form factors of proton are discussed using the quark-hadron duality theory. We also debate the form factor of proton in a bound state.It may be an effective approach to study the form factor of proton in media.
Duality and confinement in D=3 models driven by condensation of topological defects
Wotzasek, P G C; Wotzasek, Patricio and Gaete Clovis
2005-01-01
We study the interplay of duality and confinement in certain three-dimensional models induced by the condensation of topological defects. To this end we check for the confinement phenomenon, in both sides of the duality, using the static quantum potential within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy contains a linear term leading to the confinement of static probe charges.
Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems
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Jianke Zhang
2013-01-01
Full Text Available The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.
Algebraic K-theory and derived equivalences suggested by T-duality for torus orientifolds
Rosenberg, Jonathan
2016-01-01
We show that certain isomorphisms of (twisted) KR-groups that underlie T-dualities of torus orientifold string theories have purely algebraic analogues in terms of algebraic K-theory of real varieties and equivalences of derived categories of (twisted) coherent sheaves. The most interesting conclusion is a kind of Mukai duality in which the "dual abelian variety" to a smooth projective genus-1 curve over R with no real points is (mildly) noncommutative.
From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
Institute of Scientific and Technical Information of China (English)
WU Hong-Tu; HUANG Chao-Guang; GUO Han-Ying
2008-01-01
@@ By means of the Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the dS special relativity and their UV-IR duality. Starting from a dimensionless dS5-space in a (5+1)-dimensional Mink-space a complete Yang model at both classical and quantum level can be presented and there really exists Snyder's model, the dS special relativity and the duality.
Duality in massive spin 2 theories in 2+1 dimensions
Arias, Pio J
2009-01-01
The equations of motion that must be satisfied by fields that constitute realizations of the Poincare group algebra, for integral spin, and mass m, are obtained. For the case of massive spin 2 these equations are satisfied by the selfdual, intermediate and the linear topologically massive models, whose actions are connected by duality transformations. These duality transformations incorporate the gauge invariances that distinguish one action from the other. The relation between their partition functions is briefly discussed.
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
A requiem for AdS4×C P3 fermionic self-T duality
O'Colgáin, E.; Pittelli, A.
2016-11-01
Strong evidence for dual superconformal symmetry in N =6 superconformal Chern-Simons theory has fueled expectations that the AdS /CFT dual geometry AdS4×C P3 is self-dual under T duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T duality, a symmetry originally proposed by Berkovits and Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T duality and comment on T duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T duality for AdS4×C P3 or its TsT deformations but leave the door open for new possibilities.
Generalized dualities in one-time physics as holographic predictions from two-time physics
Araya, Ignacio J.; Bars, Itzhak
2014-03-01
In the conventional formalism of physics, with one time, systems with different Hamiltonians or Lagrangians have different physical interpretations and are considered to be independent systems unrelated to each other. However, in this paper we construct explicitly canonical maps in one-time (1T) phase space (including timelike components, specifically the Hamiltonian) to show that it is appropriate to regard various 1T physics systems, with different Lagrangians or Hamiltonians, as being duals of each other. This concept is similar in spirit to dualities discovered in more complicated examples in field theory or string theory. Our approach makes it evident that such generalized dualities are widespread. This suggests that, as a general phenomenon, there are hidden relations and hidden symmetries that conventional 1T physics does not capture, implying the existence of a more unified formulation of physics that naturally supplies the hidden information. In fact, we show that two-time (2T) physics in (d +2) dimensions is the generator of these dualities in 1T physics in d dimensions by providing a holographic perspective that unifies all the dual 1T systems into one. The unifying ingredient is a gauge symmetry in phase space. Via such dualities it is then possible to gain new insights toward new physical predictions not suspected before, and suggest new methods of computation that yield results not obtained before. As an illustration, we will provide concrete examples of 1T systems in classical mechanics that are solved analytically for the first time via our dualities. These dualities in classical mechanics have counterparts in quantum mechanics and field theory, and in some simpler cases they have already been constructed in field theory. We comment on the impact of our approach on the meaning of space-time and on the development of new computational methods based on dualities.
Duality picture of Superconductor-insulator transitions on Superconducting nanowire
Makise, Kazumasa; Terai, Hirotaka; Tominari, Yukihiro; Tanaka, Shukichi; Shinozaki, Bunju
2016-06-01
In this study, we investigated the electrical transport properties of niobium titanium nitride (NbTiN) nanowire with four-terminal geometries to clarify the superconducting phase slip phenomena and superconducting-insulator transitions (SIT) for one-dimensional superconductors. We fabricated various nanowires with different widths and lengths from epitaxial NbTiN films using the electron beam lithography method. The temperature dependence of resistance R(T) below the superconducting transition temperature Tc was analyzed using thermal activation phase slip (TAPS) and quantum phase slip (QPS) theories. Although the accuracy of experimental data at low temperatures can deviate when using the TAPS model, the QPS model thoroughly represents the R(T) characteristic with resistive tail at low temperatures. From the analyses of data on Tc, we found that NbTiN nanowires exhibit SIT because of the change in the ratio of kinetic inductance energy and QPS amplitude energy with respect to the flux-charge duality theory.
Nonabelian Duality and Solvable Large N Lattice Systems
Dubin, A Yu
2000-01-01
We introduce the basics of the nonabelian duality transformation of SU(N) or U(N) vector-field models defined on a lattice. The dual degrees of freedom are certain species of the integer-valued fields complemented by the symmetric groups' øtimes_{n} S(n) variables. While the former parametrize relevant irreducible representations, the latter play the role of the Lagrange multipliers facilitating the fusion rules involved. As an application, I construct a novel solvable family of SU(N) D-matrix systems graded by the rank Their large N solvability is due to a hidden invariance (explicit in the dual formulation) which allows for a mapping onto the recently proposed eigenvalue-models \\cite{Dub1} with the largest k=D symmetry. Extending energy given (modulo the volume factor) by the free energy of a given proposed formalism provides with the basis for higher-dimensional generalizations of the Gross-Taylor stringy representation of strongly coupled 2d gauge theories.
Constraints on the duality relation from ACT cluster data
Gonçalves, R S; Holanda, R F L; Alcaniz, J S
2014-01-01
The cosmic distance-duality relation (CDDR), $d_L(z) (1 + z)^{2}/d_{A}(z) = \\eta$, where $\\eta = 1$ and $d_L(z)$ and $d_A(z)$ are, respectively, the luminosity and the angular diameter distances, holds as long as the number of photons is conserved and gravity is described by a metric theory. Testing such hypotheses is, therefore, an important task for both cosmology and fundamental physics. In this paper we use 91 measurements of the gas mass fraction of galaxy clusters recently reported by the Atacama Cosmology Telescope (ACT) survey along with type Ia supernovae observations of the Union2.1 compilation to probe a possible deviation from the value $\\eta = 1$. Although in agreement with the standard hyphothesis, we find that this combination of data tends to favor negative values of $\\eta$ which might be associated with some physical processes increasing the number of photons and modifying the above relation to $d_L < (1+z)^2d_A$.
Global Distance Duality Relation and the Shape of Galaxy Clusters
Holanda, R F L; Ribeiro, M B
2010-01-01
Observations in the cosmological domain are heavily dependent on the validity of distance duality relation, $\\eta=D_{L}(L)(1+z)^{-2}/D_{A}(z)=1$, an exact result required by the Etherington reciprocity theorem, where $D_{A}(z)$ and $D_{L}(z)$ are the angular and luminosity distances, respectively. In the limit of very small redshifts, $D_{A}(z) \\approx D_{L}(z)$, and this ratio is trivially satisfied. In this letter we investigate some consequences of such a relation by assuming that $\\eta$ is a function of the redshift parameterized by two different relations: $\\eta(z) = 1 + \\eta_{0}z$ and $\\eta(z) = 1 + \\eta_{0}z/(1+z)$, where $\\eta_0$ is a constant parameter quantifying a possible departing from the strict validity of the reciprocity relation. In order to determine the pdf of $\\eta_{0}$ we consider the angular diameter distances from galaxy clusters recently studied by two different groups assuming elliptical and spherical $\\beta$ models. It is found that the elliptical geometry is in good agreement with n...
Duality picture of Superconductor-insulator transitions on Superconducting nanowire
Makise, Kazumasa; Terai, Hirotaka; Tominari, Yukihiro; Tanaka, Shukichi; Shinozaki, Bunju
2016-01-01
In this study, we investigated the electrical transport properties of niobium titanium nitride (NbTiN) nanowire with four-terminal geometries to clarify the superconducting phase slip phenomena and superconducting-insulator transitions (SIT) for one-dimensional superconductors. We fabricated various nanowires with different widths and lengths from epitaxial NbTiN films using the electron beam lithography method. The temperature dependence of resistance R(T) below the superconducting transition temperature Tc was analyzed using thermal activation phase slip (TAPS) and quantum phase slip (QPS) theories. Although the accuracy of experimental data at low temperatures can deviate when using the TAPS model, the QPS model thoroughly represents the R(T) characteristic with resistive tail at low temperatures. From the analyses of data on Tc, we found that NbTiN nanowires exhibit SIT because of the change in the ratio of kinetic inductance energy and QPS amplitude energy with respect to the flux-charge duality theory. PMID:27311595
Fuzzy bags, Polyakov loop and gauge/string duality
Directory of Open Access Journals (Sweden)
Zuo Fen
2014-01-01
Full Text Available Confinement in SU(N gauge theory is due to the linear potential between colored objects. At short distances, the linear contribution could be considered as the quadratic correction to the leading Coulomb term. Recent lattice data show that such quadratic corrections also appear in the deconfined phase, in both the thermal quantities and the Polyakov loop. These contributions are studied systematically employing the gauge/string duality. “Confinement” in N${\\cal N}$ = 4 SU(N Super Yang-Mills (SYM theory could be achieved kinematically when the theory is defined on a compact space manifold. In the large-N limit, deconfinement of N${\\cal N}$ = 4 SYM on S3${{\\Bbb S}^3}$ at strong coupling is dual to the Hawking-Page phase transition in the global Anti-de Sitter spacetime. Meantime, all the thermal quantities and the Polyakov loop achieve significant quadratic contributions. Similar results can also be obtained at weak coupling. However, when confinement is induced dynamically through the local dilaton field in the gravity-dilaton system, these contributions can not be generated consistently. This is in accordance with the fact that there is no dimension-2 gauge-invariant operator in the boundary gauge theory. Based on these results, we suspect that quadratic corrections, and also confinement, should be due to global or non-local effects in the bulk spacetime.
Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
Cherman, Aleksey; Unsal, Mithat
2016-01-01
We show that there exists a special compactification of QCD on $\\mathbb{R}^3 \\times S^1$ in which the theory has a domain where continuous chiral symmetry breaking is analytically calculable. We give a microscopic derivation of the chiral lagrangian, the chiral condensate, and the Gell-Mann-Oakes-Renner relation $m_{\\pi}^2 f_{\\pi}^2 = m_q \\langle \\bar{q} q \\rangle$. Abelian duality, monopole operators, and flavor-twisted boundary conditions, or a background flavor holonomy, play the main roles. The flavor twisting leads to the new effect of fractional jumping of fermion zero modes among monopole-instantons. Chiral symmetry breaking is induced by monopole-instanton operators, and the Nambu-Goldstone pions arise by color-flavor transmutation from gapless "dual photons". We also give a microscopic picture of the "constituent quark" masses. Our results are consistent with expectations from chiral perturbation theory at large $S^1$, and yield strong support for adiabatic continuity between the small-$S^1$ and larg...
The Distance Duality Relation from Strong Gravitational Lensing
Liao, Kai; Li, Zhengxiang; Cao, Shuo; Biesiada, Marek; Zheng, Xiaogang; Zhu, Zong-Hong
2016-05-01
Under very general assumptions of the metric theory of spacetime, photons traveling along null geodesics and photon number conservation, two observable concepts of cosmic distance, i.e., the angular diameter and the luminosity distances are related to each other by the so-called distance duality relation (DDR) {D}L={D}A{(1+z)}2. Observational validation of this relation is quite important because any evidence of its violation could be a signal of new physics. In this paper we introduce a new method to test the DDR based on strong gravitational lensing systems and type Ia supernovae (SNe Ia) under a flat universe. The method itself is worth attention because unlike previously proposed techniques, it does not depend on all other prior assumptions concerning the details of cosmological model. We tested it using a new compilation of strong lensing (SL) systems and JLA compilation of SNe Ia and found no evidence of DDR violation. For completeness, we also combined it with previous cluster data and showed its power on constraining the DDR. It could become a promising new probe in the future in light of forthcoming massive SL surveys and because of expected advances in galaxy cluster modeling.
Testing the distance duality relation with present and future data
Cardone, Vincenzo F; Hook, Isobel; Scaramella, Roberto
2012-01-01
The assumptions that "light propagates along null geodesics of the spacetime metric" and "the number of photons is conserved along the light path" lead to the distance duality relation (DDR), $\\eta = D_L(z) (1 + z)^{-2}/D_A(z) = 1$, with $D_L(z)$ and $D_A(z)$ the luminosity and angular diameter distances to a source at redshift $z$. In order to test the DDR, we follow the usual strategy comparing the angular diameter distances of a set of clusters, inferred from X - ray and radio data, with the luminosity distance at the same cluster redshift using the local regression technique to estimate $D_L(z)$ from Type Ia Supernovae (SNeIa) Hubble diagram. In order to both strengthen the constraints on the DDR and get rid of the systematics related to the unknown cluster geometry, we also investigate the possibility to use Baryon Acoustic Oscillations (BAO) to infer $D_A(z)$ from future BAO surveys. As a test case, we consider the proposed Euclid mission investigating the precision can be afforded on $\\eta(z)$ from the...
Duality, Confinement and Supersymmetry in Restricted Quantum Chromodynamics (rcd)
Rana, J. M. S.
Electromagnetic duality has been utilized to study the isocolor charge-dyon interactions in Restricted Quantum Chromodynamics (RCD),in terms of current-current correlation (in magnetic gauge)using dielectric and permeability parameters of the associated vacuum. In the state of dyonic superconductivity, it has been shown that the dual propagators behave as 1/k4 (for small k2), which in analogy with superconductivity (dual superconductivity) leads to the confinement of colored fluxes associated with dyonic quarks vide generalized Meissner effect. Based on semi-quantitative analysis of vortex solutions of RCD and by calculating the masses for the massive collective modes of the condensed vacuum, the expressions for the London penetration depth, coherence length and the associated flux energy functions for the type I and type II superconducting media have been obtained. It has further been demonstrated that in the type I medium, vortices tend to coalesce and hence are attractive, while the energy function supports repulsive forces between vortices in the type II superconducting medium. The RCD has been supersymmetrized in N=1 limit and the supersymmetric dyonic solutions have been obtained. In the dyonic background gauge one-loop quantum corrections to the dyonic mass have been calculated and it has been shown that the one-loop quantum corrections lead no change in classical mass of the dyon.
Analyzing Nonblocking Switching Networks using Linear Programming (Duality)
Ngo, Hung Q; Le, Anh N; Nguyen, Thanh-Nhan
2012-01-01
The main task in analyzing a switching network design (including circuit-, multirate-, and photonic-switching) is to determine the minimum number of some switching components so that the design is non-blocking in some sense (e.g., strict- or wide-sense). We show that, in many cases, this task can be accomplished with a simple two-step strategy: (1) formulate a linear program whose optimum value is a bound for the minimum number we are seeking, and (2) specify a solution to the dual program, whose objective value by weak duality immediately yields a sufficient condition for the design to be non-blocking. We illustrate this technique through a variety of examples, ranging from circuit to multirate to photonic switching, from unicast to $f$-cast and multicast, and from strict- to wide-sense non-blocking. The switching architectures in the examples are of Clos-type and Banyan-type, which are the two most popular architectural choices for designing non-blocking switching networks. To prove the result in the multir...
Four-dimensional unsubtraction from the loop-tree duality
Sborlini, German F R; Hernandez-Pinto, Roger; Rodrigo, German
2016-01-01
We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes with the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at the integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for $\\gamma^* \\to q \\bar{q}(g)$, at its generalisation to multi-leg processes...
Duality, Phase Structures and Dilemmas in Symmetric Quantum Games
Ichikawa, T; Ichikawa, Tsubasa; Tsutsui, Izumi
2006-01-01
Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of...
Duality picture of Superconductor-insulator transitions on Superconducting nanowire.
Makise, Kazumasa; Terai, Hirotaka; Tominari, Yukihiro; Tanaka, Shukichi; Shinozaki, Bunju
2016-01-01
In this study, we investigated the electrical transport properties of niobium titanium nitride (NbTiN) nanowire with four-terminal geometries to clarify the superconducting phase slip phenomena and superconducting-insulator transitions (SIT) for one-dimensional superconductors. We fabricated various nanowires with different widths and lengths from epitaxial NbTiN films using the electron beam lithography method. The temperature dependence of resistance R(T) below the superconducting transition temperature Tc was analyzed using thermal activation phase slip (TAPS) and quantum phase slip (QPS) theories. Although the accuracy of experimental data at low temperatures can deviate when using the TAPS model, the QPS model thoroughly represents the R(T) characteristic with resistive tail at low temperatures. From the analyses of data on Tc, we found that NbTiN nanowires exhibit SIT because of the change in the ratio of kinetic inductance energy and QPS amplitude energy with respect to the flux-charge duality theory.
Proving the PP-Wave/CFT_2 Duality
Gava, E; Gava, Edi
2002-01-01
We study the duality between IIB string theory on a pp-wave background, arising as a Penrose limit of the $AdS_3 \\times S^3\\times M$, where $M$ is $T^4$ (or $K3$), and the 2D CFT which is given by the ${\\cal N}=(4,4)$ orbifold $(M)^N/S_N$, resolved by a blowing-up mode. After analizying the action of the supercharges on both sides, we establish a correspondence between the states of the two theories. In particular and for the $T^4$ case, we identify both massive and massless oscillators on the pp-wave, with certain classes of excited states in the resolved CFT carrying large $R$-charge $n$. For the former, the excited states involve fractional modes of the generators of the ${\\cal N}=4$ chiral algebra acting on the $Z_n$ ground states. For the latter, they involve, fractional modes of the $U(1)^4_L\\times U(1)^4_R$ super-current algebra acting on the $Z_n$ ground states. By using conformal perturbation theory we compute the leading order correction to the conformal dimensions of the first class of states, due ...
Deciphering the Enigma of Wave-Particle Duality
Bhaumik, Mani
2016-01-01
A satisfactory explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view a quantum particle is an objectively real wave packet consisting of irregular disturbances of underlying quantum fields. It travels holistically as a unit and thereby acts as a particle. Only the totality of the entire wave packet at any instance embodies all the conserved quantities, for example the energy-momentum, rest mass, and charge of the particle, and as such must be acquired all at once during detection. On this basis, many of the bizarre behaviors observed in the quantum domain, such as wave function collapse, the limitation of prediction to only a probability rather than an actuality, the apparent simultaneous existence of a particle in more than one place, and the inherent uncertainty can be reasonably comprehended. The necessity of acquiring the wave function in its entirety for detection, as evinced by the appearance of collapse of the ...
On KKLT/CFT and LVS/CFT dualities
Energy Technology Data Exchange (ETDEWEB)
Alwis, Senarath de [UCB 390, Physics Department, University of Colorado,Boulder CO 80309 (United States); Gupta, Rajesh Kumar [ICTP,Strada Costiera 11, 34151 Trieste (Italy); Quevedo, Fernando [ICTP,Strada Costiera 11, 34151 Trieste (Italy); DAMTP, CMS, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Valandro, Roberto [ICTP,Strada Costiera 11, 34151 Trieste (Italy); Dipartimento di Fisica dell’Università di Trieste and INFN - Sezione di Trieste,Strada Costiera 11, 34151 Trieste (Italy)
2015-07-08
We present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifications. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both cases we identify the large ‘central charge’, find a separation of scales between the radius of AdS and the size of the extra dimensions and show that the dual CFT has only a limited number of operators with small conformal dimension. Differences between the two sets of duals are identified. Besides a different amount of supersymmetry (N=1 for KKLT and N=0 for LVS) we find that the LVS CFT dual has only one scalar operator with O(1) conformal dimension, corresponding to the volume modulus, whereas in KKLT the whole set of h{sup 1,1} Kähler moduli have this property. Also, the maximal number of degrees of freedom is estimated to be larger in LVS than in KKLT duals. In both cases we explicitly compute the coefficient of the logarithmic contribution to the one-loop vacuum energy which should be invariant under duality and therefore provides a non-trivial prediction for the dual CFT. This coefficient takes a particularly simple form in the KKLT case.
On KKLT/CFT and LVS/CFT dualities
de Alwis, Senarath; Gupta, Rajesh Kumar; Quevedo, Fernando; Valandro, Roberto
2015-07-01
We present a general discussion of the properties of three dimensional CFT duals to the AdS string theory vacua coming from type IIB Calabi-Yau flux compactifi-cations. Both KKLT and Large Volume Scenario (LVS) minima are considered. In both cases we identify the large `central charge', find a separation of scales between the radius of AdS and the size of the extra dimensions and show that the dual CFT has only a limited number of operators with small conformal dimension. Differences between the two sets of duals are identified. Besides a different amount of supersymmetry ( for KKLT and for LVS) we find that the LVS CFT dual has only one scalar operator with O(1) conformal dimension, corresponding to the volume modulus, whereas in KKLT the whole set of h 1,1 Kähler moduli have this property. Also, the maximal number of degrees of freedom is estimated to be larger in LVS than in KKLT duals. In both cases we explic-itly compute the coefficient of the logarithmic contribution to the one-loop vacuum energy which should be invariant under duality and therefore provides a non-trivial prediction for the dual CFT. This coefficient takes a particularly simple form in the KKLT case.
T-duality and α{sup ′}-corrections
Energy Technology Data Exchange (ETDEWEB)
Marqués, Diego [Instituto de Astronomía y Física del Espacio (IAFE-CONICET-UBA),Buenos Aires (Argentina); Nuñez, Carmen A. [Instituto de Astronomía y Física del Espacio (IAFE-CONICET-UBA),Buenos Aires (Argentina); Departamento de Física, FCEyN, Universidad de Buenos Aires (UBA),Buenos Aires (Argentina)
2015-10-13
We construct an O(d,d) invariant universal formulation of the first-order α{sup ′}-corrections of the string effective actions involving the dilaton, metric and two-form fields. Two free parameters interpolate between four-derivative terms that are even and odd with respect to a Z{sub 2}-parity transformation that changes the sign of the two-form field. The Z{sub 2}-symmetric model reproduces the closed bosonic string, and the heterotic string effective action is obtained through a Z{sub 2}-parity-breaking choice of parameters. The theory is an extension of the generalized frame formulation of Double Field Theory, in which the gauge transformations are deformed by a first-order generalized Green-Schwarz transformation. This deformation defines a duality covariant gauge principle that requires and fixes the four-derivative terms. We discuss the O(d,d) structure of the theory and the (non-)covariance of the required field redefinitions.
Open/closed string duality and relativistic fluids
Niarchos, Vasilis
2015-01-01
We propose an open/closed string duality in general backgrounds extending previous ideas about open string completeness by Ashoke Sen. Our proposal sets up a general version of holography that works in gravity as a tomographic principle. We argue, in particular, that previous expectations of a supergravity/Dirac-Born-Infeld (DBI) correspondence are naturally embedded in this conjecture and can be tested in a well-defined manner. As an example, we consider the correspondence between open string field theories on extremal D-brane setups in flat space in the large-N, large 't Hooft limit, and asymptotically flat solutions in ten-dimensional type II supergravity. We focus on a convenient long-wavelength regime, where specific effects of higher-spin open string modes can be traced explicitly in the dual supergravity computation. For instance, in this regime we show how the full abelian DBI action arises from supergravity as a straightforward reformulation of relativistic hydrodynamics. In the example of a (2+1)-di...
Four-dimensional unsubtraction from the loop-tree duality
Sborlini, Germán F. R.; Driencourt-Mangin, Félix; Hernández-Pinto, Roger J.; Rodrigo, Germán
2016-08-01
We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes, and the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for {γ}^{ast}to qoverline{q}(g) , and its generalisation to multi-leg processes. The extension to next-to-next-to-leading order (NNLO) is briefly commented.
Penguins with charm and quark-hadron duality
Energy Technology Data Exchange (ETDEWEB)
Beneke, M. [RWTH Aachen University, Institut fuer Theoretische Physik E, Aachen (Germany); CERN Theory Department, Geneve (Switzerland); Buchalla, G. [Ludwig-Maximilians-Universitaet Muenchen, Fakultaet fuer Physik, Arnold Sommerfeld Center for Theoretical Physics, Muenchen (Germany); Neubert, M. [Johannes Gutenberg-Universitaet, Institut fuer Physik (THEP), Mainz (Germany); Sachrajda, C.T. [University of Southampton, School of Physics and Astronomy, Southampton (United Kingdom)
2009-06-15
The integrated branching fraction of the process B{yields}X{sub s}l{sup +}l{sup -} is dominated by resonance background from narrow charmonium states, such as B{yields}X{sub s}{psi}{yields}X{sub s}l{sup +}l{sup -}, which exceeds the non-resonant charm-loop contribution by two orders of magnitude. The origin of this fact is discussed in view of the general expectation of quark-hadron duality. The situation in B{yields}X{sub s}l{sup +}l{sup -} is contrasted with charm-penguin amplitudes in two-body hadronic B decays of the type B{yields}{pi}{pi}, for which it is demonstrated that resonance effects and the potentially non-perturbative c anti c threshold region do not invalidate the standard picture of QCD factorization. This holds irrespective of whether the charm quark is treated as a light or a heavy quark. (orig.)
Multibeam Satellite Frequency/Time Duality Study and Capacity Optimization
Lei, Jiang
2011-01-01
In this paper, we investigate two new candidate transmission schemes, Non-Orthogonal Frequency Reuse (NOFR) and Beam-Hoping (BH). They operate in different domains (frequency and time/space, respectively), and we want to know which domain shows overall best performance. We propose a novel formulation of the Signal-to-Interference plus Noise Ratio (SINR) which allows us to prove the frequency/time duality of these schemes. Further, we propose two novel capacity optimization approaches assuming per-beam SINR constraints in order to use the satellite resources (e.g. power and bandwidth) more efficiently. Moreover, we develop a general methodology to include technological constraints due to realistic implementations, and obtain the main factors that prevent the two technologies dual of each other in practice, and formulate the technological gap between them. The Shannon capacity (upper bound) and current state-of-the-art coding and modulations are analyzed in order to quantify the gap and to evaluate the performa...
Type I/heterotic duality and M-theory amplitudes
Green, Michael B
2016-01-01
This paper investigates relationships between low-energy four-particle scattering amplitudes with external gauge particles and gravitons in the E_8 X E_8 and SO(32) heterotic string theories and the type I and type IA superstring theories by considering a variety of tree level and one-loop Feynman diagrams describing such amplitudes in eleven-dimensional supergravity in a Horava--Witten background compactified on a circle. This accounts for a number of perturbative and non-perturbative aspects of low order higher derivative terms in the low-energy expansion of string theory amplitudes, which are expected to be protected by half maximal supersymmetry from receiving corrections beyond one or two loops. It also suggests the manner in which type I/heterotic duality may be realised for certain higher derivative interactions that are not so obviously protected. For example, our considerations suggest that R**4 interactions (where R is the Riemann curvature) might receive no perturbative corrections beyond one loop ...
Finite Heisenbeg Groups and Seiberg Dualities in Quiver Gauge Theories
Burrington, B A; Mahato, M; Pando-Zayas, L A; Burrington, Benjamin A.; Liu, James T.; Mahato, Manavendra; Zayas, Leopoldo A. Pando
2006-01-01
A large class of quiver gauge theories admits the action of finite Heisenberg groups of the form Heis(Z_q x Z_q). This Heisenberg group is generated by a manifest Z_q shift symmetry acting on the quiver along with a second Z_q rephasing (clock) generator acting on the links of the quiver. Under Seiberg duality, however, the action of the shift generator is no longer manifest, as the dualized node has a different structure from before. Nevertheless, we demonstrate that the Z_q shift generator acts naturally on the space of all Seiberg dual phases of a given quiver. We then prove that the space of Seiberg dual theories inherits the action of original finite Heisenberg group, where now the shift generator Z_q is a map among fields belonging to different Seiberg phases. As examples, we explicitly consider the action of the Heisenberg group on Seiberg phases for C^3/Z_3, Y^{4,2} and Y^{6,3} quiver.
Type I/heterotic duality and M-theory amplitudes
Green, Michael B.; Rudra, Arnab
2016-12-01
This paper investigates relationships between low-energy four-particle scattering amplitudes with external gauge particles and gravitons in the E 8 × E 8 and SO(32) heterotic string theories and the type I and type IA superstring theories by considering a variety of tree level and one-loop Feynman diagrams describing such amplitudes in eleven-dimensional supergravity in a Horava-Witten background compactified on a circle. This accounts for a number of perturbative and non-perturbative aspects of low order higher derivative terms in the low-energy expansion of string theory amplitudes, which are expected to be protected by half maximal supersymmetry from receiving corrections beyond one or two loops. It also suggests the manner in which type I/heterotic duality may be realised for certain higher derivative interactions that are not so obviously protected. For example, our considerations suggest that R 4 interactions (where R is the Riemann curvature) might receive no perturbative corrections beyond one loop by virtue of a conspiracy involving contributions from (non-BPS) {Z}_2 D-instantons in the type I and heterotic SO(32) theories.
Type I/heterotic duality and M-theory amplitudes
Energy Technology Data Exchange (ETDEWEB)
Green, Michael B. [Department of Applied Mathematics and Theoretical Physics,Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Rudra, Arnab [Department of Applied Mathematics and Theoretical Physics,Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Center for Quantum Mathematics and Physics (QMAP),Department of Physics, University of California,One Shields Avenue, Davis, CA 95616 (United States)
2016-12-14
This paper investigates relationships between low-energy four-particle scattering amplitudes with external gauge particles and gravitons in the E{sub 8}×E{sub 8} and SO(32) heterotic string theories and the type I and type IA superstring theories by considering a variety of tree level and one-loop Feynman diagrams describing such amplitudes in eleven-dimensional supergravity in a Ho?rava-Witten background compactified on a circle. This accounts for a number of perturbative and non-perturbative aspects of low order higher derivative terms in the low-energy expansion of string theory amplitudes, which are expected to be protected by half maximal supersymmetry from receiving corrections beyond one or two loops. It also suggests the manner in which type I/heterotic duality may be realised for certain higher derivative interactions that are not so obviously protected. For example, our considerations suggest that R{sup 4} interactions (where R is the Riemann curvature) might receive no perturbative corrections beyond one loop by virtue of a conspiracy involving contributions from (non-BPS) ℤ{sub 2} D-instantons in the type I and heterotic SO(32) theories.
Power centroid radar and its rise from the universal cybernetics duality
Feria, Erlan H.
2014-05-01
Power centroid radar (PC-Radar) is a fast and powerful adaptive radar scheme that naturally surfaced from the recent discovery of the time-dual for information theory which has been named "latency theory." Latency theory itself was born from the universal cybernetics duality (UC-Duality), first identified in the late 1970s, that has also delivered a time dual for thermodynamics that has been named "lingerdynamics" and anchors an emerging lifespan theory for biological systems. In this paper the rise of PC-Radar from the UC-Duality is described. The development of PC-Radar, US patented, started with Defense Advanced Research Projects Agency (DARPA) funded research on knowledge-aided (KA) adaptive radar of the last decade. The outstanding signal to interference plus noise ratio (SINR) performance of PC-Radar under severely taxing environmental disturbances will be established. More specifically, it will be seen that the SINR performance of PC-Radar, either KA or knowledgeunaided (KU), approximates that of an optimum KA radar scheme. The explanation for this remarkable result is that PC-Radar inherently arises from the UC-Duality, which advances a "first principles" duality guidance theory for the derivation of synergistic storage-space/computational-time compression solutions. Real-world synthetic aperture radar (SAR) images will be used as prior-knowledge to illustrate these results.
Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
Aharony, Ofer; Hsin, Po-Shen; Seiberg, Nathan
2016-01-01
In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between $SO(N)_k$ Chern-Simons theories coupled to $N_f$ real scalars in the fundamental representation, and $SO(k)_{-N+N_f/2}$ coupled to $N_f$ real (Majorana) fermions in the fundamental. For $N_f=0$ these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For $k=1$ we get an interesting low-energy duality between $N_f$ free Majorana fermions and an $SO(N)_1$ Chern-Simons theory coupled to $N_f$ scalar fields (with $N_f \\leq N-2$).
Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group
Park, Jaemo
2013-01-01
We work out Seiberg-like dualities for 3d $\\cN=2$ theories with SU(N) gauge group. We use the $SL(2,\\IZ)$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\\IZ)$ acts as gauging of the U(1) global symmetry. Utilizing $S=S^{-1}$ up to charge conjugation, we obtain Seiberg-like dual of SU(N) theories by gauging topological U(1) symmetry of the Seiberg-like dual of U(N) theories with the same matter content. We work out the Aharony dualities for SU(N) gauge theory with $N_f$ fundamental/anti-fundamnetal flavors, with/without one adjoint matter with the superpotential. We also work out the Giveon-Kutasov dualities for SU(N) gauge theory with Chern-Simons term and with $N_f$ fundamental/anti-fundamental flavors. For all the proposed dualities, we give various evidences such as chiral ring matching and the superconformal index computations. For all dualities proposed, we find the perfect matchings.
Duality methods in networks, computer science models, and disordered condensed matter systems
Mitchell, Joseph Dan
In this thesis, I explore lattice independent duality and systems to which it can be applied. I first demonstrate classical duality on models in an external field, including the Ising, Potts, and x -- y models, showing in particular how this modifies duality to be lattice independent and applicable to networks. I then present a novel application of duality on the boolean satsifiability problem, one of the most important problems in computational complexity, through mapping to a low temperature Ising model. This establishes the equivalence between boolean satisfiability and a problem of enumerating the positive solutions to a Diophantine system of equations. I continue by combining duality with a prominent tool for models on networks, belief propagation, deriving a new message passing procedure, dual belief propagation. In the final part of my thesis, I shift to propose and examine a semiclassical model, the two-component Coulomb glass model, which can explain the giant magnetoresistance peak present in disordered films near a superconductor-insulator transition as the effect of competition between single particle and localized pair transport. I numerically analyze the density of states and transport properties of this model.
A Duality Web in 2+1 Dimensions and Condensed Matter Physics
Seiberg, Nathan; Wang, Chong; Witten, Edward
2016-01-01
Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in $2+1$ dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For example, the long distance behavior of the $2+1$-dimensional analog of QED with a single Dirac fermion (a theory known as $U(1)_{1/2}$) is identified with the $O(2)$ Wilson-Fisher fixed point. The gauged version of that fixed point with a Chern-Simons coupling at level one is identified as a free Dirac fermion. The latter theory also has a dual version as a fermion interacting with some gauge fields. Assuming some of these dualities, other dualities can be derived. Our analysis resolves a number of confusing issues in the literature including how time reversal is realized in these theories. It also has many applications in condensed matter physics like the theory of topological insulators (and their gapped bounda...
Cheong, Yong Wook; Song, Jinwoong
2014-01-01
There is no consensus on the genuine meaning of wave-particle duality and the interpretation of quantum theory. How can we teach duality and quantum theory despite this lack of consensus? This study attempts to answer this question. This research argues that reality issues are at the core of both the endless debates concerning the interpretation…
Institute of Scientific and Technical Information of China (English)
G.J. Zalmai; Qing-hong Zhang
2007-01-01
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of parametric duality results under various generalized (η, p)-invexity assumptions for a semi-infinite minmax fractional programming problem.
Pop, P.C.; Still, Georg J.
1999-01-01
In linear programming it is known that an appropriate non-homogeneous Farkas Lemma leads to a short proof of the strong duality results for a pair of primal and dual programs. By using a corresponding generalized Farkas lemma we give a similar proof of the strong duality results for semidefinite
Cheong, Yong Wook; Song, Jinwoong
2014-01-01
There is no consensus on the genuine meaning of wave-particle duality and the interpretation of quantum theory. How can we teach duality and quantum theory despite this lack of consensus? This study attempts to answer this question. This research argues that reality issues are at the core of both the endless debates concerning the interpretation…
Gauge/gravity duality. Exploring universal features in quantum matter
Energy Technology Data Exchange (ETDEWEB)
Klug, Steffen
2013-07-09
In this dissertation strongly correlated quantum states of matter are explored with the help of the gauge/gravity duality, relating strongly coupled gauge theories to weakly curved gravitational theories. The main focus of the present work is on applications to condensed matter systems, in particular high temperature superconductors and quantum matter close to criticality at zero temperature. The gauge/gravity duality originates from string theory and is a particular realization of the holographic principle. Therefore, a brief overview of the conceptual ideas behind string theory and the ramifications of the holographic principle are given. Along the way, supersymmetry and supersymmetric field theories needed to understand the low energy effective field theories of superstring theory will be discussed. Armed with the string theory background, the double life of D-branes, extended object where open strings end, is explained as massive solitonic solutions to the type II supergravity equations of motion and their role in generating supersymmetric Yang-Mills theories. Connecting these two different pictures of D-branes will give an explicit construction of a gauge/gravity duality, the AdS{sub 5}/CFT{sub 4} correspondence between N=4 supersymmetric SU(N{sub c}) Yang-Mills theory in four dimensions with vanishing β-function to all orders, describing a true CFT, and type IIB supergravity in ten-dimensional AdS{sub 5} x S{sup 5} spacetime. Furthermore, the precise dictionary relating operators of the conformal field theory to fields in the gravitational theory is established. More precisely, the partitions functions of the strongly coupled N=4 supersymmetric Yang-Mills theory in the large N{sub c} limit is equal to the on-shell supergravity partition evaluated at the boundary of the AdS space. Applying the knowledge of perturbative quantum field theory and its relation to the quantum partition function the dictionary may be extended to finite temperature and finite
Coag-Frag duality for a class of stable Poisson-Kingman mixtures
James, Lancelot F
2010-01-01
Exchangeable sequences of random probability measures (partitions of mass) and their corresponding exchangeable bridges play an important role in a variety of areas in probability, statistics and related areas, including Bayesian statistics, physics, finance and machine learning. An area of theoretical as well as practical interest, is the study of coagulation and fragmentation operators on partitions of mass. In this regard, an interesting but formidable question is the identification of operators and distributional families on mass partitions that exhibit interesting duality relations. In this paper we identify duality relations for a large sub-class of mixed Poisson-Kingman models generated by a stable subordinator. Our results are natural generalizations of the duality relations developed in Pitman, Bertoin and Goldschmidt, and Dong, Goldschmidt and Martin for the two-parameter Poisson Dirichlet family. These results are deduced from results for corresponding bridges.
Recent Developments in String Theory From Perturbative Dualities to M-Theory
Haack, M; Lüst, Dieter; Haack, Michael; Kors, Boris; Lust, Dieter
1999-01-01
These lectures intend to give a pedagogical introduction into some of the developments in string theory during the last years. They include perturbative T-duality and non perturbative S- and U-dualities, their unavoidable demand for D-branes, an example of enhanced gauge symmetry at fixed points of the T-duality group, a review of classical solitonic solutions in general relativity, gauge theories and tendimensional supergravity, a discussion of their BPS nature, Polchinski's observations that allow to view D-branes as RR charged states in the non perturbative string spectrum, the application of all this to the computation of the black hole entropy and Hawking radiation and finally a brief survey of how everything fits together in M-theory.
Heterotic-type IIA duality and degenerations of K3 surfaces
Energy Technology Data Exchange (ETDEWEB)
Braun, A.P. [Department of Mathematics, University of Oxford,Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG (United Kingdom); Watari, T. [Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwano-ha 5-1-5, 277-8583 (Japan)
2016-08-04
We study the duality between four-dimensional N=2 compactifications of heterotic and type IIA string theories. Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification. This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory. The theory of degenerations of K3 surfaces can then be used to find which solitons can be present on the heterotic side. Similar to small instanton transitions, these solitons escort singular transitions between different Calabi-Yau threefolds. Starting from well-known examples of heterotic-type IIA duality, such transitions can take us to type IIA compactifications with unknown heterotic duals.
Exact Duality of The Dissipative Hofstadter Model on a Triangular Lattice
Lee, Taejin
2016-01-01
We study the dissipative Hofstadter model on a triangular lattice, making use of the $O(2,2;R)$ T-dual transformation of string theory. The $O(2,2;R)$ dual transformation transcribes the model in a commutative basis into the model in a non-commutative basis. In the zero temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence condition, which identifies the points on the two dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.
Higher-spin extensions of the linear-chiral duality in three dimensions
Kuzenko, Sergei M
2016-01-01
The linear-chiral duality provides dual descriptions in terms of chiral superfields for general models of self-interacting N=2 vector multiplets in three dimensions and N=1 tensor multiplets in four dimensions. Here we present a higher-spin generalisation of the linear-chiral duality in three dimensions. It provides a dual description for models formulated in terms of the linearised higher-spin analogues of the N=2 super-Cotton tensor. While the original model is a higher-derivative theory, the dual theory contains at most two derivatives at the component level. By applying N=2 --> N=1 superspace reduction, we obtain a new type of duality for higher-spin N=1 supersymmetric theories in three dimensions.
Contact terms and duality symmetry in the critical dissipative Hofstadter model
Freed, D E
1993-01-01
The dissipative Hofstadter model describes the quantum mechanics of a charged particle in two dimensions subject to a periodic potential, uniform magnetic field, and dissipative force. Its phase diagram exhibits an SL(2,Z) duality symmetry and has an infinite number of critical circles in the dissipation/magnetic field plane. In addition, multi-critical points on a particular critical circle correspond to non-trivial solutions of open string theory. The duality symmetry is expected to provide relations between correlation functions at different multi-critical points. Many of these correlators are contact terms. However we expect them to have physical significance because under duality they transform into functions that are non-zero for large separations of the operators. Motivated by the search for exact, regulator independent solutions for these contact terms, in this paper we derive many properties and symmetries of the coordinate correlation functions at the special multi-critical points. In particular, we...
On the dimensional dependence of duality groups for massive p-forms
Noronha, J L; Guimarães, M S; Wotzasek, C
2003-01-01
We study the soldering formalism in the context of abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia-Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even dimensional spacetimes, in this way confirming the Higgs/Julia-Toulouse duality proposed by Quevedo and Trugenberger \\cite{QT} a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.
Seiberg duality for Chern-Simons quivers and D-brane mutations
Closset, Cyril
2012-03-01
Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons quivers with chiral matter content: They arise from a change of brane basis (or mutation), in complete analogy with the better known Seiberg dualities for D3-brane quivers. This perspective reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills theories with unitary gauge groups. We provide explicit examples of dual theories for the quiver dual to the {Y^{{p,q}}}left( {mathbb{C}{mathbb{P}^{{2}}}} right) geometries. We also comment on the string theory derivation of CS quivers dual to massive type IIA geometries.
Seiberg duality for Chern-Simons quivers and D-brane mutations
Closset, Cyril
2012-01-01
Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons quivers with chiral matter content: They arise from a change of brane basis (or mutation), in complete analogy with the better known Seiberg dualities for D3-brane quivers. This perspective reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills theories with unitary gauge groups. We provide explicit examples of dual theories for the quiver dual to the Y^{p,q}(CP^2) geometries. We also comment on the string theory derivation of CS quivers dual to massive type IIA geometries.
Particle-vortex and Maxwell duality in the $AdS_4\\times \\mathbb{CP}^3$/ABJM correspondence
Murugan, Jeff; Rughoonauth, Nitin; Shock, Jonathan P
2014-01-01
We revisit the notion of particle-vortex duality in abelian theories of complex scalar fields coupled to gauge fields, formulating the duality as a transformation at the level of the path integral. This transformation is then made symmetric and cast as a self-duality that maps the original theory into itself with the role of particles and vortices interchanged. After defining the transformation for a pure Chern-Simons gauge theory, we show how to embed it into (a sector of) the $(2+1)-$dimensional ABJM model, and argue that this duality can be understood as being related to 4-dimensional Maxwell duality in the $AdS_{4}\\times\\mathbb{CP}^{3}$ bulk.
Theoretical photon origin, a didactic introduction to the wave particle duality
L., Paco H Talero
2016-01-01
In modern physics courses the idea of photon has been teaching through from the einsteinian formulation based on the photoelectric effect. Einstein's photon concept allow the quantization of the electromagnetic field, but does not dwell on the idea of photon as particle. The objective of this paper was to demonstrate that the photon has its origin essentially in the special relativity, the electromagnetic theory and in the symmetry between the Lorentz's transformations associated flat monochromatic electromagnetic waves and particles with zero rest mass. This approach allows to understand the wave-particle duality of photon and allows to propose an alternative teaching focused on this duality to develop the course of modern physics.
Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous Spaces
Marrani, Alessio
2015-01-01
Freudenthal duality can be defined as an anti-involutive, non-linear map acting on symplectic spaces. It was introduced in four-dimensional Maxwell-Einstein theories coupled to a non-linear sigma model of scalar fields. In this short review, I will consider its relation to the U-duality Lie groups of type E7 in extended supergravity theories, and comment on the relation between the Hessian of the black hole entropy and the pseudo-Euclidean, rigid special (pseudo)Kaehler metric of the pre-homogeneous spaces associated to the U-orbits.
T-duality, Quotients and Currents for Non-Geometric Closed Strings
Bakas, Ioannis
2015-01-01
We use the canonical description of T-duality as well as the formulation of T-duality in terms of chiral currents to investigate the geometric and non-geometric faces of closed string backgrounds originating from principal torus bundles with constant H-flux. Employing conformal field theory techniques, the non-commutative and non-associative structures among generalized coordinates in the so called Q-flux and R-flux backgrounds emerge by gauging the Abelian symmetries of an enlarged Rocek-Verlinde sigma-model and projecting the associated chiral currents of the enlarged theory to the T-dual coset models carrying non-geometric fluxes.
Minimal duality breaking in the Kallen Lehman approach to 3D Ising model: A numerical test
Astorino, Marco; Canfora, Fabrizio; Martínez, Cristián; Parisi, Luca
2008-06-01
A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatures. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the Monte Carlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte Carlo results by introducing a more general duality breaking is shortly discussed.
D-Branes, RR-Fields and Duality on Noncommutative Manifolds
Brodzki, J; Rosenberg, J; Szabó, R J; Brodzki, Jacek; Mathai, Varghese; Rosenberg, Jonathan; Szabo, Richard J.
2006-01-01
We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincare duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant K-theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.
Radiation damping of a BPS monopole: An illustration of S duality
Bak, Dongsu; Min, Hyunsoo
1997-11-01
The radiation reaction of a BPS monopole in the presence of incident electromagnetic waves as well as massless Higgs waves is analyzed classically. The reactive force and higher-order (finite size) effect are compared to those of the W boson that is interpreted as a dual partner of the BPS monopole. It is shown that the damping of acceleration is dual to each other, while in the case of the finite size effect the duality is broken explicitly. Their implications on the duality are discussed.
On the duality in CPT-even Lorentz-breaking theories
Energy Technology Data Exchange (ETDEWEB)
Scarpelli, A.P.B. [Departamento de Policia Federal, Sao Paulo (Brazil); Ribeiro, R.F.; Nascimento, J.R.; Petrov, A.Yu. [Universidade Federal da Paraiba, Departamento de Fisica (Brazil)
2015-07-15
We generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is shown using the gauge embedding procedure, both in free and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical. (orig.)
The wave-particle duality in the Weyl-Dirac theory
Agop, M.; Nica, P.
2000-09-01
The solution of a static two-dimensional wave equation in the Gauss-Mainardi-Codazzi formalism of Weyl-Dirac theory is obtained in terms of the elliptic function with a complex argument. In particular, by double degenerating the elliptic function, wave-particle duality results. Associating a superconducting behaviour to matter, by means of the duality, we find some superconducting parameters: Bc2, the average carrier density, the gap energy and the pair-breaking time. The discontinuities of these parameters for sequences (1/3), (1/5), (1/7),... imply that the quantum spacetime is Cantorian.
Institute of Scientific and Technical Information of China (English)
GAO Ying; RONG Wei-dong
2008-01-01
This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of (F, α, ρ, d)-V-convexity.Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.
Some statistical aspects of the spinor field Fermi-Bose duality
Directory of Open Access Journals (Sweden)
V.M. Simulik
2012-12-01
Full Text Available The structure of 29-dimensional extended real Clifford-Dirac algebra, which has been introduced in our paper Phys. Lett. A, 2011, Vol. 375, 2479, is considered in brief. Using this algebra, the property of Fermi-Bose duality of the Dirac equation with nonzero mass is proved. It means that Dirac equation can describe not only the fermionic but also the bosonic states. The proof of our assertion based on the examples of bosonic symmetries, solutions and conservation laws is given. Some statistical aspects of the spinor field Fermi-Bose duality are discussed.
KUHN-TUCKER CONDITION AND WOLFE DUALITY OF PREINVEX SET-VALUED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
SHENG Bao-huai; LIU San-yang
2006-01-01
The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.
Splitting Spacetime and Cloning Qubits: Linking No-Go Theorems across the ER=EPR Duality
Bao, Ning; Remmen, Grant N
2015-01-01
We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement.
Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality
Energy Technology Data Exchange (ETDEWEB)
Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States); Pollack, Jason; Remmen, Grant N. [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)
2015-11-15
We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
José, Jorge V.
2017-03-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
José, Jorge V.
2013-06-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
T-Duality Transformation and Universal Structure of Non-Critical String Field Theory
Asatani, T; Okawa, Y; Sugino, F; Yoneya, T; Asatani, Takashi; Kuroki, Tsunehide; Okawa, Yuji; Sugino, Fumihiko; Yoneya, Tamiaki
1996-01-01
We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the c=1/2 model in the scaling limit is T-duality symmetric in the sphere approximation. The duality symmetry is however violated when the higher-genus effects are taken into account, owing to the existence of global Z_2 vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by the last two authors are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes...
Nucleon Structure Function F2 in the Resonance Region and Quark-Hadron Duality
Institute of Scientific and Technical Information of China (English)
DONG Yu-Bing; LI Ming-Fei
2003-01-01
Based on a simple nonrelativistic constituent quark model, the nucleon structure function F2 in theresonance region is estimated by taking the contributions from low-lying nucleon resonances into account. Calculatedresults are employed to study quark-hardon duality in the nucleon electron scattering process by comparing them to thescaling behavior from the data in deep inelastic scattering region.
THE DUALITY OF CREATIVITY AND TECHNOLOGY IN IS AND ISD ORGANIZATIONS
DEFF Research Database (Denmark)
Mengiste, Shegaw Anagaw; Ulrich, Frank
2014-01-01
of the iterative cycle of ideation and innovation in IS and ISD organizations. To create the framework, we have used Weick et al. (2005) view on sensemaking and Orlikowski's (1992) duality of technology theory. The theoretical framework, with the notion of ergodic connections suggests that sensemaking will cause...
On the Classical String Solutions and String/Field Theory Duality
Aleksandrova, D.; Bozhilov, P.
2003-01-01
We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical string solutions in general string theory backgrounds, when the string embedding coordinates depend non-linearly on the worldsheet time parameter.
Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
García-Compéan, H; Plebanski, J F; Ramírez, C
1998-01-01
It is well known that Yang-Mills theories do possess a phase of non-Abelian strong-weak duality invariance. Moreover, dual theories, with inverted couplings, to non-Abelian, non-supersymmetric gauge theories have been constructed. Following a similar procedure we propose a non-dynamical gravitational analog to this kind of theories.
T-Duality in Type II String Theory via Noncommutative Geometry and Beyond
Mathai, V.
This brief survey on how nocommutative and nonassociative geometry appears naturally in the study of T-duality in type II string theory, is essentially a transcript of my talks given at the 21st Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics: Noncommutative Geometry and Quantum Spacetime in Physics, Japan, 11--15 November 2006.
Duality for spatially interacting Fleming-Viot processes with mutation and selection
Dawson, Donald A
2011-01-01
Consider a system $X = ((x_\\xi(t)), \\xi \\in \\Omega_N)_{t \\geq 0}$ of interacting Fleming-Viot diffusions with mutation and selection which is a strong Markov process with continuous paths and state space $(\\CP(\\I))^{\\Omega_N}$, where $\\I$ is the type space, ${\\Omega_N}$ the geographic space is assumed to be a countable group and $\\CP$ denotes the probability measures. We establish various duality relations for this process. These dualities are function-valued processes which are driven by a coalescing-branching random walk, that is, an evolving particle system which in addition exhibits certain changes in the function-valued part at jump times driven by mutation. In the case of a finite type space $\\I$ we construct a set-valued dual process, which is a Markov jump process, which is very suitable to prove ergodic theorems which we do here. The set-valued duality contains as special case a duality relation for any finite state Markov chain. In the finitely many types case there is also a further tableau-valued ...
Time scales: from Nabla calculus to Delta calculus and vice versa via duality
Caputo, M. Cristina
2009-01-01
In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.
Labor Market Duality and the Impact of Prolonged Recession on Employment in Croatia
Directory of Open Access Journals (Sweden)
Mislav Brkić
2015-06-01
Full Text Available The term labor market duality can be used to describe different forms of labor market segmentation. Nevertheless, this term is most often used to describe the segregation between permanent employees and workers employed on a temporary basis. There is a consensus in the literature that labor market duality most often occurs after governments engage in asymmetric reforms of the labor market legislation, which significantly liberalize the use of temporary contracts, while retaining a high level of employment protection for permanent workers. This paper analyzes whether in Croatia as a country with relatively rigid labor market legislation there are signs of labor market duality. The analysis is motivated by the recent data on employment flows showing that companies have intensified temporary hiring in recent years, which might be considered as a sign of increasing labor market duality. However, this paper discusses labor market developments in the context of persistent recession, taking into account that such changes in the employment flows could be a cyclical phenomenon reflecting high risk aversion of companies.
Vocational Training in India and the Duality Principle: A Case for Evidence-Based Reform
Mehrotra, Santosh; Kalaiyarasan, A.; Kumra, Neha; Ravi Raman, K.
2015-01-01
This article explores the notion of the duality principle, as embodied in the German dual system of Vocational Education and Training (VET), within the context of a field survey of skill shortages faced by German and Indian firms operating in India. The study finds that these firms experience problems with the quantity and quality of skills…