We develop the idea of local duality symmetry (LDS) in gauge field theories. Using Clifford algebra techniques we construct dually invariant scalar Lagrangian of electrodynamics in the presence of sources and demonstrate that in tensor formalism it is exactly the same as the usual one. Then we localize the duality symmetry with two possible options for the appearing pseudovector field - massive and massless. The first option might be interpreted as a candidate for dark matter. Perspectives of the application of LDS in QCD are briefly discussed.
We show the derivation of the self-duality relation of abelian higher-form gauge field strength in the topologically nontrivial spacetime background. The so-called Pasti-Sorokin-Tonin action for the self-dual abelian gauge field assumes that the spacetime topology is trivial to derive the self-duality relation using a gauge transformation of the action. In this paper we find a new gauge transformation of the same theory and show that this new gauge transformation enables us to derive the self-duality relation even in the topologically nontrivial spacetime background.
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.
We introduce the concept of duality between quantum field theories in the Batalin-Vilkovisky formalism, which is interpreted either as a BV morphism, the result of dual BV pushforwards or a combination of both. When a BV morphism affects only the target space of a given model, we call it T-duality. To justify this name, we demonstrate how topological aspects of T-duality in string theory such as the relation between curvature and H-flux or isomorphisms of Courant algebroids are equivalent to dualities of topological sigma models in two and three dimensions.
We deal with the duality symmetry of the Dilaton field in cosmology and specifically with the so-called Gasperini-Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the Dilaton field, and we show that under conformal transformations Gasperini-Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the Dilaton field. Finally, we show that the Lagrangian of the Dilaton field is equiva…
We investigate a new property of nets of local algebras over 4-dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point $p$ of the spacetime. Punctured Haag duality implies Haag duality and local definiteness. Our main result is that, if the theory is locally covariant in the sense of Brunetti, Fredenhagen and Verch, then also the converse holds. The free Klein-Gordon field provides an example in which this property is verified.
Using a mathematical framework which provides a generalization of the de Rham complex (well-designed for p-form gauge fields), we study the gauge structure and duality properties of theories for free gauge fields transforming in arbitrary irreducible representations of GL(D,R). We prove a generalization of the Poincare lemma which enables us to solve the above-mentioned problems in a systematic and unified way.
We propose a duality for N=2 d=3 Chern-Simons gauge theories with orthogonal gauge groups and matter in the vector representation. This duality generalizes level-rank duality for pure Chern-Simons gauge theories with orthogonal gauge groups and is reminiscent of Seiberg duality in four dimensions. We perform extensive checks by comparing partition functions of theories related by dualities. We also determine the conformal dimensions of fields using Z-extremization.
Lectures given by C.G. in the Advanced School on Effective Theories (Almuñecar, Granada, 1995) on duality in N=2 supersymmetric Yang-Mills, and the coupling to gravity.
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
Duality in supersymmetric SU(N) gauge theory with a symmetric tensor is studied using the technique of deconfining and Seiberg's duality. By construction the gauge group of the dual theory necessarily becomes a product group. In order to check the duality, several nontrivial consistency conditions are examined. In particular we find that by deforming along a flat direction, the duality flows to the Seiberg's duality of SO(N) gauge theory.
Duality symmetries are discussed for non-linear gauge theories of (n-1)-th rank antisymmetric tensor fields in general even dimensions d=2n. When there are M field strengths and no scalar fields, the duality symmetry groups should be compact. We find conditions on the Lagrangian required by compact duality symmetries and show an example of duality invariant non-linear theories. We also discuss how to enlarge the duality symmetries to non-compact groups by coupling scalar fields described by non-linear sigma models.
The quantum Yang-Mills theory describing dual ($\tilde g$) and non-dual ($g$) charges and revealing the generalized duality symmetry was developed by analogy with the Zwanziger formalism in QED.
We suggest IR-dual descriptions for d=3 N=2 supersymmetric gauge theories with gauge groups USp(2N_c) and U(N_c) and matter in the fundamental representation. We relate this duality to the IR duality of d=4 N=1 SQCD theories, and in one case also to mirror symmetry.
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.
Recently Seiberg has conjectured a duality symmetry connecting different theories of the supersymmetric QCD type. We provide support for this conjecture by analyzing a flat direction of the theory along which the two dual theories go over to the same theory in the IR.
In this paper we study U(1) gauge transformations on the space-time coordinates and on the background fields $g_{μν}$ and $ϕ$. For some special gauge functions, gauged coordinates and gauged U(1) field are equivalent to the rotated coordinates and rotated gauge field. We find gauge transformations that are symmetries of the string action. Also we obtain general $T$-duality transformations for the background fields. For special background fields this duality is equivalent to a gauge transformation.
We study the significance of T-duality in the context of the gravitational description of gauge theories. We found that T-duality relates the deferents points of the moduli of a given gauge theory always far from the conformal fixed point. Also the described gauge theories seems to flow naturally to the able conformal points, those that naturally saturate all the possible known examples of near horizon geometries. Supersymmetry properties and T-duality breaking of it are discuss.
An intriguing connection, based on duality symmetry, between ordinary (commutative) Born-Infeld type theory and non-commutative Maxwell type theory, is pointed out. Both discrete as well as continuous duality transformations are considered and their implications for self duality condition and Legendre transformations are analysed.
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 partons consist of extremely soft constituents and `hadrons' are made out of open Wilson lines.
It is well known that the classical equations of motion of Maxwell and Born-Infeld theories are invariant under a duality symmetry acting on the field strengths. We review the implementation of the SL(2,Z) duality in these theories as linear but non-local transformations of the potentials.
In this letter we implement a recently proposed {\it spacetime duality} approach to dualize a two dimensional, Abelian, gauge field theory, which has no dual version under $p$--duality. Our result suggests that spacetime duality spans a new, wider, class of dual theories, which cannot be related one to another by $p$--duality transformations.
This Ph.D. thesis was submitted to the Catholic University of Leuven. We discuss two main topics: various formulations of duality-symmetric theories and D=5 supergravity (both construction and supersymmetric solutions). The thesis is structured as follows: Ch. 1 Introduction; Ch. 2 String theory toolkit; Ch. 3 Free duality-symmetric theories; Ch. 4 Interacting duality-symmetric theories; Ch. 5 Conformal supergravity in D=5: Weyl multiplets; Ch. 6 Conformal supergravity in D=5: matter and gauge-fixing; Ch. 7 Supersymmetric solutions in D=5 gauged supergravity.
We propose an explicit description of duality walls which encode at low energy the global symmetry enhancement expected in the UV completion of certain five-dimensional gauge theories. The proposal is supported by explicit localization computations and implies that the instanton partition function of these theories satisfies novel and unexpected integral equations.
We study the Aharony duality for three dimensional $\mathcal N=2$ supersymmetric gauge theories for orthogonal gauge groups with matters in vector representation. We provide the evidence for the duality by working out the partition function on $S^3$ and the superconformal index, which show perfect agreement.
Dynamical origin of duality between gauge theory and gravity is studied using the dual transformation and the formation of graviton as a collective excitation of dual gauge bosons. In this manner, electric-magnetic duality in gauge theory is reduced to the duality between gauge theory and gravity.
T-duality has been shown to arise from a gauge symmetry in some string theories. However, in the case of \IIA\ compactified on a circle, it is not possible to show that this is the case. This situation is rather uncomfortable since string string duality suggests that all T-dualities should arise from a gauge symmetry. Here we show that the T-duality of \IIA\ compactified on a circle arises from the reparametrization of the supermembrane. Then we show how this reparametrization can be understood in terms of a gauge symmetry of the supermembrane, thus allowing to connect T-duality in \II\ to a g…
These lectures are an introduction to gauge/gravity duality, presented at TASI 2010. The first three sections present the basics, focusing on $AdS_5 \times S^5$. The last section surveys a variety of ways to generate duals of reduced symmetry.
We start by describing two of the main proposals for duality in Abelian gauge theories, namely $F$(ield strength)-duality approach and the $S$% -duality formalism. We then discuss how $F$-duality and $S$-duality can be applied to the case of linearized gravity. By emphasizing the similarities and differences between these two type of dualities we explore the possibility of combining them in just one duality formalism.
We examine the electric-magnetic duality for a U(1) gauge theory on a general 4-manifold. The partition function for such a theory transforms as a modular form of specific weight. However, in the canonical approach, we show that S-duality, like T-duality, is generated by a canonical transformation leading to a modular invariant partition function.
We study soliton gauge states in the spectrum of bosonic string compatified on torus. The enhenced Kac-Moody gauge symmetry, and thus T-duality, is shown to be related to the existence of these soliton gauge states in some moduli points.
This is a review of some basic features on the relation between supergravity and pure gauge theories with special emphasis on the relation between T-duality and supersymmetry. Some new results concerning the interplay between T-duality and near horizon geometries are presented
We study the equivalence/duality between various non-commutative gauge models at the classical and quantum level. The duality is realised by a linear Seiberg-Witten-like map. The infinitesimal form of this map is analysed in more details.
It has been conjectured that duality cascade occurs in the $\mathcal{N}=3$ supersymmetric Yang-Mills Chern-Simons theory with the gauge group $U(N )_k \times U(N+M )_{-k}$ coupled to two bi-fundamental hypermultiplets. The brane picture suggests that this duality cascade can be generalized to a class of 3d $\mathcal{N}=3$ supersymmetric quiver gauge theories coming from so-called Hanany-Witten type brane configurations. In this paper we perform non-perturbative tests of the duality cascades using supersymmetry localization. We focus on $S^3$ partition functions and prove predictions from the d…
We review the current status of the construction of unitary representations of U-duality groups of supergravity theories in five, four and three dimensions. We focus mainly on the maximal supergravity theories and on the N=2 Maxwell-Einstein supergravity (MESGT) theories defined by Jordan algebras of degree three in five dimensions and their descendants in four and three dimensions. Entropies of the extremal black hole solutions of these theories in five and four dimensions are given by certain invariants of their U-duality groups. The five dimensional U-duality groups admit extensions to spec…
In this work, we show that duality symmetry can be implemented for massive theories at the level of the action, whenever we can formulate appropriates gauge invariant actions. For a massive vectorial field, we use a known gauge invariant description, while for a massive graviton, we introduce a novel gauge invariant action in order to show duality invariance.
Using D-brane techniques, we compute the spectrum of stable BPS states in N=4 supersymmetric gauge theory, and find it is consistent with Montonen-Olive duality.
We briefly review the basics of electric-magnetic duality symmetry and their geometric interpretation in the M-theory context. Then we recall some no-go theorems that prevent a simple extension of the duality symmetry to non-Abelian gauge theories.
We explore the dynamics of three-dimensional Chern-Simons gauge theories with N=2 supersymmetry and matter in the fundamental and adjoint representations of the gauge group. Realizing the gauge theories of interest in a setup of threebranes and fivebranes in type IIB string theory we argue for a Seiberg duality that relates Chern-Simons theories with non-trivial superpotentials.
We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane R-R charge and a 0-brane R-R charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N=2 SU(N_c) gauge theories in four dimensions. We discuss the generalization to the N=1 duality scenario.
For non-Abelian tensor gauge fields we have found an alternative form of duality transformation, which has the property that the direct and the inverse transformations coincide. This duality transformation has the desired property that the direct and the inverse transformations map Lagrangian forms into each other.
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.
We analyze the Coulomb phase of theories of $N=2$ SQCD with $SU(N_c)$ gauge groups which are conjectured to have exact electric-magnetic duality. We discuss the duality transformation of the particle spectrum, emphasizing the differences between the general case and the $SU(2)$ case. Some difficulties associated with the definition of the duality transformation for a general gauge group are discussed. We compute the classical monopole spectrum of these theories, and when it is possible we use it to check the consistency of the duality. Generally these theories may have phase transitions betwee…
We consider new issues of duality in four-dimensional Lorentz-breaking field theories. In particular, we demonstrate that the arising of the aether-like Lorentz-breaking term is necessary in order for the 4D models to display the duality analog between the MCS and self-dual models in 3D. We further study the dispersion relations in both theories and discuss the physical contents of the models involved in this new dualilty.
We point out that for N=4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality groups of these theories are the Hecke groups with elliptic elements of order six and four, respectively. These groups extend certain subgroups of SL(2,Z) by elements with a non-trivial action on the moduli space. We show that under an embedding of these gauge theories into string theory, the Hecke duality groups are represented by T-duality transformations.
Recently N. Seiberg has shown that certain N=1 supersymmetric Yang -- Mills theories have the property that their infrared physics can be equivalently described by {\it two different} gauge theories, with the strong coupling region of one corresponding to the weak coupling region of the other. This duality leads to interesting results about the infrared dynamics of these theories. We generalize Seiberg's ideas to a new class of models for which a similar duality allows one to obtain rather detailed dynamical information about the long distance physics.
We describe some of the novel 6d quantum field theories which have been discovered in studies of string duality. The role these theories (and their 4d descendants) may play in alleviating the vacuum degeneracy problem in string theory is reviewed. The DLCQ of these field theories is presented as one concrete way of formulating them, independent of string theory.
In this paper we propose a duality for non-holomorphic N=1 CS-matter theories living on M2 branes probing Spin(7) cones. We call this duality Spin(7) duality. Two theories are named Spin(7) dual if they have the same moduli space: a real Spin(7) cone with base a weak G_2 manifold, and they are hence holographic dual to the same AdS_4 x G_2 M theory solution. We provide a systematic way to generate these dualities, derived by combining toric duality for N=2 CS-matter theories and generalized non-holomorphic orientifold projections to N=1. Brane construction, AdS/CFT correspondence, and the comp…
We review the emergence of gravity from gauge theory in the context of AdS/CFT duality. We discuss the evidence for the duality, its lessons for gravitational physics, generalizations, and open questions.
The supersymmetric generalization of Poisson-Lie T-duality in superconformal WZNW models is considered. It is shown that the classical N=2 superconformal WZNW models posses a natural Poisson-Lie symmetry which allows to construct dual $σ$- models.
We study four N=1 SU(N)^6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP_3 which is the blowup of P^2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class--an example of a phenomenon that has been termed "toric duality." However, little independent evidence has been given that such theories are infrared-equivalent. In fact, we show that …
The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle $θ$. This extended S-duality conjecture includes the case when the unbroken gauge group is non-abelian and a definite prediction for the spectrum of dyons results.
We present more examples of dual N=1 SUSY gauge theories. This set of theories is connected by flows to both Seiberg's and Kutasov's dual theories. This provides a unifying picture of the various dual theories. We investigate the dual theories, their flat directions and mass perturbations.
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.
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.)
