Vanishing superconformal indices and the chiral symmetry breaking

Spiridonov, V. P.; Vartanov, G. S.

doi:10.1007/jhep06(2014)062

Cited by 30 publications

(41 citation statements)

References 62 publications

(167 reference statements)

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“…The boundary conditions for the Boltzmann weights play a role of the "chiral" symmetry breaking phenomenon on the gauge theory side [6,80]. It is not well-studied subject on the level of supersymmetric partition functions and much work remains to be done in this direction.…”

Section: 3mentioning

confidence: 99%

The star-triangle relation, lens partition function, and hypergeometric sum/integrals

Gahramanov

Kels

2017

J. High Energ. Phys.

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The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens (S 3 b /Z r ) partition functions, for certain three-dimensional N = 2 supersymmetric gauge theories.

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Section: 3mentioning

confidence: 99%

The star-triangle relation, lens partition function, and hypergeometric sum/integrals

Gahramanov

Kels

2017

J. High Energ. Phys.

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“…This is a consequence of confinement and chiral symmetry breaking [36,37]. At low energies the theory on the left-hand side is described by the mesons and the baryons.…”

Section: Quiver Gauge Theories and Their Supersymmetric Indicesmentioning

confidence: 99%

Surface defects as transfer matrices

Maruyoshi

Yagi

2016

Prog. Theor. Exp. Phys.

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The supersymmetric index of the 4d N = 1 theory realized by a brane tiling coincides with the partition function of an integrable 2d lattice model. We argue that a class of half-BPS surface defects in brane tiling models are represented on the lattice model side by transfer matrices constructed from L-operators. For the simplest surface defects in theories with SU(2) flavor groups, we identify the relevant L-operator as that discovered by Sklyanin in the context of the eight-vertex model. We verify this identification by computing the indices of class-S and -S k theories in the presence of the surface defects.A Definitions and useful formulas 53 A.1 Theta functions 53 A.2 Elliptic gamma function 54

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“…If we give vevs to baryons of fugacities (α The theory has a vacuum where M = Λ 2 and B =B = 0, which would precisely Higgs the left and right SU(N ) 2 gauge groups and thus bring us back to the standard theory with two fewer minimal punctures, except for the extra baryonic degrees of freedom B,B. Even at the level of the index, one finds that the N f = N node effectively produces a delta function [36] of the fugacities of the left and right SU(N ) z 2 gauge groups, multiplied by the index of the baryons B,B with fugacities (α…”

Section: Jhep07(2015)073mentioning

confidence: 99%

N = 1 $$ \mathcal{N}=1 $$ theories of class S k $$ {\mathcal{S}}_k $$

Gaiotto

Razamat

2015

J. High Energ. Phys.

106

209

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We construct classes of N = 1 superconformal theories elements of which are labeled by punctured Riemann surfaces. Degenerations of the surfaces correspond, in some cases, to weak coupling limits. Different classes are labeled by two integers (N, k). The k = 1 case coincides with A N −1 N = 2 theories of class S and simple examples of theories with k > 1 are Z k orbifolds of some of the A N −1 class S theories. For the space of N = 1 theories to be complete in an appropriate sense we find it necessary to conjecture existence of new N = 1 strongly coupled SCFTs. These SCFTs when coupled to additional matter can be related by dualities to gauge theories. We discuss in detail the A 1 case with k = 2 using the supersymmetric index as our analysis tool. The index of theories in classes with k > 1 can be constructed using eigenfunctions of elliptic quantum mechanical models generalizing the Ruijsenaars-Schneider integrable model. When the elliptic curve of the model degenerates these eigenfunctions become polynomials with coefficients being algebraic expressions in fugacities, generalizing the Macdonald polynomials with rational coefficients appearing when k = 1.

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Vanishing superconformal indices and the chiral symmetry breaking

Cited by 30 publications

References 62 publications

The star-triangle relation, lens partition function, and hypergeometric sum/integrals

The star-triangle relation, lens partition function, and hypergeometric sum/integrals

Surface defects as transfer matrices

N = 1 $$ \mathcal{N}=1 $$ theories of class S k $$ {\mathcal{S}}_k $$

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