Integrability from 2d N=(2,2) Dualities

Abstract

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.

30 pages, 8 figures

References in corpus (12)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• A topologically twisted index for three-dimensional supersymmetric theories
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Witten Index and Wall Crossing
• Brane Tilings and Their Applications
• Supersymmetric gauge theory and the Yangian
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Quivers, YBE and 3-manifolds
• An Index Formula for Supersymmetric Quantum Mechanics
• Emergent 3-manifolds from 4d Superconformal Indices
• Exactly marginal deformations of quiver gauge theories as seen from brane tilings
• Supersymmetric index on T^2 x S^2 and elliptic genus

Cited by in corpus (17)

• Brane Brick Models and 2d (0,2) Triality
• A slow review of the AGT correspondence
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Supersymmetric localization in two dimensions
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• Surface defects as transfer matrices
• A-twisted correlators and Hori dualities
• Integrable lattice spin models from supersymmetric dualities
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• Bethe/Gauge Correspondence for linear quiver theories with ABCD gauge symmetry and spin chains
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• Integrability As Duality: The Gauge/YBE Correspondence
• Exactly Solved Models and Beyond: a special issue in honour of R J Baxter's 75th birthday