Integrability from 2d dualities

Abstract

We study integrable models in the context of the recently discovered Gauge/YBE correspondence, where the Yang–Baxter equation (YBE) is promoted to a duality between two supersymmetric gauge theories. We study flavored elliptic genus of 2d quiver gauge theories, which are defined from statistical lattices regarded as quiver diagrams. Our R-matrices are written in terms of theta functions and simplify 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.