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

TL;DR

This paper explores the connection between integrable models and supersymmetric gauge theories via the Gauge/YBE correspondence, focusing on elliptic genus computations and R-matrix structures in 2d N=(2,2) theories.

Contribution

It introduces a novel approach to constructing R-matrices from 2d supersymmetric gauge theories and analyzes their properties, including modularity and simplifications in Abelian cases.

Findings

R-matrices expressed in theta functions

Simplification of R-matrices for Abelian gauge groups

Discussion of modularity and string theory realizations

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.