New Integrable Models from the Gauge/YBE Correspondence

TL;DR

This paper introduces a new class of integrable lattice models derived from the Gauge/YBE correspondence, linking supersymmetric gauge theories with classical integrable systems, and reveals their deep connection with dualities in quantum field theories.

Contribution

It presents a novel integrable model from the Gauge/YBE correspondence, with a general solution to the Yang-Baxter equation and a new perspective on dualities in supersymmetric gauge theories.

Findings

New integrable models labeled by N and r

Solution to the Yang-Baxter equation generalizes known models

Integrability linked to Seiberg duality invariance

Abstract

We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of a large class of SU(N) quiver gauge theories with the partition function of 2d classical integrable spin models. The integrability of the model (star-star relation) is equivalent with the invariance of the index under the Seiberg duality. Our solution to the Yang-Baxter equation is one of the most general known in the literature, and reproduces a number of known integrable models. Our analysis identifies the Yang-Baxter equation with a particular duality (called the Yang-Baxter duality) between two 4d N=1 supersymmetric quiver gauge theories. This suggests that the integrability goes beyond 4d lens indices and can be extended to the full physical equivalence among the IR fixed points.