Relating Gauge Theories via Gauge/Bethe Correspondence

TL;DR

This paper explores the Gauge/Bethe correspondence to relate different quiver gauge theories and their associated Bethe equations, providing insights into the connection between supersymmetric gauge theories and integrable systems.

Contribution

It demonstrates how the Gauge/Bethe correspondence can relate three distinct quiver gauge theories through their Bethe equations, advancing understanding of gauge-integrable system relations.

Findings

Established relations between three quiver gauge theories

Connected gauge theories to the Bethe equations of the tJ model

Enhanced understanding of gauge/integrable system correspondence

Abstract

In this note, we use techniques from integrable systems to study relations between gauge theories. The Gauge/Bethe correspondence, introduced by Nekrasov and Shatashvili, identifies the supersymmetric ground states of an N=(2,2) supersymmetric gauge theory in two dimensions with the Bethe states of a quantum integrable system. We make use of this correspondence to relate three different quiver gauge theories which correspond to three different formulations of the Bethe equations of an integrable spin chain called the tJ model.