The Gauge-Bethe Correspondence and Geometric Representation Theory

TL;DR

This paper proposes that geometric representation theory underpins the Gauge/Bethe correspondence, offering a unified mathematical framework to understand the relationship between integrable spin chains and supersymmetric gauge theories.

Contribution

It identifies geometric representation theory as the foundational mathematical structure behind the Gauge/Bethe correspondence, moving beyond mere observation.

Findings

Geometric representation theory explains the Gauge/Bethe correspondence.

Provides a unified framework for families of gauge theories.

Clarifies the mathematical basis of the spectrum-spin chain relationship.

Abstract

The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive. We argue here that geometrical representation theory is the mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.