On Elliptic Algebras and Large-n Supersymmetric Gauge Theories

TL;DR

This paper explores the duality between supersymmetric gauge theories and elliptic integrable systems, focusing on large-n limits and non-Abelian generalizations, revealing new connections in mathematical physics.

Contribution

It advances the understanding of gauge theory and integrable system dualities by extending previous results to non-Abelian cases and large-n limits.

Findings

Established a correspondence between gauge theories and elliptic integrable models.

Provided a non-Abelian generalization of the intermediate long wave model.

Analyzed the large-n limit to deepen the duality understanding.

Abstract

In this note we further develop the duality between supersymmetric gauge theories in various dimensions and elliptic integrable systems such as Ruijsenaars-Schneider model and periodic intermediate long wave hydrodynamics. These models arise in instanton counting problems and are described by certain elliptic algebras. We discuss the correspondence between the two types of models by employing the large-n limit of the dual gauge theory. In particular we provide non-Abelian generalization of our previous result on the intermediate long wave model.