Unification of integrability in supersymmetric gauge theories

TL;DR

This paper demonstrates how a six-dimensional supersymmetric gauge theory, via string theory dualities, unifies various integrable models like the eight-vertex and XYZ spin chain, revealing deep connections between gauge theories and integrability.

Contribution

It introduces a unifying framework linking supersymmetric gauge theories, string theory, and integrable lattice models, extending the understanding of integrability in high-dimensional theories.

Findings

Unified description of integrable models from supersymmetric gauge theories

Connection between 6D gauge theories and lattice models like XYZ spin chain

Application of string dualities to relate gauge theories and integrable systems

Abstract

A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six dimensions, topologically twisted and subjected to an \Omega-deformation. By realizing the six-dimensional theory in string theory and applying dualities, we unify various phenomena in which the eight-vertex model and the XYZ spin chain, as well as variants thereof, emerge from supersymmetric gauge theories.