Integrable lattice spin models from supersymmetric dualities

TL;DR

This paper explores the connection between supersymmetric gauge theories and integrable lattice models, showing how dualities in gauge theories can generate new integrable models and deepen understanding of their mathematical structure.

Contribution

It provides a concise overview of recent progress in deriving integrable lattice models from supersymmetric dualities, highlighting the role of gauge theory identities in integrability.

Findings

Dualities correspond to partition function identities

New integrable models can be generated from gauge theory dualities

Yang-Baxter equation relates to gauge theory partition functions

Abstract

Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the quiver diagram, the partition function of the lattice model is the partition function of the gauge theory and the Yang-Baxter equation expresses the identity of partition functions for dual pairs. This correspondence is a powerful tool which enables us to generate new integrable models. The aim of the present paper is to give a short account on a progress in integrable lattice models which has been made due to the relationship with supersymmetric gauge theories.