The star-square relation and the generalized star-triangle relation from 3d supersymmetric dualities I

TL;DR

This paper explores duality transformations in integrable lattice spin models derived from 3D supersymmetric gauge theories, leading to new solutions for star-square and star-triangle relations with multi-spin interactions.

Contribution

It introduces new solutions to duality relations in integrable models using gauge/YBE correspondence from supersymmetric dualities.

Findings

Constructed hyperbolic, lens hyperbolic, trigonometric, and rational solutions.

Developed models with four-spin and three-spin interactions.

Connected supersymmetric dualities to integrable lattice models.

Abstract

We study duality transformations of the star-square relation and the generalized star-triangle relation for Ising-like integrable lattice spin models. The integrable models are obtained via gauge/YBE correspondence which connects the supersymmetric gauge theories and lattice spin models of statistical mechanics. By the use of integral identities coming from the duality of three-dimensional supersymmetric gauge theories, we construct hyperbolic, lens hyperbolic, trigonometric, and rational solutions to the duality transformations. These duality transformations allow us to construct spin lattice models with four-spin (the star-square relation) and three-spin (the generalized star-triangle relation) interactions.