Comments on the multi-spin solution to the Yang-Baxter equation and basic hypergeometric sum/integral identity

TL;DR

This paper introduces a multi-spin solution to the Yang-Baxter equation derived from a hypergeometric sum-integral identity linked to supersymmetric index equivalences in 3D N=2 theories, advancing integrable models in statistical mechanics.

Contribution

It provides a novel multi-spin solution to the Yang-Baxter equation based on hypergeometric identities from supersymmetric dualities.

Findings

New multi-spin solution to Yang-Baxter equation

Connection between hypergeometric identities and integrable models

Application of supersymmetric index equality to statistical mechanics

Abstract

We present a multi-spin solution to the Yang-Baxter equation. The solution corresponds to the integrable lattice spin model of statistical mechanics with positive Boltzmann weights and parameterized in terms of the basic hypergeometric functions. We obtain this solution from a non-trivial basic hypergeometric sum-integral identity which originates from the equality of supersymmetric indices for certain three-dimensional N=2 Seiberg dual theories.