Hyperbolic and trigonometric hypergeometric solutions to the star-star equation

TL;DR

This paper constructs hyperbolic and trigonometric solutions to the star-star relation using gauge theory dualities and hypergeometric functions, linking supersymmetric gauge theories with solvable statistical models.

Contribution

It introduces new solutions to the star-star relation derived from supersymmetric gauge theory dualities and hypergeometric function identities.

Findings

Derived hyperbolic and trigonometric solutions to the star-star relation.

Established integral identities for hyperbolic and basic hypergeometric functions.

Linked supersymmetric gauge theories with solvable statistical mechanics models.

Abstract

We construct the hyperbolic and trigonometric solutions to the star-star relation via the gauge/YBE correspondence by using the three-dimensional lens partition function and superconformal index for a certain N=2 supersymmetric gauge dual theories. This correspondence relates supersymmetric gauge theories to exactly solvable models of statistical mechanics. The equality of partition functions for the three-dimensional supersymmetric dual theories can be written as an integral identity for hyperbolic and basic hypergeometric functions.