Gamma function solutions to the star-triangle equation

TL;DR

This paper explores solutions to the star-triangle equation using gamma functions, linking hypergeometric identities with supersymmetric theories and clarifying their interrelations.

Contribution

It introduces gamma function-based solutions to the star-triangle equation derived from hypergeometric integral identities and their connection to supersymmetric dualities.

Findings

Derived gamma function solutions from hypergeometric identities

Linked star-triangle solutions to supersymmetric partition functions

Clarified relations via gauge/YBE correspondence

Abstract

In the paper, we clarify some relations between solutions to the star-triangle equation via the gauge/YBE correspondence. We consider two solutions to the star-triangle relation in terms of Euler's gamma function. We derive these solutions from the reduction of certain basic and hyperbolic hypergeometric integral identities. These identities can be interpreted as equality of the supersymmetric partition functions of a specific three-dimensional N=2 supersymmetric dual theories.