Pentagon identities arising in supersymmetric gauge theory computations

TL;DR

This paper explores pentagon identities derived from partition functions of 3D N=2 supersymmetric gauge theories, revealing their geometric and algebraic significance, including connections to Pachner moves and quantum Yang-Baxter solutions.

Contribution

It demonstrates how supersymmetric gauge theory partition functions lead to pentagon identities, linking physics, geometry, and algebra in novel ways.

Findings

Derivation of pentagon identities from gauge theory partition functions

Connection of identities to Pachner moves in triangulated manifolds

Potential applications to quantum Yang-Baxter equation solutions

Abstract

The partition functions of three-dimensional N=2 supersymmetric gauge theories on different manifolds can be expressed as q-hypergeometric integrals. By comparing the partition functions of three-dimensional mirror dual theories, one finds complicated integral identities. In some cases, these identities can be written in the form of pentagon relations. Such identities often have an interpretation as the Pachner's 3-2 move for triangulated manifolds via the so-called 3d-3d correspondence. From the physics perspective, another important application of pentagon identities is that they may be used to construct new solutions to the quantum Yang-Baxter equation.