Notes on the lens integral pentagon identity

TL;DR

This paper derives the lens integral pentagon identity for 3D mirror dual theories using hyperbolic hypergeometric functions, based on supersymmetric partition function dualities.

Contribution

It introduces a new derivation of the lens integral pentagon identity from supersymmetric dualities and hypergeometric functions.

Findings

Derived the lens integral pentagon identity for 3D mirror dual theories.

Connected supersymmetric partition functions with hyperbolic hypergeometric functions.

Provided a new mathematical framework for understanding 3D dualities.

Abstract

We obtain the lens integral pentagon identity for three-dimensional mirror dual theories in terms of hyperbolic hypergeometric functions via reduction of equality for $\mathcal N=2$ lens supersymmetric partition functions of a certain supersymmetric IR duality.