Bailey pairs for the q-hypergeometric integral pentagon identity

TL;DR

This paper introduces new Bailey pairs related to the q-hypergeometric integral pentagon identity, connecting supersymmetric dual theories and integrable lattice models through advanced mathematical functions.

Contribution

It constructs novel Bailey pairs for the integral pentagon identity using q-hypergeometric functions, linking supersymmetric theories and integrable models.

Findings

New Bailey pairs for the integral pentagon identity

Connection between supersymmetric dual theories and lattice models

Mathematical framework for star-triangle relation

Abstract

In this work, we construct a new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents equality of the partition functions of a certain three-dimensional supersymmetric dual theories. It can be also interpreted as the star-triangle relation for the Ising-type integrable lattice model.