Ordinary limits of the hyperbolic hypergeometric integral identities

TL;DR

This paper derives new ordinary hypergeometric identities from hyperbolic hypergeometric integral identities, using supersymmetric dualities in gauge theories to connect complex special functions with physical theories.

Contribution

It introduces novel hypergeometric identities by linking supersymmetric gauge theory partition functions to hyperbolic hypergeometric integrals.

Findings

New hypergeometric identities derived from supersymmetric dualities

Connections established between gauge theory partition functions and special functions

Advances in understanding hyperbolic hypergeometric integrals

Abstract

The computation of the partition function of supersymmetric gauge theories on compact manifolds can be reduced to matrix integrals by using the supersymmetric localization technique. Such matrix integrals in the case of three-dimensional supersymmetric gauge theories on lens space can be expressed in terms of hyperbolic hypergeometric integrals. By studying partition functions of supersymmetric dual theories, one can obtain new complicated identities for this type of special function. We derive new ordinary hypergeometric identities from the reduction of certain hyperbolic hypergeometric integral identities obtained via supersymmetric infrared dualities.