Basic hypergeometry of supersymmetric dualities

TL;DR

This paper introduces new hypergeometric identities relevant to superconformal index calculations in 3D supersymmetric dual theories, providing both mathematical proofs and physical insights.

Contribution

It presents novel identities involving basic hypergeometric sums and integrals with applications in supersymmetric dualities.

Findings

New hypergeometric identities derived and proved

Applications to superconformal index computations

Physical interpretations of mathematical identities

Abstract

We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic proofs and physical interpretations of the presented identities.