A new pentagon identity for the tetrahedron index

TL;DR

This paper presents a novel pentagon identity for tetrahedron indices derived from superconformal index dualities in 3D N=2 theories, with a rigorous mathematical proof.

Contribution

It introduces a new pentagon identity for tetrahedron indices based on superconformal index equivalences, expanding the mathematical understanding of these functions.

Findings

Derived a new pentagon identity for tetrahedron indices.

Provided a mathematical proof of the identity.

Linked the identity to dualities in 3D N=2 supersymmetric theories.

Abstract

Recently Kashaev, Luo and Vartanov, using the reduction from a four-dimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following their idea we have obtained a new pentagon identity for a certain combination of so-called tetrahedron indices arising from the equality of superconformal indices of dual three-dimensional N=2 supersymmetric theories and give a mathematical proof of it.