From rarefied elliptic beta integral to parafermionic star-triangle relation

TL;DR

This paper explores limits of the rarefied elliptic beta integral to derive an integral identity involving parafermionic hyperbolic gamma functions, illuminating the star-triangle relation in parafermionic Liouville theory.

Contribution

It introduces a new integral identity for parafermionic hyperbolic gamma functions derived from the rarefied elliptic beta integral.

Findings

Derived a star-triangle relation for parafermionic Liouville theory.

Established a connection between elliptic beta integrals and parafermionic functions.

Provided new mathematical tools for studying parafermionic conformal field theories.

Abstract

We consider the rarefied elliptic beta integral in various limiting forms. In particular, we obtain an integral identity for parafermionic hyperbolic gamma functions which describes the star-triangle relation for parafermionic Liouville theory.