From rarefied elliptic beta integral to parafermionic star-triangle relation

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.

19 pages

References in corpus (7)

• Essays on the theory of elliptic hypergeometric functions
• Exact solution of the Faddeev-Volkov model
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• On the fusion matrix of the N=1 Neveu-Schwarz blocks
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• Comments on fusion matrix in N=1 super Liouville field theory

Cited by in corpus (5)

• Lens partition function, pentagon identity and star-triangle relation
• General modular quantum dilogarithm and beta integrals
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations