General modular quantum dilogarithm and beta integrals

Abstract

We consider a univariate beta integral composed from general modular quantum dilogarithm functions and prove its exact evaluation formula. It represents the partition function of a particular $3d$ supersymmetric field theory on the general squashed lens space. Its possible applications to $2d$ conformal field theory are briefly discussed as well.

typos corrected, 20 pages

References in corpus (10)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Essays on the theory of elliptic hypergeometric functions
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• Properties of generalized univariate hypergeometric functions
• Exact solution of the Faddeev-Volkov model
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• On beta pentagon relations

Cited by in corpus (3)

• A parafermionic hypergeometric function and supersymmetric 6j-symbols
• Superconformal indices, Seiberg dualities and special functions
• S-move matrix in the NS sector of $N=1$ super Liouville field theory