General Modular Quantum Dilogarithm and Beta Integrals

Gor A. Sarkissian ; Vyacheslav P. Spiridonov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 269-289.

Résumé

We consider a univariate beta integral composed of 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.

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