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Title: Lens partition function, pentagon identity, and star-triangle relation
Authors: Bozkurt, Deniz N.
Gahramanov, Ilmar
Mullahasanoglu, Mustafa
Issue Date: 23-Jun-2021
Publisher: Physical Review D
Series/Report no.: Vol. 103;
Abstract: We study the three-dimensional lens partition function for N=2 supersymmetric gauge dual theories on S3/Zr by using the gauge/Yang-Baxter equation correspondence. This correspondence relates supersymmetric gauge theories to exactly solvable models of statistical mechanics. The equality of partition functions for the three-dimensional supersymmetric dual theories can be written as an integral identity for hyperbolic hypergeometric functions. We obtain such an integral identity which can be written as the star-triangle relation for Ising type integrable models and as the integral pentagon identity. The latter represents the basic 2-3 Pachner move for triangulated 3-manifolds. A special case of our integral identity can be used for proving orthogonality and completeness relation of the Clebsch-Gordan coefficients for the self-dual continuous series of Uq(osp(1|2)).
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