Lens partition function, pentagon identity and star-triangle relation

DOI10.1103/PHYSREVD.103.126013arXiv2009.14198MaRDI QIDQ6350169

Mustafa Mullahasanoglu, Ilmar Gahramanov, Deniz N. Bozkurt

Publication date: 28 September 2020

Abstract: We study the three-dimensional lens partition function for $mathcalN=2$ supersymmetric gauge dual theories on $S^3/mathbb{Z}_r$ by using the gauge/YBE 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 $U_q(osp(1|2))$.

Mathematics Subject Classification ID

Yang-Baxter equations (16T25) Basic hypergeometric functions (33Dxx) Hypergeometric functions (33Cxx)

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