Publication:
Lens partition function, pentagon identity, and star-triangle relation

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Gahramanov, Ilmar
Mullahasanoğlu, Mustafa

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Publication Date

2021

Language

English

Type

Journal Article

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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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Source:

Physical Review D

Publisher:

American Physical Society (APS)

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Astronomy and astrophysics, Physics

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