Lens partition function, pentagon identity and star-triangle relation
| Autor: | Bozkurt, Deniz N., Gahramanov, Ilmar, Mullahasanoglu, Mustafa |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Phys. Rev. D 103, 126013 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.103.126013 |
| Popis: | We study the three-dimensional lens partition function for $\mathcal N=2$ 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 $U_q(osp(1|2))$. Comment: 22 pages, v2: minor corrections and comments, v3: minor corrections |
| Databáze: | arXiv |
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