Year: 2021
Type: article
Abstract: 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/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 ${U}_{q}(osp(1|2))$.
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Awards: G5051536600, G6700863588
OpenAlex ID: W3091749827