No abstract

We study lens partitions functions for the three-dimensional N = 2 supersymmetric gauge theories on S 3 b /Z r . We consider equality as a new hyperbolic hypergeometric solution to the star-star relation via gauge/YBE correspondence. The correspondence allows the construction of integrable lattice spin models of statistical mechanics by the usage of integral identities. Additionally, we obtain new hyperbolic hypergeometric integral identities of gauge theories.

We construct the hyperbolic and trigonometric solutions to the star-star relation via the gauge/YBE correspondence by using the three-dimensional lens partition function and superconformal index for a certain $$\mathcal N=2$$ N = 2 supersymmetric gauge dual theories. 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 and basic hypergeometric functions.