Regular Article - Theoretical Physics
Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
Department of Physics, Istanbul University, 34134, Istanbul, Turkey
2 Department of Physics, Bogazici University, Bebek, 34342, Istanbul, Turkey
3 Department of Mathematics, Khazar University, Mehseti St. 41, AZ1096, Baku, Azerbaijan
4 Institute of Radiation Problems, Azerbaijan National Academy of Sciences, B.Vahabzade St. 9, AZ1143, Baku, Azerbaijan
Accepted: 1 August 2022
Published online: 5 September 2022
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 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.
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