Hyperbolic and trigonometric hypergeometric solutions to the star-star equation

Erdal Catak; Ilmar Gahramanov; Mustafa Mullahasanoglu

doi:10.1140/epjc/s10052-022-10661-x

2021 Impact factor 4.991

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 789
https://doi.org/10.1140/epjc/s10052-022-10661-x

Regular Article - Theoretical Physics

Hyperbolic and trigonometric hypergeometric solutions to the star-star equation

Erdal Catak¹, Ilmar Gahramanov²^,3^,4^b and Mustafa Mullahasanoglu²

¹ 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

^b ilmar.gahramanov@boun.edu.tr

Received: 29 May 2022
Accepted: 1 August 2022
Published online: 5 September 2022

Abstract

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.

© The Author(s) 2022

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