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Hyperbolic and trigonometric hypergeometric solutions to the star-star equation

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arxiv 2107.06880 v3 pith:ODSZ4W5G submitted 2021-07-14 hep-th math-phmath.MPnlin.SI

Erdal Catak , Ilmar Gahramanov , Mustafa Mullahasanoglu This is my paper · ORCID
classification hep-thmath-phmath.MPnlin.SI
keywords gaugehyperbolicsupersymmetrictheoriescorrespondencedualfunctionshypergeometric
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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 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.

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  1. Flipping relation as a reduced star-star relation

    hep-th 2025-08 conditional novelty 5.0 of 10

    A specific limit of the star-star relation produces the flipping relation, and new flipping solutions are given in several gamma-function families.

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