Hyperbolic and trigonometric hypergeometric solutions to the star-star equation

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 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.

14 pages, v2: minor corrections and comments, v3: minor corrections

References in corpus (8)

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• Quivers, YBE and 3-manifolds
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Cited by in corpus (2)

• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations