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arXiv · 1610.09229

The star-triangle relation, lens partition function, and hypergeometric sum/integrals

Ilmar Gahramanov·Andrew P. Kels
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Abstract

The aim of the present paper is to consider the hyperbolic limit of an elliptic hypergeometric sum/integral identity, and associated lattice model of statistical mechanics previously obtained by the second author. The hyperbolic sum/integral identity obtained from this limit, has two important physical applications in the context of the so-called gauge/YBE correspondence. For statistical mechanics, this identity is equivalent to a new solution of the star-triangle relation form of the Yang-Baxter equation, that directly generalises the Faddeev-Volkov models to the case of discrete and continuous spin variables. On the gauge theory side, this identity represents the duality of lens ($S_b^3/\mathbb{Z}_r$) partition functions, for certain three-dimensional $\mathcal N = 2$ supersymmetric gauge theories.

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Ilmar Gahramanov, Andrew P. Kels. 2016-10-28. The star-triangle relation, lens partition function, and hypergeometric sum/integrals. https://doi.org/10.1007/jhep02(2017)040

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