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 \( \left({S}_b^3/{\mathrm{\mathbb{Z}}}_r\right) \) partition functions, for certain three-dimensional \( \mathcal{N}=2 \) supersymmetric gauge theories.
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Gahramanov, I., Kels, A.P. The star-triangle relation, lens partition function, and hypergeometric sum/integrals. J. High Energ. Phys. 2017, 40 (2017). https://doi.org/10.1007/JHEP02(2017)040
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DOI: https://doi.org/10.1007/JHEP02(2017)040