The star-triangle relation, lens partition function, and hypergeometric sum/integrals
arXiv:1610.09229 · doi:10.1007/JHEP02(2017)040
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 () partition functions, for certain three-dimensional supersymmetric gauge theories.
42 pages, 4 figures
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