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Mathematical Physics, math-ph, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,High Energy Physics - Theory, hep-th,Mathematics, Mathematical Physics, math.MP
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.
