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

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1610.09229.pdf

(Preprint), 521KB

JHEP02(2017)040.pdf

(Publisher version), 750KB

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##### Citation

Gahramanov, I., & Kels, A. P. (2017). The star-triangle relation, lens partition
function, and hypergeometric sum/integrals.* Journal of high energy physics: JHEP,* *2017*(02): 040. doi:10.1007/JHEP02(2017)040.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002C-3991-8

##### 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.