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Journal Article

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


Gahramanov,  Ilmar
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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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
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.