English

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

Mathematical Physics 2017-02-15 v1 Statistical Mechanics High Energy Physics - Theory 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 (Sb3/ZrS_b^3/\mathbb{Z}_r) partition functions, for certain three-dimensional N=2\mathcal N = 2 supersymmetric gauge theories.

Keywords

Cite

@article{arxiv.1610.09229,
  title  = {The star-triangle relation, lens partition function, and hypergeometric sum/integrals},
  author = {Ilmar Gahramanov and Andrew P. Kels},
  journal= {arXiv preprint arXiv:1610.09229},
  year   = {2017}
}

Comments

42 pages, 4 figures

R2 v1 2026-06-22T16:35:20.259Z