publication . Other literature type . Preprint . Article . 2015

New solutions of the star–triangle relation with discrete and continuous spin variables

Andrew P Kels;
  • Published: 30 Oct 2015
  • Publisher: IOP Publishing
Abstract
A new solution to the star-triangle relation is given, for an Ising type model that involves interacting spins, that contain integer and real valued components. Boltzmann weights of the model are given in terms of the lens elliptic-gamma function, and are based on Yamazaki's recently obtained solution of the star-star relation. The star-triangle given here, implies Seiberg duality for the $4\!-\!d$ $\mathcal{N}=1$ $S_1\times S_3/\mathbb{Z}_r$ index of the $SU(2)$ quiver gauge theory, and the corresponding two component spin case of the star-star relation of Yamazaki. A proof of the star-triangle relation is given, resulting in a new elliptic hypergeometric integ...
Subjects
arXiv: Astrophysics::Galaxy AstrophysicsAstrophysics::Solar and Stellar AstrophysicsAstrophysics::Earth and Planetary AstrophysicsAstrophysics::Cosmology and Extragalactic Astrophysics
free text keywords: Mathematical Physics, Condensed Matter - Statistical Mechanics, High Energy Physics - Theory, Modelling and Simulation, Statistics and Probability, General Physics and Astronomy, Statistical and Nonlinear Physics, Gauge theory, S-duality, Ising model, Mathematical analysis, Elliptic gamma function, Seiberg duality, Integer, Dependence relation, Mathematics, Quantum mechanics, Quiver
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publication . Other literature type . Preprint . Article . 2015

New solutions of the star–triangle relation with discrete and continuous spin variables

Andrew P Kels;