Lens elliptic gamma function solution of the Yang–Baxter equation at roots of unity. (16th February 2018) - Kels, Andrew P; Yamazaki, Masahito
Abstract: We study the root of unity limit of the lens elliptic gamma function solution of the star-triangle relation, for an integrable model with continuous and discrete spin variables. This limit involves taking an elliptic nome to a primitive rN th root of unity, where r is an existing integer parameter of the lens elliptic gamma function, and N is an additional integer parameter. This is a singular limit of the star-triangle relation, and at subleading order of an asymptotic expansion, another star-triangle relation is obtained for a model with discrete spin variables in Z r N . Some special choices of solutions of equation of motion are shown to result in well-known discrete spin solutions of the star-triangle relation. The saddle point equations themselves are identified with three-leg forms of '3D-consistent' classical discrete integrable equations, known as Q 4 and Q 3 ( δ = 0 ) . We also comment on the implications for supersymmetric gauge theories, and in particular comment on a close parallel with the works of Nekrasov and Shatashvili.