Progress in integrable statistical models inspired by supersymmetric gauge theories

by Ilmar Gahramanov (AEI Potsdam)

Thursday 13 Apr 2017, 13:15 → 14:15 Europe/Stockholm

132:028

Recently, there has been observed several connections of integrable models to supersymmetric gauge theories and special functions of hypergeometric type. One of such connections is a correspondence between supersymmetric quiver gauge theories and integrable lattice models such that the integrability emerges as a manifestation of supersymmetric dualities. Particularly, partition functions of supersymmetric quiver gauge theories with four supercharge on different manifolds can be identified with partition functions of two-dimensional exactly solvable statistical models. This relationship has led to the construction of new exactly solvable models of statistical mechanics, namely the Yang-Baxter equation was solved in terms of new special functions. In the talk, I will present some new solutions of the Yang-Baxter equation and related basic and hyperbolic hypergeometric integral identities.