Integrable lattice spin models from supersymmetric gauge theories

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 supercharges on different manifolds can be identified with partition functions of two-dimensional exactly solvable statistical models. This relationship has led to construction of new exactly solvable models of statistical mechanics, namely the Yang-Baxter equation was solved in terms of new special functions. The aim of the talk is to give a short account on progress in integrable lattice models which has been made due to the relationship with supersymmetric quiver gauge theories.