Workshop, Victor Mishnyakov: Refined Matrix Models and DIM Recursion Relations

Speaker
Victor Mishnyakov,  Nordic Institute for Theoretical Physics

Abstract
We study solutions of q-Virasoro constraints in refined (or (q,t)-deformed) matrix models with various potentials. Our goal is to establish an analogue of the W (or cut-and-joint) representation and its relation to “superintegrability”—a special form of averages of Macdonald polynomials. The examples considered come from localization of 3D SUSY theories, including the refined Chern-Simons model or gauge theories with adjoint and fundamental matter. I will start by briefly reminding what happens to non-deformed models such as the Gaussian Hermitian model. Eventually, I will derive recursion relations given by quantum toroidal algebra operators that are satisfied by the partition functions of these models. For the Chern-Simons model at q=t these recursions seem to reproduce the recently obtained skein recursion relations for the unknot.