Solving q-Virasoro constraints

2018-10-04

Authors: Rebecca Lodin, Aleksandr Popolitov, Shamil Shakirov, Maxim Zabzine

Preprint number: UUITP-44/18

We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for β-ensembles. From free field point of view the models considered have zero momentum of the highest weight, which leads to an extra constraint T_{−1}Z = 0. We then show how to solve these q-Virasoro constraints recursively and comment on the possible applications for gauge theories, for instance calculation of (supersymmetric) Wilson loop averages in gauge theories on D^2 × S^1 and S^3.