Solving q-Virasoro constraints

TL;DR

This paper derives q-Virasoro constraints for (q,t)-deformed eigenvalue matrix models using q-difference operators, providing recursive solutions with potential applications in gauge theory calculations.

Contribution

It introduces a novel elementary method to derive q-Virasoro constraints for a broad class of deformed matrix models and explores their recursive solutions.

Findings

Derived q-Virasoro constraints for (q,t)-deformed models.

Established recursive solution method for these constraints.

Discussed applications in gauge theory Wilson loop calculations.

Abstract

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 beta-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 \cross S^1 and S^3.