Solving q-Virasoro constraints

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.

arXiv comment31 page

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• Genus expansion of matrix models and $\hslash$ expansion of KP hierarchy
• Non-stationary difference equation for q-Virasoro conformal blocks
• Virasoro Constraint for Uglov Matrix Model
• Combinatorics of KP hierarchy structural constants
• On refined Chern-Simons and refined ABJ matrix models
• CMM formula as superintegrability property of unitary model
• A new kind of anomaly: on W-constraints for GKM