Solving q-Virasoro constraints

Source abstract

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 $$\beta$$ β -ensembles. From free field point of view, the models considered have zero momentum of the highest weight, which leads to an extra constraint $$T_{-1} \mathcal {Z} = 0$$ 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 $$D^2 \times S^1$$ D 2 × S 1 and $$S^3$$ S 3 .