Virasoro Constraint for Uglov Matrix Model

Abstract

We study the root of unity limit of (q, t)-deformed Virasoro matrix models, for which we call the resulting model Uglov matrix model. We derive the associated Virasoro constraints on the partition function, and find agreement of the central charge with the expression obtained from the level-rank duality associated with the parafermion CFT.

NSR singular vectors from Uglov polynomials

“…Our computations here are very close to ones in [IOY13]. It is expected that in more general root of unity limit q-deformed Virasoro algebra will contain certain coset or parafermion algebra, see [BBT13], [IOY14], [KK22].…”