Virasoro Constraint for Uglov Matrix Model

TL;DR

This paper investigates the Uglov matrix model derived from the root of unity limit of deformed Virasoro matrix models, establishing Virasoro constraints and connecting the central charge to parafermion CFT via level-rank duality.

Contribution

It introduces the Uglov matrix model and derives Virasoro constraints, linking the model's central charge to parafermion conformal field theory.

Findings

Derived Virasoro constraints for the Uglov matrix model.

Confirmed the central charge matches parafermion CFT predictions.

Established the connection via level-rank duality.

Abstract

We study the root of unity limit of $(\textbf{q}, \textbf{t})$-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.