q-Virasoro constraints in matrix models

TL;DR

This paper derives q-Virasoro constraints for elliptic generalizations of hermitian matrix models, expanding understanding of their algebraic structures and connections to supersymmetric gauge theories.

Contribution

It introduces the derivation of q-Virasoro constraints for elliptic matrix models related to supersymmetric gauge theories, a novel extension of classical Virasoro constraints.

Findings

Derived q-Virasoro constraints for elliptic matrix models.

Identified algebraic properties of the q-Virasoro algebra.

Connected matrix models to supersymmetric gauge theory partition functions.

Abstract

The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new families of matrix models and we have very limited knowledge about these matrix models. We concentrate on elliptic generalization of hermitian matrix model which corresponds to calculation of partition function on $S^3 \times S^1$ for vector multiplet. We derive the $q$-Virasoro constraints for this matrix model. We also observe some interesting algebraic properties of the $q$-Virasoro algebra.