q-Virasoro constraints in matrix models

Understand

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.