On matrix models and their q-deformations

Authors: Luca Cassia, Rebecca Lodin and Maxim Zabzine

Preprint number: UUITP-25/20

Motivated by the BPS/CFT correspondence, we explore the similarities between the classical β-deformed Hermitean matrix model and the q-deformed matrix models associated to 3d N=2 supersymmetric gauge theories on D² ×_q S¹ and S_b³ by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the W-algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.