On matrix models and their q-deformations

Abstract

Abstract Motivated by the BPS/CFT correspondence, we explore the similarities be- tween the classical β-deformed Hermitean matrix model and the q-deformed matrix models associated to 3d N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories on D 2 × q S 1 and S b 3 $$ {S}_b^3 $$ 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.

Keywords

• Conformal and W Symmetry
• Matrix Models
• Supersymmetric Gauge Theory