On matrix models and their q-deformations
Luca Cassia, Rebecca Lodin, Maxim Zabzine
Abstract
A bstract 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 2 supersymmetric gauge theories on D 2 × q S 1 and $$ {S}_b^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>S</mml:mi><mml:mi>b</mml:mi><mml:mn>3</mml:mn></mml:msubsup></mml:math> 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.