On (q,t)-deformation of Gaussian matrix model

TL;DR

This paper explores a q,t-deformation of Gaussian matrix models by replacing Schur polynomials with Macdonald polynomials, leading to new integral representations and constraints.

Contribution

It introduces a novel q,t-deformation framework for Gaussian matrix models using Macdonald polynomials, extending existing perturbative correlator formulas.

Findings

Eigenvalue integral representations derived

Virasoro-like constraints established

Framework generalizes Schur-preservation property

Abstract

The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schur-preservation property of Gaussian measures. Then substitution of Schur by, say, Macdonald polynomials, defines a q,t-deformation of the matrix model. Eigenvalue integral representations and Virasoro-like constraints are immediate consequences.