Unified description of correlators in non-Gaussian phases of Hermitean matrix model

TL;DR

This paper develops a unified, phase-independent operator framework to describe connected correlators in non-Gaussian phases of Hermitean matrix models, extending previous Gaussian case methods.

Contribution

It introduces a phase-independent check-operator approach for non-Gaussian Hermitean matrix models, generalizing known Gaussian phase techniques.

Findings

Check-operators resemble Gaussian case after definitions and ordering

Proposed explicit expressions are consistent with known properties

Framework potentially unifies correlator descriptions across phases

Abstract

Following the program, proposed in hep-th/0310113, of systematizing known properties of matrix model partition functions (defined as solutions to the Virasoro-like sets of linear differential equations), we proceed to consideration of non-Gaussian phases of the Hermitean one-matrix model. A unified approach is proposed for description of "connected correlators" in the form of the phase-independent "check-operators" acting on the small space of T-variables (which parameterize the polynomial W(z)). With appropriate definitions and ordering prescriptions, the multidensity check-operators look very similar to the Gaussian case (however, a reliable proof of suggested explicit expressions in all loops is not yet available, only certain consistency checks are performed).