Correlation functions of two-matrix models

TL;DR

This paper presents a method for calculating correlation functions in two-matrix models using integrable hierarchies and W-constraints, avoiding continuum limit techniques to discover new solutions.

Contribution

It introduces a novel approach leveraging integrable hierarchies and W-constraints for explicit correlation function calculations in two-matrix models.

Findings

Explicit solutions satisfying W-constraints are obtained.

Many solutions are found without using continuum limit techniques.

The method enhances understanding of multi-matrix models.

Abstract

We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models. The second ingredient we use are the $W$--constraints. In fact an explicit solution of the relevant hierarchy, satisfying the $W$--constraints (string equation), underlies the explicit calculation of the correlation functions. In the course of our derivation we do not use any continuum limit tecnique. This allows us to find many solutions which are invisible to the latter technique.