Correlation functions of two-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 technique. This allows us to find many solutions which are invisible to the latter technique.