Exact Correlators of Two-Matrix Models

TL;DR

This paper provides exact, genus-by-genus correlation functions for two-matrix models, differentiating between unconstrained models related to $c=1$ string theory and constrained models linked to topological field theories and gravity.

Contribution

It offers the first exact solutions for two-matrix models, including detailed genus expansions for both unconstrained and constrained types, especially those related to KdV and Boussinesq hierarchies.

Findings

Exact genus-by-genus correlation functions derived.

Distinction between unconstrained and constrained models clarified.

Connections to $c=1$ string theory and topological gravity established.

Abstract

We compute exact solutions of two--matrix models, i.e. detailed genus by genus expressions for the correlation functions of these theories, calculated without any approximation. We distinguish between two types of models, the unconstrained and the constrained ones. Unconstrained two--matrix models represent perturbations of $c=1$ string theory, while the constrained ones correspond to topological field theories coupled to topological gravity. Among the latter we treat in particular detail the ones based on the KdV and on the Boussinesq hierarchies.