Multi-loop correlators for rational theories of 2D gravity from the generalized Kontsevich models

TL;DR

This paper develops a new parametrization of the generalized Kontsevich models' coupling space, derives explicit genus zero multi-loop correlators for certain rational matter fields coupled to 2D gravity, and explores their relation to two-matrix models.

Contribution

It introduces a moment-based parametrization and provides explicit formulas for multi-loop correlators in rational 2D gravity models.

Findings

Explicit genus zero multi-loop correlators for (3,3m-1) and (3,3m-2) models

A new parametrization of the coupling constant space using moments

Insights into the relation between two-matrix models and generalized Kontsevich models

Abstract

We introduce a parametrization of the coupling constant space of the generalized Kontsevich models in terms of a set of moments equivalent to those introduced recently in the context of topological gravity. For the simplest generalization of the Kontsevich model we express the moments as elementary functions of the susceptibilities and the eigenvalues of the external field. We furthermore use the moment technique to derive a closed expression for the genus zero multi-loop correlators for $(3,3m-1)$ and $(3,3m-2)$ rational matter fields coupled to gravity. We comment on the relation between the two-matrix model and the generalized Kontsevich models