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