Higher genus correlators from the hermitian one-matrix model

Abstract

We develop an iterative algorithm for the genus expansion of the hermitian N × N one-matrix model (is the Penner model in an external field). By introducing moments of the external field, we prove that the genus g contribution to the m-loop correlator depends only on 3 g−2+ m lower moments (3 g−2 for the partition function). We present the explicit results for the partition function and the one-loop correlator in genus one. We compare the correlators for the hermitian one-matrix model with those at zero momenta for c = 1 CFT and show an agreement of the one-loop correlators for genus zero.