Two dimensional gravity in genus one in Matrix Models, Topological and Liouville approaches

TL;DR

This paper evaluates the genus one correlation functions in a one-matrix model at the p-critical point on a torus, demonstrating their consistency with topological gravity relations and connecting matrix models with conformal field theory.

Contribution

It provides explicit calculations of genus one correlation numbers in matrix models and shows their agreement with topological gravity and CFT frameworks.

Findings

Correlation numbers satisfy Witten topological gravity relations

Explicit genus one correlation functions are computed

Connections between matrix models, topological gravity, and CFT are established

Abstract

One-matrix model in $p$-critical point on torus is considered. The generating function of correlation numbers in genus one is evaluated and used for computation correlation numbers in KdV and CFT frames. It is shown that the correlation numbers in KdV frame in genus one satisfy the Witten topological gravity recurrence relations.