Minimal Liouville Gravity on the Torus via Matrix Models

TL;DR

This paper computes the torus correlation numbers in (3,p) minimal Liouville gravity by leveraging matrix model results, specifically calculating the partition function to derive one- and two-point correlators.

Contribution

It introduces a method to derive torus correlation functions in minimal Liouville gravity using matrix models and resonance relations, extending previous approaches to the torus topology.

Findings

Calculated the torus generating partition function for (3,p) matrix models.

Derived one- and two-point correlation numbers in minimal Liouville gravity.

Established a link between matrix models and minimal Liouville gravity on the torus.

Abstract

In this paper we use recent results on resonance relations between the matrix models and the minimal Liouville gravity to compute the torus correlation numbers in (3,p) minimal Liouville gravity. Namely, we calculate the torus generating partition function of the (3,p) matrix models and use it to obtain the one- and two-point correlation numbers in the minimal Liouville gravity.