On Correlation Numbers in 2D Minimal Gravity and Matrix Models

TL;DR

This paper verifies four-point correlation numbers in 2D Minimal Gravity using matrix models, constructs a resonance transformation linking parameters, and proposes its general form.

Contribution

It provides a detailed comparison between Liouville Gravity and Matrix Models, introducing a resonance transformation and conjecturing its general structure.

Findings

Full agreement between correlation numbers in both approaches

Construction of a resonance transformation relating parameters

Proposal of the general form of the resonance transformation

Abstract

We test recent results for the four-point correlation numbers in Minimal Liouville Gravity against calculations in the one-Matrix Models, and find full agreement. In the process, we construct the resonance transformation which relates coupling parameters of the Liouville Gravity with the couplings of the Matrix Models, up to the terms of the order 4. We also conjecture the general form of this transformation.