Five-point correlation numbers in minimal Liouville gravity and matrix models

TL;DR

This paper derives explicit five-point correlation numbers in minimal Liouville gravity using Zamolodchikov's equations and compares these results with matrix model calculations, advancing understanding of quantum gravity models.

Contribution

It provides the first explicit expression for five-point correlation numbers in minimal Liouville gravity and bridges these results with matrix model computations.

Findings

Explicit 5-point correlation numbers derived

Comparison with matrix model calculations performed

Advances in understanding minimal Liouville gravity achieved

Abstract

In this article, we will show how to use Zamolodchikov's higher equations of motion in Liouville field theory to explicitly calculate $N$-point correlation numbers in minimal Liouville gravity for $N>4$. We find the explicit expression for the 5-point correlation numbers and compare it with calculations in the one-matrix models.