Boundary Correlators in 2D Quantum Gravity: Liouville versus Discrete Approach

TL;DR

This paper compares boundary correlators in 2D quantum gravity derived from a microscopic loop gas model with those from Liouville theory, establishing their equivalence and providing geometric insights.

Contribution

It demonstrates the agreement between discrete loop gas models and Liouville theory for boundary correlators in 2D quantum gravity, offering a geometric interpretation.

Findings

Exact match between loop gas and Liouville boundary correlators

Geometric interpretation of the functional equation for correlators

Validation of microscopic models against continuum theory

Abstract

We calculate a class of two-point boundary correlators in 2D quantum gravity using its microscopic realization as loop gas on a random surface. We find a perfect agreement with the two-point boundary correlation function in Liouville theory, obtained by V. Fateev, A. Zamolodchikov and Al. Zamolodchikov. We also give a geometrical meaning of the functional equation satisfied by this two-point function.