On the Liouville Approach to Correlation Functions for 2-D Quantum Gravity

TL;DR

This paper evaluates three-point correlation functions in 2D quantum gravity coupled with minimal models, validating the continuation method for Liouville screening charges through semi-classical analysis.

Contribution

It provides a direct semi-classical validation of the Liouville screening charge continuation in computing correlation functions in 2D quantum gravity.

Findings

Validated the continuation in Liouville screening charges

Computed three-point functions for arbitrary states

Confirmed the semi-classical approach's consistency

Abstract

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions is shown directly from the Liouville functional integral using semi-classical methods.