Logarithmic Correlation Functions in Liouville Field Theory

TL;DR

This paper investigates logarithmic four-point correlation functions in Liouville field theory and their relation to two-dimensional quantum gravity coupled with conformal field theories, highlighting conditions for their emergence.

Contribution

It provides a detailed analysis of logarithmic correlation functions in Liouville theory and explores their occurrence in minimal conformal models coupled to gravity.

Findings

Logarithmic correlation functions appear under specific conditions in Liouville theory.

The study connects these functions to gravitationally dressed operators in minimal models.

Conditions for the emergence of logarithmic behavior are identified in the gravitational sector.

Abstract

We study four-point correlation functions with logarithmic behaviour in Liouville field theory on a sphere, which consist of one kind of the local operators. We study them as non-integrated correlation functions of the gravitational sector of two-dimensional quantum gravity coupled to an ordinary conformal field theory in the conformal gauge. We also examine, in the (p,q) minimal conformal field theories, a condition of the appearance of logarithmic correlation functions of gravitationally dressed operators.