Quantum Liouville Field Theory as Solution of a Flow Equation

TL;DR

This paper develops a framework using an exact renormalization group equation to quantize Liouville field theory with Weyl invariance, revealing a flow connecting two conformal field theories with different central charges.

Contribution

It introduces a novel flow equation approach for Weyl invariant quantization of Liouville theory and identifies a universality class linking two conformal field theories.

Findings

Flow equation describes scale dependence of effective action with infrared cutoff.

Derived Ward identities for Weyl transformations with cutoff.

Identified a trajectory connecting conformal field theories with central charges 25-c and 26-c.

Abstract

A general framework for the Weyl invariant quantization of Liouville field theory by means of an exact renormalization group equation is proposed. This flow equation describes the scale dependence of the effective average action which has a built-in infrared cutoff. For c<1 it is solved approximately by a truncation of the space of action functionals. We derive the Ward identities associated to Weyl transformations in presence of the infrared cutoff. They are used to select a specific universality class for the renormalization group trajectory which is found to connect two conformal field theories with central charges 25-c and 26-c, respectively.