Liouville theory revisited

TL;DR

This paper aims to unify various perspectives on Liouville theory as a 2D conformal field theory, developing new methods to construct exponential operators and establish their locality.

Contribution

It introduces a construction of exponential field operators from covariant chiral operators and demonstrates their locality through braid relations.

Findings

Construction of exponential operators from covariant chiral operators

Proof of locality of exponential fields using braid relations

Unified framework for Liouville theory approaches

Abstract

We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we need to develop further some of these approaches. This includes in particular a construction of general exponential field operators from a set of covariant chiral operators. The latter are shown to satisfy braid relations that allow one to prove the locality of the former.