Quantum Liouville Theory from a Diffeomorphism Chern-Simons Action

TL;DR

This paper demonstrates how a Chern-Simons action based on Christoffel Symbols naturally leads to a boundary Wess-Zumio-Witten model, which under chiral diffeomorphism restrictions becomes equivalent to quantum Liouville theory.

Contribution

It introduces a novel approach linking a Christoffel Symbols-based Chern-Simons action to quantum Liouville theory via boundary Wess-Zumio-Witten models.

Findings

Establishes a connection between Chern-Simons actions and Liouville theory.

Shows the boundary Wess-Zumio-Witten model arises naturally from the bulk action.

Demonstrates equivalence under chiral diffeomorphism restrictions.

Abstract

A Chern-Simons action written with Christoffel Symbols has a natural gauge symmetry of diffeomorphisms. This Chern-Simons action will induce a Wess-Zumio-Witten model on the boundary of the manifold. If we restrict the diffeomorphisms to chiral diffeomorphism, the Wess-Zumio-Witten model is equivalent to a quantum Liouville action.