On the equivalence of the SO(2,1) gauged WZW form and Liouville theory

TL;DR

This paper demonstrates the on-shell equivalence between Liouville theory and the SO(2,1) gauged WZW model, providing insights that could lead to higher-dimensional generalizations of Liouville theory.

Contribution

It establishes a formal equivalence between Liouville theory and a specific gauged WZW model, revealing new connections in theoretical physics.

Findings

Liouville theory is on-shell equivalent to the SO(2,1) gauged WZW term

This equivalence suggests potential for higher-dimensional generalizations

Provides a new perspective on the structure of two-dimensional conformal theories

Abstract

It is proved that Liouville theory and the two dimensional SO(2,1) gauged Wess-Zumino-Witten term are on-shell equivalent. This shed light on a possible higher dimensional generalization of the former theory.