Extra Observables in Gauged WZW Models

TL;DR

This paper explores a complexified gauged WZW model related to Liouville theory, revealing additional observables beyond Liouville's scope and connecting certain correlators to matrix model results.

Contribution

It introduces a gauged SL(2,C)/SU(2) model obtained via analytic continuation, uncovering new observables not present in Liouville theory, and links correlators to matrix models.

Findings

Discovery of infinitely many extra observables.

Identification of correlators matching matrix model results at special coupling.

Establishment of a more rigorous derivation of Liouville theory from the analytically continued model.

Abstract

It is known that Liouville theory can be represented as an SL(2,R) gauged WZW model. We study a two dimensional field theory which can be obtained by analytically continuing some of the variables in the SL(2,R) gauged WZW model. We can derive Liouville theory from the analytically continued model, ( which is a gauged SL(2,C)/SU(2) model, ) in a similar but more rigorous way than from the original gauged WZW model. We investigate the observables of this gauged SL(2,C)/SU(2) model. We find infinitely many extra observables which can not be identified with operators in Liouville theory. We concentrate on observables which are $(1,1)$ forms and the correlators of their integrals over two dimensional spacetime. At a special value of the coupling constant of our model, the correlators of these integrals on the sphere coincide with the results from matrix models.