Extra observables in gauged WZW models

It is known that Liouville theory can be presented 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 gauged SL(2, C/SU(2) model,) in a similar but more rigorous way than from the original gauged WZW model. We investigate the obsevables 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 integralsover 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.