  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.

High Energy Physics - Theory