CLASSICAL GRAVITY COUPLED TO LIOUVILLE THEORY

We consider the two-dimensional Jackiw-Teitelboim model of gravity. We first couple the model to the Liouville action and c scalar fields an d show, treating the combined system as a non-linear sigma model, that the resulting theory can be interpreted as a critical string moving i n a target space of dimension D = c + 2. We then analyse perturbativel y a generalised model containing a kinetic term and an arbitrary poten tial for the auxiliary field. We use the background field method and w ork with covariant gauges. We show that the renormalisability of the t heory depends on the form of the potential. For a general potential, t he theory can be renormalised as a non-linear sigma model. In the part icular case of a Liouville-like potential, the theory is renormalisabl e in the usual sense.