  A model of matter-coupled gravity in two dimensions is quantized. The crucial
requirement for performing the quantization is the vanishing of the conformal
anomaly, which is achieved by tuning a parameter in the interaction potential.
The spectrum of the theory is determined by mapping the model first onto a
field theory with a Liouville interaction, then onto a linear dilaton conformal
field theory. In absence of matter fields a pure gauge theory with massless
ground state is found; otherwise it is possible to minimally couple up to 11
matter scalar fields: in this case the ground state is tachyonic and the matter
sector decouples, like the transverse oscillators in the critical bosonic
string.
