Massive Dilaton and Topological Gravity

A model in which the massive dilaton is introduced by minimally extending the two dimensional topological gravity is studied semi-classically. The theory is no longer topological because of the explicit Weyl scale symmetry breaking. Due to the dilaton the semiclassical stress-energy tensor gets renormalized and it is shown how the gravitational background coupled to the the dilaton depends on the dilaton mass as well as the renormalization mass scale, but not on the Newton's constant.