GENERAL DILATONIC GRAVITY WITH AN ASYMPTOTICALLY FREE GRAVITATIONAL COUPLING-CONSTANT NEAR 2 DIMENSIONS

We study a renormalizable, general theory of dilatonic gravity (with a kinetic-like term for the dilaton) interacting with scalar matter nea r two dimensions. The one-loop effective action and the beta functions for this general theory are written down. It is proven that the theor y possesses a nontrivial uv fixed point which yields an asymptotically free gravitational coupling constant (at epsilon --> 0) in this regim e. Moreover, at the fixed point the theory can be cast under the form of a string-inspired model with free scalar matter. The renormalizatio n of the Jackiw-Teitelboim model and of lineal gravity in 2 + epsilon dimensions is also discussed. We show that these two theories are dist inguished at the quantum level. Finally, fermion-dilatonic gravity nea r two dimensions is considered.