DILATONIC GRAVITY NEAR 2 DIMENSIONS AND ASYMPTOTIC FREEDOM OF THE GRAVITATIONAL COUPLING-CONSTANT

Two models of dilatonic gravity are investigated: (i) dilaton-Yang-Mil ls gravity and (ii) higher-derivative dilatonic gravity. Both are reno rmalizable in 2 + epsilon dimensions and have a smooth limit for epsil on --> 0. The corresponding one-loop effective actions and beta-functi ons are found. Both theories are shown to possess a non-trivial ultrav iolet fixed point - for all dilatonic couplings - in which the gravita tional constant is asymptotically free (at epsilon --> 0). It is shown that in the regime of asymptotic freedom the matter central charge ca n be significantly increased by two different mechanisms - as compared with pure dilatonic gravity, where n < 24.