DILATON-MAXWELL GRAVITY WITH MATTER NEAR 2 DIMENSIONS

Unlike Einstein gravity, dilaton-Maxwell gravity with matter is renorm alizable in 2 + epsilon dimensions and has a smooth epsilon --> 0 limi t. By performing a renormalization-group study of this last theory we show that the gravitational coupling constant G has a non-trivial, ult raviolet stable fixed point (asymptotic freedom) and that the dilatoni c coupling functions (including the dilatonic potential) exhibit also a real, non-trivial fixed point. At such point the theory represents a standard charged string-inspired model. Stability and gauge dependenc e of the fixed-point solution is discussed. It is shown that all these properties remain valid in a dilatonic-Yang-Mills theory with n scala rs and m spinors, that has the UF stable fixed point G() = 3 epsilon( 48 + 12N - m - 2n)(-1). In addition, it is seen that by increasing N ( number of gauge fields) the matter central charge C = n + m/2(0 < C < 24 + 6N) can be increased correspondingly (in pure dilatonic gravity 0 < C < 24).