Dilaton-Maxwell gravity with matter near two dimensions

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Unlike Einstein gravity, dilaton-Maxwell gravity with matter is renormalizable in 2+ε dimensions and has a smooth ε→ 0 limit.By performing a renormalization- group study of this last theory we show that the gravitational coupling constant G has a non-trivial,ultraviolet stable fixed point (asymptotic freedom) and that the dilatonic 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 the gauge dependence of the fixed-point solution is discussed.It is shown that all these properties remain valid in a dilatonic-Yang-Mills theory with n scalars and m spinors, that has the UF stable fixed point G* = 3ε(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).