Dilaton‐Maxwell Gravity with Matter Near Two Dimensions

Unlike Einstein gravity, dilaton‐Maxwell gravity with matter is renormalizable in 2 + e 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 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 + 12 N – m – 2 n ) −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 + 6 N ) can be increased correspondingly (in pure dilatonic gravity 0 < C < 24).