The conformal sector of Quantum Einstein Gravity beyond the local potential approximation

The anomalous scaling of Newton's constant around the Reuter fixed point is dynamically computed using the functional flow equation approach. Specifically, we thoroughly analyze the flow of the most general conformally reduced Einstein -Hilbert action. Our findings reveal that, due to the distinctive nature of gravity, the anomalous dimension eta of the Newton's constant cannot be constrained to have one single value: the ultraviolet critical manifold is characterized by a line of fixed points (g(& lowast;)(eta), lambda(& lowast;)(eta)), with a discrete (infinite) set of eigenoperators associated to each fixed point. More specifically, we find three ranges of eta corresponding to different properties of both fixed points and eigenoperators and, in particular, for the range eta < eta(c) approximate to 0.96 the ultraviolet critical manifolds has finite dimensionality.