The functional renormalization group is utilized to formulate a quantum theory of dilaton gravity that is renormalizable on a non-perturbative level. In the limit where the scalar field’s magnitude is much larger than the renormalization scale, a set of closed β-functions is revealed which accounts for a trivial fixed point scenario. Therein, only the order independent of the scalar field remains nonzero, corresponding to an Einstein-Hilbert truncation with an additional kinetic term for the scalar field.
Specializing to dilatation symmetric effective actions, we propose a new fixed point scenario that respects the symmetry and is exact for the scale k approaching 0. It comprises only the coupling of the scalar field to gravity admissible by the symmetry with no scalar potential, thus having much simpler infrared structure than the usual Einstein-Hilbert action. Moreover, fixed point candidates for the opposing limit are examined. The renormalization group flows are shown to diverge for conformal coupling parameters, thereby realizing the Weyl anomaly. Physical implications are discussed and suggestions for subsequent research are given.