R2 phase diagram of quantum Einstein gravity and its spectral dimension

Within the gravitational asymptotic safety program, the renormalization group (RG) flow of the R-2 truncation in three and four spacetime dimensions is analyzed in detail. In particular, we construct RG trajectories which emanate from the non-Gaussian UV fixed point and possess long classical regimes where the effective average action is well approximated by the classical Einstein-Hilbert action. As an application we study the spectral dimension of the effective quantum Einstein gravity spacetimes resulting from these trajectories, establishing that the picture of a multifractal spacetime is robust under the extension of the truncated theory space. We demonstrate that regimes of constant spectral dimension can either be attributed to universal features of RG fixed points or singular loci in the beta functions.