Asymptotic safety and lattice quantum gravity

We review evidence presented recently that a nonperturbative formulation of quantum gravity defined by Euclidean Dynamical Triangulations with a nontrivial measure term gives rise to a phase with extended, four-dimensional geometries. The results are strikingly consistent with those of Causal Dynamical Triangulations for both the Hausdorff dimension, which is consistent with 4, and for the spectral dimension, which exhibits a scale dependence, running to 4 at long distances and to smaller values at short distances. We discuss some of the implications that this has for the asymptotic safety scenario for quantum gravity.