Asymptotic safety in Einstein gravity and scalar-fermion matter.

Within the functional renormalization group approach we study the effective quantum field theory of Einstein gravity and one self-interacting scalar coupled to N(f) Dirac fermions. We include in our analysis the matter anomalous dimensions induced by all the interactions and analyze the highly nonlinear beta functions determining the renormalization flow. We find the existence of a nontrivial fixed point structure both for the gravity and the matter sector, besides the usual Gaussian matter one. This suggests that asymptotic safety could be realized in the gravitational sector and in the standard model. Nontriviality in the Higgs sector might involve gravitational interactions.