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Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter

Within the functional renormalization group approach we study the effective QFT 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 non linear beta functions determining the renormalization flow. We find the existence of a non trivial fixed point structure both for the gravity and the matter sector, besides the usual gaussian matter one. This suggest that asymptotic safety could be realized in the gravitational sector \emph{and} in the standard model. Non triviality in the Higgs sector might involve gravitational interactions.