Towards the determination of the dimension of the critical surface in asymptotically safe gravity

We compute the beta functions of Higher Derivative Gravity within the Functional Renormalization Group approach, going beyond previously studied approximations. We find that the presence of a nontrivial Newtonian coupling induces, in addition to the free fixed point of the one-loop approximation, also two nontrivial fixed points, of which one has the right signs to be free from tachyons. Our results are consistent with earlier suggestions that the dimension of the critical surface for pure gravity is three. (C) 2020 The Authors. Published by Elsevier B.V.