Asymptotic Safety within on-shell perturbation theory

We investigate the renormalisation of Einstein gravity using a novel subtraction scheme in dimensional regularisation. The one-loop beta function for Newton's constant receives contributions from poles in even dimensions and can be mapped to the beta function obtained using a proper-time cutoff. Field redefinitions are used to remove off-shell contributions to the renormalisation group equations. To check the consistency of our approximations we use a general parametrisation of the metric fluctuation. Within truncations of the derivative expansion and the expansion in Newton's constant, we show that the parametrisation dependence can be removed order by order. Going to all orders in the scalar curvature an all-order beta function for Newton's constant is obtained that is independent of the parameterisation. The beta function vanishes at the Reuter fixed point and the critical exponent is in good agreement with non-perturbative calculations. Finally, we compare the critical exponent to the counterpart computed via Causal Dynamical Triangulations (CDT).
Comment: 33 pages, 4 figures