The continuum limit of quantum gravity at second order in perturbation theory

Abstract

We show that perturbative quantum gravity based on the Einstein–Hilbert action, has a novel continuum limit. The renormalized trajectory emanates from the Gaussian fixed point along (marginally) relevant directions but enters the diffeomorphism invariant subspace only well below a dynamically generated scale. We show that for pure quantum gravity to second order in perturbation theory, and with vanishing cosmological constant, the result is the same as computed in the standard quantisation. Although this case is renormalizable at second order for kinematic reasons, the structure we uncover works in general. One possibility is that gravity has a genuine consistent continuum limit even though it has an infinite number couplings. However we also suggest a possible non-perturbative mechanism, based on the parabolic properties of these flow equations, which would fix all higher order couplings in terms of Newton’s constant and the cosmological constant.