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

Kellett, Matthew, Mitchell, Alex and Morris, Tim R. (2021) The continuum limit of quantum gravity at second order in perturbation theory. Classical and Quantum Gravity, 38 (11), 115006. (doi:10.1088/1361-6382/abf2f4).

Record type: Article

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.

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

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