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

The continuum limit of quantum gravity at second order in perturbation theory
The continuum limit of quantum gravity at second order in perturbation theory
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.
0264-9381
Kellett, Matthew
74ad925d-ae69-45ee-b3b7-2fa5ec1e14b8
Mitchell, Alex
068b4348-a75e-45da-a582-65c866bb95ab
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Kellett, Matthew
74ad925d-ae69-45ee-b3b7-2fa5ec1e14b8
Mitchell, Alex
068b4348-a75e-45da-a582-65c866bb95ab
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

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. (In Press)

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
Restricted to Repository staff only until 19 March 2022.
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Accepted/In Press date: 19 March 2021
Additional Information: arxiv is am

Identifiers

Local EPrints ID: 447985
URI: http://eprints.soton.ac.uk/id/eprint/447985
ISSN: 0264-9381
PURE UUID: 64a1ede7-4e9c-4d2e-a486-d4ea43356c66
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

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Date deposited: 29 Mar 2021 16:37
Last modified: 30 Mar 2021 01:34

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