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The continuum limit of the conformal sector at second order in perturbation theory

The continuum limit of the conformal sector at second order in perturbation theory
The continuum limit of the conformal sector at second order in perturbation theory
Recently a novel perturbative continuum limit for quantum gravity has been proposed and demonstrated to work at first order. Every interaction monomial σ is dressed with a coefficient function fσ Λ(ϕ) of the conformal factor field, ϕ. Each coefficient function is parametrised by an infinite number of underlying couplings, and decays at large ϕ with a characteristic amplitude suppression scale which can be chosen to be at a common value, Λp. Although the theory is perturbative in couplings it is non-perturbative in ~. At second order in perturbation theory, one must sum over all melonic Feynman diagrams to obtain the particular integral. We show that it leads to a well defined renormalized trajectory and thus continuum limit, provided it is solved by starting at an arbitrary cutoff scale Λ = µ which lies in the range 0 < µ < aΛp (a some non-universal number). If µ lies above this range the resulting coefficient functions become singular, and the flow ceases to exist, before the physical limit is reached. To this one must add a well-behaved complementary solution, containing irrelevant couplings determined uniquely by the first-order interactions, and renormalized relevant couplings. Even though some irrelevant couplings diverge in the limit Λp→∞, domains for the underlying relevant couplings can be chosen such that diffeomorphism invariance will be recovered in this limit, and where the underlying couplings disappear to be replaced by effective diffeomorphism invariant couplings.
1550-7998
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Morris, Tim R. (2021) The continuum limit of the conformal sector at second order in perturbation theory. Physical Review D. (In Press)

Record type: Article

Abstract

Recently a novel perturbative continuum limit for quantum gravity has been proposed and demonstrated to work at first order. Every interaction monomial σ is dressed with a coefficient function fσ Λ(ϕ) of the conformal factor field, ϕ. Each coefficient function is parametrised by an infinite number of underlying couplings, and decays at large ϕ with a characteristic amplitude suppression scale which can be chosen to be at a common value, Λp. Although the theory is perturbative in couplings it is non-perturbative in ~. At second order in perturbation theory, one must sum over all melonic Feynman diagrams to obtain the particular integral. We show that it leads to a well defined renormalized trajectory and thus continuum limit, provided it is solved by starting at an arbitrary cutoff scale Λ = µ which lies in the range 0 < µ < aΛp (a some non-universal number). If µ lies above this range the resulting coefficient functions become singular, and the flow ceases to exist, before the physical limit is reached. To this one must add a well-behaved complementary solution, containing irrelevant couplings determined uniquely by the first-order interactions, and renormalized relevant couplings. Even though some irrelevant couplings diverge in the limit Λp→∞, domains for the underlying relevant couplings can be chosen such that diffeomorphism invariance will be recovered in this limit, and where the underlying couplings disappear to be replaced by effective diffeomorphism invariant couplings.

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The continuum limit of the conformal sector at second order in perturbation theory - Accepted Manuscript
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Accepted/In Press date: 20 March 2021
Additional Information: arxiv is am

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Local EPrints ID: 447987
URI: http://eprints.soton.ac.uk/id/eprint/447987
ISSN: 1550-7998
PURE UUID: 1ee18733-a4bd-4f6a-b174-b6564d5424d2
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

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Date deposited: 29 Mar 2021 16:38
Last modified: 30 Mar 2021 01:34

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Author: Tim R. Morris ORCID iD

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