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Quantum gravity, renormalizability and diffeomorphism invariance

Quantum gravity, renormalizability and diffeomorphism invariance
Quantum gravity, renormalizability and diffeomorphism invariance
We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Around the Gaussian fixed point, RG properties of the conformal factor of the metric allow the construction of a Hilbert space L of renormalizable interactions, non-perturbative in ℏ, and involving arbitrarily high powers of the gravitational fluctuations. We show that diffeomorphism invariance is violated for interactions that lie inside L, in the sense that only a trivial quantum BRST cohomology exists for interactions at first order in the couplings. However by taking a limit to the boundary of L, the couplings can be constrained to recover Newton's constant, and standard realisations of diffeomorphism invariance, whilst retaining renormalizability. The limits are sufficiently flexible to allow this also at higher orders. This leaves open a number of questions that should find their answer at second order. We develop much of the framework that will allow these calculations to be performed.
2542-4653
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Morris, Tim R. (2018) Quantum gravity, renormalizability and diffeomorphism invariance. Scipost Physics, 5, [40]. (doi:10.21468/SciPostPhys.5.4.040).

Record type: Article

Abstract

We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Around the Gaussian fixed point, RG properties of the conformal factor of the metric allow the construction of a Hilbert space L of renormalizable interactions, non-perturbative in ℏ, and involving arbitrarily high powers of the gravitational fluctuations. We show that diffeomorphism invariance is violated for interactions that lie inside L, in the sense that only a trivial quantum BRST cohomology exists for interactions at first order in the couplings. However by taking a limit to the boundary of L, the couplings can be constrained to recover Newton's constant, and standard realisations of diffeomorphism invariance, whilst retaining renormalizability. The limits are sufficiently flexible to allow this also at higher orders. This leaves open a number of questions that should find their answer at second order. We develop much of the framework that will allow these calculations to be performed.

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More information

Accepted/In Press date: 26 October 2018
e-pub ahead of print date: 30 October 2018

Identifiers

Local EPrints ID: 429253
URI: http://eprints.soton.ac.uk/id/eprint/429253
ISSN: 2542-4653
PURE UUID: 861a1342-78c2-47e4-883a-5396222eb605
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

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Date deposited: 25 Mar 2019 17:30
Last modified: 22 Nov 2021 02:34

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