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Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity

Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity
Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity
The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. Generically for the conformal sector, complete flows exist only in the reverse direction (i.e. from the infrared to the ultraviolet). The Gaussian fixed point supports infinite sequences of composite eigenoperators of increasing infrared relevancy (increasingly negative mass dimension), which are orthonormal and complete for bare interactions that are square integrable under the appropriate measure. These eigenoperators are non-perturbative in h and evanescent. For R4 spacetime, each renormalized physical operator exists but only has support at vanishing field amplitude. In the generic case of infinitely many non-vanishing couplings, if a complete RG flow exists, it is characterised in the infrared by a scale Λp > 0, beyond which the field amplitude is exponentially suppressed. On other spacetimes, of length scale L, the flow ceases to exist once a certain universal measure of inhomogeneity exceeds O(1) + 2πL2Λ2p . Importantly for cosmology, the minimum size of the universe is thus tied to the degree of inhomogeneity, with spacetimes of vanishing size being required to be almost homogeneous. We initiate a study of this exotic quantum field theory at the interacting level, and discuss what the full theory of quantum gravity should look like, one which must thus be perturbatively renormalizable in Newton’s constant but non-perturbative in h.
1029-8479
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Morris, Tim R. (2018) Renormalization group properties in the conformal sector: towards perturbatively renormalizable quantum gravity. Journal of High Energy Physics, 2018 (24). (doi:10.1007/JHEP08(2018)024).

Record type: Article

Abstract

The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. Generically for the conformal sector, complete flows exist only in the reverse direction (i.e. from the infrared to the ultraviolet). The Gaussian fixed point supports infinite sequences of composite eigenoperators of increasing infrared relevancy (increasingly negative mass dimension), which are orthonormal and complete for bare interactions that are square integrable under the appropriate measure. These eigenoperators are non-perturbative in h and evanescent. For R4 spacetime, each renormalized physical operator exists but only has support at vanishing field amplitude. In the generic case of infinitely many non-vanishing couplings, if a complete RG flow exists, it is characterised in the infrared by a scale Λp > 0, beyond which the field amplitude is exponentially suppressed. On other spacetimes, of length scale L, the flow ceases to exist once a certain universal measure of inhomogeneity exceeds O(1) + 2πL2Λ2p . Importantly for cosmology, the minimum size of the universe is thus tied to the degree of inhomogeneity, with spacetimes of vanishing size being required to be almost homogeneous. We initiate a study of this exotic quantum field theory at the interacting level, and discuss what the full theory of quantum gravity should look like, one which must thus be perturbatively renormalizable in Newton’s constant but non-perturbative in h.

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Accepted/In Press date: 27 July 2018
e-pub ahead of print date: 7 August 2018

Identifiers

Local EPrints ID: 422727
URI: http://eprints.soton.ac.uk/id/eprint/422727
ISSN: 1029-8479
PURE UUID: 024676ba-0bd4-4638-bdc5-fae93870ec43
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

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Date deposited: 01 Aug 2018 16:30
Last modified: 26 Nov 2021 02:33

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