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Large curvature and background scale independence in single-metric approximations to asymptotic safety

Large curvature and background scale independence in single-metric approximations to asymptotic safety
Large curvature and background scale independence in single-metric approximations to asymptotic safety
In single-metric approximations to the exact renormalization group (RG) for quantum gravity, it has been not been clear how to treat the large curvature domain beyond the point where the effective cutoff scale k is less than the lowest eigenvalue of the appropriate modified Laplacian. We explain why this puzzle arises from background dependence, resulting in Wilsonian RG concepts being inapplicable. We show that when properly formulated over an ensemble of backgrounds, the Wilsonian RG can be restored. This in turn implies that solutions should be smooth and well defined no matter how large the curvature is taken. Even for the standard single-metric type approximation schemes, this construction can be rigorously derived by imposing a modified Ward identity (mWI) corresponding to rescaling the background metric by a constant factor. However compatibility in this approximation requires the space-time dimension to be six. Solving the mWI and flow equation simultaneously, new variables are then derived that are independent of overall background scale.
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Morris, Tim R. (2016) Large curvature and background scale independence in single-metric approximations to asymptotic safety. Journal of High Energy Physics, 2016 (11), [160]. (doi:10.1007/JHEP11(2016)160).

Record type: Article

Abstract

In single-metric approximations to the exact renormalization group (RG) for quantum gravity, it has been not been clear how to treat the large curvature domain beyond the point where the effective cutoff scale k is less than the lowest eigenvalue of the appropriate modified Laplacian. We explain why this puzzle arises from background dependence, resulting in Wilsonian RG concepts being inapplicable. We show that when properly formulated over an ensemble of backgrounds, the Wilsonian RG can be restored. This in turn implies that solutions should be smooth and well defined no matter how large the curvature is taken. Even for the standard single-metric type approximation schemes, this construction can be rigorously derived by imposing a modified Ward identity (mWI) corresponding to rescaling the background metric by a constant factor. However compatibility in this approximation requires the space-time dimension to be six. Solving the mWI and flow equation simultaneously, new variables are then derived that are independent of overall background scale.

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More information

Accepted/In Press date: 22 November 2016
e-pub ahead of print date: 25 November 2016
Published date: November 2016
Organisations: Theoretical Partical Physics Group

Identifiers

Local EPrints ID: 403359
URI: http://eprints.soton.ac.uk/id/eprint/403359
PURE UUID: 84cb776d-9e52-44c1-9f0a-9a7a67427791
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

Catalogue record

Date deposited: 30 Nov 2016 11:46
Last modified: 22 Nov 2021 02:34

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