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The local potential approximation in the background field formalism

The local potential approximation in the background field formalism
The local potential approximation in the background field formalism
Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.
renormalization group, models of quantum gravity, nonperturbative effects
1-35
Bridle, I. Hamzaan
fdb2ecb0-26a0-4eff-a397-4bf7520349a4
Dietz, Juergen A.
25b4e470-3534-476d-8844-ada94b16feeb
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6
Bridle, I. Hamzaan
fdb2ecb0-26a0-4eff-a397-4bf7520349a4
Dietz, Juergen A.
25b4e470-3534-476d-8844-ada94b16feeb
Morris, Tim R.
a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Bridle, I. Hamzaan, Dietz, Juergen A. and Morris, Tim R. (2014) The local potential approximation in the background field formalism. Journal of High Energy Physics, 2014 (93), 1-35. (doi:10.1007/JHEP03(2014)093).

Record type: Article

Abstract

Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.

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art_10.1007_JHEP03(2014)093-1.pdf - Accepted Manuscript
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e-pub ahead of print date: 20 March 2014
Published date: March 2014
Keywords: renormalization group, models of quantum gravity, nonperturbative effects
Organisations: Physics & Astronomy

Identifiers

Local EPrints ID: 368135
URI: http://eprints.soton.ac.uk/id/eprint/368135
PURE UUID: 105dc664-e9e4-4d50-a31c-514da92b0982
ORCID for Tim R. Morris: ORCID iD orcid.org/0000-0001-6256-9962

Catalogue record

Date deposited: 18 Aug 2014 14:29
Last modified: 21 Nov 2021 02:34

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Contributors

Author: I. Hamzaan Bridle
Author: Juergen A. Dietz
Author: Tim R. Morris ORCID iD

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