Bulk renormalization and the AdS/CFT correspondence
Bulk renormalization and the AdS/CFT correspondence
We develop a systematic renormalization procedure for QFT in anti-de Sitter spacetime. UV infinities are regulated using a geodesic point-splitting method, which respects AdS isometries, while IR infinities are regulated by cutting off the radial direction (as in holographic renormalization). The renormalized theory is defined by introducing $Z$ factors for all parameters in the Lagrangian and the boundary conditions of bulk fields (sources of dual operators), and a boundary counterterm action, S_{ct}$, such that the limit of removing the UV and IR regulators exists. The results are in general scheme dependent (mirroring the analogous result in flat space) and require renormalization conditions. These may be provided by the dual CFT (or by string theory in AdS). Our analysis amounts also to a first principles derivation of the Feynman rules regarding Witten diagrams. The presence and treatment of IR divergences is essential for correctly accounting for anomalous dimensions of dual operators. We apply the method to scalar $\Phi^4$ theory and obtain the renormalized 2-point function of the dual operator to 2-loops, and the renormalized 4-point function to 1-loop order, for operators of any dimension $\Delta$ and bulk spacetime dimension up to d+1=7.
Banados, Maximo
8a5669a3-a2a1-4f4d-ae5b-285cf3f6f052
Bianchi, Ernesto
b10c4873-8b38-4ff6-879e-2411665304f5
Munoz, Ivan
f5f3806c-4a56-4789-a83a-853ddc86ab27
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
27 January 2023
Banados, Maximo
8a5669a3-a2a1-4f4d-ae5b-285cf3f6f052
Bianchi, Ernesto
b10c4873-8b38-4ff6-879e-2411665304f5
Munoz, Ivan
f5f3806c-4a56-4789-a83a-853ddc86ab27
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Banados, Maximo, Bianchi, Ernesto, Munoz, Ivan and Skenderis, Kostas
(2023)
Bulk renormalization and the AdS/CFT correspondence.
Physical Review D, 107 (2), [L021901].
(doi:10.1103/PhysRevD.107.L021901).
Abstract
We develop a systematic renormalization procedure for QFT in anti-de Sitter spacetime. UV infinities are regulated using a geodesic point-splitting method, which respects AdS isometries, while IR infinities are regulated by cutting off the radial direction (as in holographic renormalization). The renormalized theory is defined by introducing $Z$ factors for all parameters in the Lagrangian and the boundary conditions of bulk fields (sources of dual operators), and a boundary counterterm action, S_{ct}$, such that the limit of removing the UV and IR regulators exists. The results are in general scheme dependent (mirroring the analogous result in flat space) and require renormalization conditions. These may be provided by the dual CFT (or by string theory in AdS). Our analysis amounts also to a first principles derivation of the Feynman rules regarding Witten diagrams. The presence and treatment of IR divergences is essential for correctly accounting for anomalous dimensions of dual operators. We apply the method to scalar $\Phi^4$ theory and obtain the renormalized 2-point function of the dual operator to 2-loops, and the renormalized 4-point function to 1-loop order, for operators of any dimension $\Delta$ and bulk spacetime dimension up to d+1=7.
Text
PhysRevD.107.L021901
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Accepted/In Press date: 6 January 2023
Published date: 27 January 2023
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Funding Information::
M. B. would like to thank Glenn Barnich, Alberto Faraggi and Stefan Theisen for illuminative discussions. M. B., I. M. and E. B. were partially funded by Fondecyt Grant No. 1201145. I. M. also acknowledges financial support from Agencia Nacional de Investigación (ANID)-PCHA/Doctorado Nacional/2016-21160784 and would like to thank the Theoretical Physics & Applied Mathematics group in Mathematical Sciences, University of Southampton for hospitality during part of this work. K. S. acknowledge support from the Science and Technology Facilities Council (Consolidated Grant “Exploring the Limits of the Standard Model and Beyond”).
Identifiers
Local EPrints ID: 474814
URI: http://eprints.soton.ac.uk/id/eprint/474814
ISSN: 2470-0010
PURE UUID: 382c59c7-61f6-4eea-b108-0a1d77bf7619
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Date deposited: 03 Mar 2023 17:32
Last modified: 17 Mar 2024 03:27
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Author:
Maximo Banados
Author:
Ernesto Bianchi
Author:
Ivan Munoz
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