A handbook of holographic 4-point functions
A handbook of holographic 4-point functions
We present a comprehensive discussion of tree-level holographic 4-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid conformal correlator. When the β = ∆ − d/2 are half-integral, with ∆ the dimensions of the operators and d the spacetime dimension, the Witten diagrams can be evaluated in closed form and we present explicit formulae for the case d = 3 and ∆ = 2, 3. These correlators require renormalization, which we carry out explicitly, and lead to new conformal anomalies and beta functions. Correlators of operators of different dimension may be linked via weight-shifting operators, which allow new correlators to be generated from given ‘seed’ correlators. We present a new derivation of weight-shifting operators in momentum space and uncover several subtleties associated with their use: such operators map exchange diagrams to a linear combination of exchange and contact diagrams, and special care must be taken when renormalization is required.
AdS-CFT Correspondence, Conformal and W Symmetry, Renormalization and Regularization, Scale and Conformal Symmetries
Bzowski, Adam Witold
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McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
7 December 2022
Bzowski, Adam Witold
fda39beb-8f6f-480a-99ba-101a54965fbe
McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Bzowski, Adam Witold, McFadden, Paul and Skenderis, Kostas
(2022)
A handbook of holographic 4-point functions.
Journal of High Energy Physics, 2022 (12), [39].
(doi:10.1007/JHEP12(2022)039).
Abstract
We present a comprehensive discussion of tree-level holographic 4-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid conformal correlator. When the β = ∆ − d/2 are half-integral, with ∆ the dimensions of the operators and d the spacetime dimension, the Witten diagrams can be evaluated in closed form and we present explicit formulae for the case d = 3 and ∆ = 2, 3. These correlators require renormalization, which we carry out explicitly, and lead to new conformal anomalies and beta functions. Correlators of operators of different dimension may be linked via weight-shifting operators, which allow new correlators to be generated from given ‘seed’ correlators. We present a new derivation of weight-shifting operators in momentum space and uncover several subtleties associated with their use: such operators map exchange diagrams to a linear combination of exchange and contact diagrams, and special care must be taken when renormalization is required.
Text
JHEP12(2022)039
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Accepted/In Press date: 17 October 2022
Published date: 7 December 2022
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© 2022, The Author(s).
Keywords:
AdS-CFT Correspondence, Conformal and W Symmetry, Renormalization and Regularization, Scale and Conformal Symmetries
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Local EPrints ID: 473748
URI: http://eprints.soton.ac.uk/id/eprint/473748
ISSN: 1126-6708
PURE UUID: 86f6500f-4429-4245-937a-06d57eae103b
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Date deposited: 30 Jan 2023 20:07
Last modified: 11 May 2024 01:45
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Author:
Adam Witold Bzowski
Author:
Paul McFadden
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