The University of Southampton
University of Southampton Institutional Repository

A handbook of holographic 4-point functions

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
1126-6708
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
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).

Record type: Article

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 - Version of Record
Available under License Creative Commons Attribution.
Download (1MB)

More information

Accepted/In Press date: 17 October 2022
Published date: 7 December 2022
Additional Information: Publisher Copyright: © 2022, The Author(s).
Keywords: AdS-CFT Correspondence, Conformal and W Symmetry, Renormalization and Regularization, Scale and Conformal Symmetries

Identifiers

Local EPrints ID: 473748
URI: http://eprints.soton.ac.uk/id/eprint/473748
ISSN: 1126-6708
PURE UUID: 86f6500f-4429-4245-937a-06d57eae103b
ORCID for Kostas Skenderis: ORCID iD orcid.org/0000-0003-4509-5472

Catalogue record

Date deposited: 30 Jan 2023 20:07
Last modified: 11 May 2024 01:45

Export record

Altmetrics

Contributors

Author: Adam Witold Bzowski
Author: Paul McFadden

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×