Browse by author
Lookup NU author(s): Dr Paul McFaddenORCiD
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
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.
Author(s): Bzowski A, McFadden P, Skenderis K
Publication type: Article
Publication status: Published
Journal: Journal of High Energy Physics
Year: 2022
Volume: 12
Print publication date: 07/12/2022
Online publication date: 07/12/2022
Acceptance date: 17/10/2022
Date deposited: 14/12/2022
ISSN (electronic): 1029-8479
Publisher: Springer
URL: https://doi.org/10.1007/JHEP12(2022)039
DOI: 10.1007/JHEP12(2022)039
Altmetrics provided by Altmetric
