A handbook of holographic 4-point functions

Journal of High Energy Physics

Regular Article - Theoretical Physics

Adam Bzowski¹  Kostas Skenderis²  Paul McFadden³ 

[1] Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland;STAG Research Center & Mathematical Sciences, University of Southampton, Highfield, SO17 1BJ, Southampton, UK;School of Mathematics, Statistics & Physics, Newcastle University, NE1 7RU, Newcastle, UK;

关键词: AdS-CFT Correspondence;    Conformal and W Symmetry;    Renormalization and Regularization;    Scale and Conformal Symmetries;   

DOI  :  10.1007/JHEP12(2022)039

 received in 2022-07-12, accepted in 2022-10-17,  发布年份 2022

来源: Springer

【 摘 要 】

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.

【 授权许可】

Unknown   
© The Author(s) 2022