A handbook of holographic 4-point functions
Jul 6, 2022100 pages
Published in:
- JHEP 12 (2022) 039,
- JHEP 12 (2022) 039
- Published: Dec 7, 2022
e-Print:
- 2207.02872 [hep-th]
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Abstract: (Springer)
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.Note:
- 98 pp, 7 figs. v2: published version, new material on the OPE limit and exchange diagrams with derivative vertices
- AdS-CFT Correspondence
- Conformal and W Symmetry
- Renormalization and Regularization
- Scale and Conformal Symmetries
- operator: scalar
- operator: dimension
- n-point function: 4
- anomaly: conformal
- Ward identity: conformal
- correlation function
References(60)
Figures(6)
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