Analyticity and the holographic S-matrix

A bstract We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphi...

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Bibliographic Details
Published in:The journal of high energy physics 2012-10, Vol.2012 (10), Article 127
Main Authors: Fitzpatrick, A. Liam, Kaplan, Jared
Format: Article
Language:English
Subjects:
Amplitudes
Classical and Quantum Gravitation
Elementary Particles
High energy physics
Mathematical analysis
Meromorphic functions
Operators (mathematics)
Physics
Physics and Astronomy
Poles
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
S matrix theory
Spacetime
String Theory
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Summary:A bstract We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the S-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2012)127