Analyticity and the Holographic S-Matrix

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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 ... continued below

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42 pages

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Fitzpatrick, A.Liam; /Stanford U., Phys. Dept.; Kaplan, Jared & /SLAC April 3, 2012.

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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.

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42 pages

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  • Journal Name: Submitted to Journal of High Energy Physics (JHEP); Journal Volume: 2012; Journal Issue: 10

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  • Report No.: SLAC-PUB-14841
  • Grant Number: AC02-76SF00515
  • DOI: 10.1007/JHEP10(2012)032 | External Link
  • Office of Scientific & Technical Information Report Number: 1038000
  • Archival Resource Key: ark:/67531/metadc835544

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  • April 3, 2012

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

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  • Nov. 22, 2016, 6:25 p.m.

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Fitzpatrick, A.Liam; /Stanford U., Phys. Dept.; Kaplan, Jared & /SLAC. Analyticity and the Holographic S-Matrix, article, April 3, 2012; United States. (digital.library.unt.edu/ark:/67531/metadc835544/: accessed September 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.