Journal of High Energy Physics (Nov 2020)

Landau diagrams in AdS and S-matrices from conformal correlators

  • Shota Komatsu,
  • Miguel F. Paulos,
  • Balt C. van Rees,
  • Xiang Zhao

DOI
https://doi.org/10.1007/JHEP11(2020)046
Journal volume & issue
Vol. 2020, no. 11
pp. 1 – 71

Abstract

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Abstract Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in [1] based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called ‘bad regions’, where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.

Keywords