Landau diagrams in AdS and S-matrices from conformal correlators

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 arXiv:1607.06109 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.

75 pages, 21 figures; v2 a footnote and a reference added

References in corpus (12)

• Writing CFT correlation functions as AdS scattering amplitudes
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Local bulk S-matrix elements and CFT singularities
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
• Four point function of $\mathcal{N}=4$ stress-tensor multiplet at strong coupling
• String scattering in flat space and a scaling limit of Yang-Mills correlators
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
• The S-matrix Bootstrap III: Higher Dimensional Amplitudes
• Rigid Holography and Six-Dimensional N=(2,0) Theories on AdS_5 times S^1

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