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Quantum field theories in AdS generate conformal correlation functions on theboundary, and in the limit where AdS is nearly flat one should be able toextract an S-matrix from such correlators. We discuss a particularly simpleposition-space procedure to do so. It features a direct map from boundarypositions to (on-shell) momenta and thereby relates cross ratios to Mandelstaminvariants. This recipe succeeds in several examples, includes themomentum-conserving delta functions, and can be shown to imply the twoproposals in arXiv:1607.06109 based on Mellin space and on the OPE data.Interestingly the procedure does not always work: the Landau singularities of aFeynman diagram are shown to be part of larger regions, to be called `badregions', where the flat-space limit of the Witten diagram diverges. To capturethese divergences we introduce the notion of Landau diagrams in AdS. As in flatspace, these describe on-shell particles propagating over large distances in acomplexified space, with a form of momentum conservation holding at each bulkvertex. As an application we recover the anomalous threshold of the four-pointtriangle diagram at the boundary of a bad region.

Landau diagrams in AdS and S-matrices from conformal correlators