  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.
