  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.
