Flat space S matrix from the AdS/CFT correspondence?

We investigate recovery of the bulk S matrix from the AdS/CFT correspondence, at large radius. It was recently argued that some of the elements of the S matrix might be read from CFT correlators, given a particular singularity structure of the latter, but leaving the question of more general S matrix elements. Since in AdS/CFT, data must be specified on the boundary, we find certain limitations on the corresponding bulk wave packets and on their localization properties. In particular, those we have found that approximately localize have low-energy tails, and corresponding power-law tails in position space. When their scattering is compared to that of sharper wave packets typically used in scattering theory, one finds apparently significant differences, suggesting a possible lack of resolution via these wave packets. We also give arguments that construction of the sharper wave packets may require nonperturbative control of the boundary theory, and particularly of the N-2 matrix degrees of freedom. These observations thus raise interesting questions about what principle would guarantee the appropriate control, and about how a boundary CFT can accurately approximate the flat space S matrix.