In an answer to this question, Ron Maimon said:
The flat-space limit of AdS/CFT boundary theory is the S-matrix theory of a flat space theory, so the result was the same--- the "boundary" theory for flat space becomes normal flat space in and out states, which define the Hilbert space, while in AdS space, these in and out states are sufficiently rich (because of the hyperbolic braching nature of AdS) that you can define a full field theory worth of states on the boundary, and the S-matrix theory turns into a unitary quantum field theory of special conformal type.
I guess this means that, in elementary flat-space scattering theory, you can consider the in and out states as in some sense lying on some sort of boundary to Minkowski space and these in and out states are the analogs of the CFT states in the AdS/CFT case.
My question is - is it possible to state this flat-space limit of AdS/CFT in more precise terms? (Maybe it involves string theory?). Any references would be appreciated.