The flat space S-matrix from the AdS/CFT correspondence?

TL;DR

This paper explores how the flat space S-matrix can be derived from the AdS/CFT correspondence, highlighting limitations in boundary data, wavepacket localization, and the potential need for non-perturbative boundary control.

Contribution

It analyzes the constraints on boundary-constructed wavepackets and discusses the challenges in recovering the flat space S-matrix from boundary CFT data.

Findings

Localized wavepackets have low-energy tails and power-law tails in position space.

Differences observed between scattering of localized and sharper wavepackets.

Constructing sharper wavepackets may require non-perturbative control of the boundary theory.

Abstract

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 wavepackets 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" wavepackets typically used in scattering theory, one finds apparently significant differences, suggesting a possible lack of resolution via these wavepackets. We also give arguments that construction of the sharper wavepackets may require non-perturbative control of the boundary theory, and particular 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.