Soft Gravitons and the Flat Space Limit of Anti-deSitter Space

Abstract

We argue that flat space amplitudes for the process $2\to n$ gravitons at center of mass energies $\sqrt{s}$ much less than the Planck scale, will coincide approximately with amplitudes calculated from correlators of a boundary CFT for AdS space of radius $R\gg L_P$, only when $n<R/L_P$ . For larger values of $n$ in AdS space, insisting that all the incoming energy enters "the arena" [arXiv:hep-th/9901079], implies the production of black holes, whereas there is no black hole production in the flat space amplitudes. We also argue, from unitarity, that flat space amplitudes for all $n$ are necessary to reconstruct the complicated singularity at zero momentum in the $2\to 2$ amplitude, which can therefore not be reproduced as the limit of an AdS calculation. Applying similar reasoning to amplitudes for real black hole production in flat space, we argue that unitarity of the flat space S-matrix cannot be assessed or inferred from properties of CFT correlators.

Comments: 11 Pages, LaTeX 2e, v.2 New references. Corrected the unitarity argument to take into account small phase space of multi-soft graviton cuts. Expanded discussion of production of soft gravitons via production, decay and re-scattering of high energy meta-stable states