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

TL;DR

This paper explores the relationship between flat space graviton scattering amplitudes and boundary CFT correlators in AdS space, highlighting limitations in reproducing flat space results from AdS calculations, especially for large numbers of gravitons.

Contribution

It demonstrates that flat space graviton amplitudes can only be approximated by AdS correlators for small numbers of gravitons and discusses the implications for black hole production and unitarity.

Findings

Flat space amplitudes match AdS correlators for n < R/L_P.

Black hole production occurs in AdS for large n, not in flat space.

Flat space amplitudes are necessary to understand certain singularities and unitarity.

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.