Analyticity and the Holographic S-Matrix

TL;DR

This paper establishes a direct relation between Mellin amplitudes in AdS/CFT and the flat spacetime S-Matrix, revealing how analyticity and poles in scattering amplitudes emerge from holographic correlators, and explores implications for locality and black holes.

Contribution

It proves a conjecture linking Mellin amplitudes to the S-Matrix and analyzes their analyticity properties through explicit loop diagram computations in AdS.

Findings

Mellin amplitudes are meromorphic with simple poles on the real axis.

Holographic correlators reproduce scattering amplitude features like poles and branch cuts.

Small black holes in AdS influence the conformal block structure of the dual CFT.

Abstract

We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the S-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.