Writing CFT correlation functions as AdS scattering amplitudes

TL;DR

This paper investigates the Mellin representation of conformal correlators, proposing a link to AdS scattering amplitudes, and highlights the utility of Mellin amplitudes in conformal gauge theories for bootstrap approaches.

Contribution

It introduces a conjecture relating bulk scattering amplitudes to Mellin amplitudes' asymptotic behavior, advancing the understanding of AdS/CFT correspondence.

Findings

Mellin amplitudes resemble scattering amplitudes in AdS/CFT.

A simple formula relates bulk scattering to Mellin amplitudes.

Mellin amplitudes are meromorphic with residues determined by two- and three-point functions.

Abstract

We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk scattering amplitudes to the asymptotic behavior of Mellin amplitudes and show that previous results on the flat space limit of AdS follow from our new formula. We find that the Mellin amplitudes are particularly useful in the case of conformal gauge theories in the planar limit. In this case, the four point Mellin amplitudes are meromorphic functions whose poles and their residues are entirely determined by two and three point functions of single-trace operators. This makes the Mellin amplitudes the ideal objects to attempt the conformal bootstrap program in higher dimensions.