A Scattering Amplitude for Massive Particles in AdS

TL;DR

This paper introduces the AdS S-matrix, a conformally covariant momentum space representation of CFT correlators that reduces to the flat space S-matrix in the large radius limit, with new computational rules and relations to Mellin space.

Contribution

It proposes a novel AdS S-matrix framework with Feynman-like rules and connects it to Mellin space representations, advancing the understanding of AdS/CFT correspondence.

Findings

Defines the AdS S-matrix as a conformally covariant momentum space representation.

Establishes the flat space limit where the AdS S-matrix reduces to the flat space S-matrix.

Provides Feynman-like rules for perturbative computation of the AdS S-matrix.

Abstract

In this paper, we propose a conformally covariant momentum space representation of CFT correlation functions. We call it the AdS S-matrix. This representation has the property that it reduces to the S-matrix in the flat space limit. The flat space limit in question is taken by keeping all the particle masses fixed as the operator conformal dimensions go to infinity along with the AdS radius $\mathtt{R}$. We give Feynman-like rules to compute the AdS S-matrix in $1/ \mathtt{R}$ perturbation theory. Moreover, we relate it to the Mellin space representation of the conformal correlators in $1/ \mathtt{R}$ perturbation theory.