On Gluing CFT Correlators to Higher-Spin Amplitudes in AdS

TL;DR

This paper shows how three-point functions in a free scalar conformal field theory can be directly related to higher-spin amplitudes in AdS space, revealing a concrete connection between boundary correlators and bulk interactions.

Contribution

It provides a detailed method to glue CFT correlators to higher-spin AdS amplitudes using the embedding space formalism and gauge-invariant vertices.

Findings

Three-point functions organize into AdS amplitudes with bulk-to-boundary propagators.

The approach relies on the embedding space formalism and gauge invariance.

Explicit correspondence between boundary correlators and bulk interactions is established.

Abstract

We demonstrate how three-point correlation functions of the free scalar U(N) model involving two scalar operators and one spin-$s$ conserved current organize themselves into corresponding AdS amplitudes involving two scalar and one spin-$s$ bulk to boundary propagators, coupled via the bulk gauge invariant interaction vertex. Our analysis relies on the general program advocated in hep-th/0308184 and some features of the embedding space formalism also play an important role.