Decoding the hologram: Scalar fields interacting with gravity

Abstract

We construct smeared conformal field theory (CFT) operators which represent a scalar field in anti--de Sitter (AdS) space interacting with gravity. The guiding principle is microcausality: scalar fields should commute with themselves at spacelike separation. To $\mathcal{O}(1/N)$ we show that a correct and convenient criterion for constructing the appropriate CFT operators is to demand microcausality in a three-point function with a boundary Weyl tensor and another boundary scalar. The resulting bulk observables transform in the correct way under AdS isometries and commute with boundary scalar operators at spacelike separation, even in the presence of metric perturbations.