On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators

TL;DR

This paper demonstrates that AdS boundary correlators can be expressed as differential operators acting on contact diagrams, revealing a flat-space-like structure, and explores color-kinematics duality and potential double copy extensions.

Contribution

It introduces a differential representation of AdS boundary correlators, analogous to flat space amplitudes, and investigates color-kinematics duality within this framework.

Findings

Boundary correlators expressed as differential operators

Reproduction of known position space results

Color-kinematics duality observed in scalar correlators

Abstract

The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams. We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space. We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results. Color-kinematics duality and BCJ relations can be defined in analogy with their flat space counterparts, and are respected by the scalar correlators with a gluon exchange. We also discuss potential approaches to the double copy and find that its direct generalization may require nontrivial extensions.