BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space

TL;DR

This paper extends the color/kinematics duality from flat-space scattering amplitudes to AdS boundary correlators using embedding space formalism, revealing new differential relations and duality representations.

Contribution

It introduces a novel generalization of BCJ amplitude relations to AdS boundary correlators, connecting flat-space duality concepts with AdS holography.

Findings

Derived differential relations among AdS correlators from color/kinematics duality.

Verified these relations for Yang-Mills and Nonlinear Sigma Model correlators.

Presented duality manifest representations for four- and six-point correlators.

Abstract

We generalize the color/kinematics duality of flat-space scattering amplitudes to the embedding space formulation of AdS boundary correlators. Kinematic numerators and propagators are replaced with differential operators acting on a scalar contact diagram that is the AdS generalization of the momentum conserving delta function of flat space scattering amplitudes. We show that color/kinematics duality implies differential relations among AdS boundary correlators that naturally generalize the flat space BCJ amplitude relations and verify them for the correlators of Yang-Mills theory and of the Nonlinear Sigma Model through four- and six-points, respectively. For the latter we also find representations of the four- and six-point correlator that manifest the duality. Possible double-copy procedures in AdS space are also discussed.