BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
Pranav Diwakar, Aidan Herderschee, Radu Roiban, Fei Teng
TL;DR
This work lifts the flat-space color/kinematics duality and BCJ relations into the AdS setting by employing embedding-space techniques and a differential-operator representation acting on a scalar AdS contact diagram. It demonstrates that AdS boundary correlators for Yang-Mills and the nonlinear sigma model can be expressed in a CK-dual form, yielding AdS-BCJ relations among partial correlators at 4–6 points and providing explicit differential representations that manifest the duality. The paper also lays groundwork for AdS double-copy procedures, exploring differential, position-space, and Mellin-space approaches and their high-energy or large-d limits, with partial success and clear avenues for refinement. Overall, it extends a powerful flat-space structure to holographic boundary data, offering new tools for computing and constraining AdS correlators and potential links to gravity via AdS double copy. This framework has implications for holographic CFT bootstrap, higher-point amplitudes, and the pursuit of a fully realized AdS double-copy map.
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.