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.
Highlights
Observables specified by boundary data, such as the S matrix in flat space and boundary correlation functions in anti-de-Sitter space, are at the core of modern developments in high energy physics
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 demonstrate that the color/kinematics dual form (3.24) of the AdS boundary correlators naturally lead to additional relations among the AdS partial correlators
Summary
Observables specified by boundary data, such as the S matrix in flat space and boundary correlation functions in anti-de-Sitter space, are at the core of modern developments in high energy physics. We discuss the AdS generalizations of color/kinematics duality and BCJ relations of flat space scattering amplitudes, focusing on Yang-Mills (YM) theory and the nonlinear sigma model (NLSM). Tree-level AdS boundary correlators are a natural starting point to study color/kinematics duality Their computation using Witten diagrams in position space is, cumbersome. We construct the explicit color/kinematics-satisfying representation of the NLSM AdS boundary correlators at four- and six-points and show that these correlators obey the AdS generalization of the BCJ amplitude relations. We will use the subscript “flat” when referring to flat-space scattering amplitudes
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