BCJ amplitude relations for Anti-de Sitter boundary correlators in embedding space

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.

Super Gluon Five-Point Amplitudes in AdS Space

“…Gauge invariance is trivial and does not change the kinematic factors. Our statement of no BCJ relations also does not contradict the "differential BCJ relations" found in [6]. For their construction, it is important that the external particles are massless while in our case they are massive.…”

“…Crucially, all flat-space particles are massless, i.e., s ii = 0 and all poles are at zero. In AdS space, however, the matrix becomes invertible thanks to the different relations (6) and the massive poles in D i . Therefore, there are no BCJ relations and all six color-ordered amplitudes are independent.…”

“…Recent explorations have led to encouraging results in the search for AdS avatars of flat-space properties. For example, there has been much evidence for AdS realizations of the color-kinematic duality [1][2][3][4][5][6] and a double copy relation has been identified in AdS 5 [7]. Both properties play a pivotal role in the modern flat-space amplitude program and have numerous applications [8].…”

One-loop gluon amplitudes in AdS

“…Furthermore, we will use the Mellin representation [35,36] to facilitate the computation. In this formalism AdS scattering amplitudes become Mellin amplitudes, which share a lot of similarities 1 For AdS gluon amplitudes in bosonic Yang-Mills theory with four or more points, recent works include [27][28][29][30].…”

Covariant color-kinematics duality

“…Last but not least is the question of color-kinematics duality beyond flat space, which has enjoyed a recent resurgence of interest [81][82][83][84][85]. Since our approach leans heavily on equations of motion, it seems straightforward to lift our framework to curved spacetime.…”