Double copy for scattering in anti-de Sitter space
In plain words
The squaring trick is proven for tree-level scattering in flat spacetime. Whether it works in anti-de Sitter space, a curved spacetime used in holography, is unclear.
Precise statement
Determine whether tree-level boundary correlators of gravitons in $\mathrm{AdS}_{d+1}$ at all multiplicities, and at one loop, follow from gluon correlators by a color-to-kinematics replacement governed by a kinematic algebra that reduces to the flat-space BCJ structure in the flat-space limit. An answer is a general construction with proof, or a counterexample correlator.
What would settle it
A proof for all multiplicities at tree level, or a correlator for which no double-copy form exists.
Status in the literature
Unverified note
Low-point tree-level examples in AdS and de Sitter exist; no general construction is established as of 2026.