Scattering on plane waves and the double copy

TL;DR

This work extends the gravity=gauge-space double copy to curved backgrounds by analyzing 3-point amplitudes on sandwich plane waves. It introduces a non-local replacement map that relates gravity amplitudes on gravitational plane waves to the square of gauge amplitudes on gauge-field plane waves, while incorporating memory effects through background-dependent tails. The results reveal that tails and the deformation tensor σ^{ab} play a central role in the gravitational amplitude, modifying the naive flat-space square and requiring a curved-background double-copy procedure. The framework connects to ambitwistor-string methods and suggests a path toward a general curved-space double copy for higher-point amplitudes, with potential implications for non-linear gravitational dynamics and memory phenomena.

Abstract

Perturbatively around flat space, the scattering amplitudes of gravity are related to those of Yang-Mills by colour-kinematic duality, under which gravitational amplitudes are obtained as the 'double copy' of the corresponding gauge theory amplitudes. We consider the question of how to extend this relationship to curved scattering backgrounds, focusing on certain 'sandwich' plane waves. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave. This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds. It must also account for new 'tail' terms arising from scattering off the background. These encode a memory effect in the scattering amplitudes, which naturally double copies as well.

Figures (1)

• Figure 1: The sandwich plane wave with $x^a$-directions suppressed. The function $H_{ab}(u)$ is non-vanishing only in the shaded region; the in- and out-regions are both flat.