Classical and quantum double copy of back-reaction

Anton Ilderton,Tim Adamo

doi:10.1007/jhep09(2020)200

Anton Ilderton, Tim Adamo

Open Access

https://doi.org/10.1007/jhep09(2020)200

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Abstract

We consider radiation emitted by colour-charged and massive particles crossing strong plane wave backgrounds in gauge theory and gravity. These backgrounds are treated exactly and non-perturbatively throughout. We compute the back-reaction on these fields from the radiation emitted by the probe particles: classically through background-coupled worldline theories, and at tree-level in the quantum theory through three-point amplitudes. Consistency of these two methods is established explicitly. We show that the gauge theory and gravity amplitudes are related by the double copy for amplitudes on plane wave backgrounds. Finally, we demonstrate that in four-dimensions these calculations can be carried out with a background-dressed version of the massive spinor-helicity formalism.

Highlights

An initially flat background [8,9,10,11,12,13,14,15,16,17]
We show that the gauge theory and gravity amplitudes are related by the double copy for amplitudes on plane wave backgrounds
In unison with the ‘standard’ double copy for scattering amplitudes in quantum field theory, these tools are having a real impact on the study of gravitational wave physics

Summary

Plane wave backgrounds

Our aim is to study emission and back-reaction at lowest order, as massive particles cross a strong radiation background field in gauge theory and general relativity These strong backgrounds will be treated exactly as plane waves, which are highly-symmetric solutions of the vacuum equations of motion [29,30,31,32,33,34]. It is easy to see that (2.2) solves the vacuum Yang-Mills equations for any Cartan-valued a⊥; we demand that a ⊥ is compactly supported in x− This ‘sandwich’ condition says that the plane wave has finite duration in lightfront time, and is physically motivated: it ensures that, as a background field, the plane wave admits a well-defined S-matrix [25, 35]. The ‘single copy’ of this metric is precisely the gauge theoretic plane wave (2.2)

Classical colour charge dynamics

Zeroth order: charge motion in the background

First order: emission and back-reaction

Classical gravitational mass dynamics

Zeroth order: particle motion in the background

Non-linear Compton scattering

Gluon emission amplitude

Graviton emission amplitude

Double copy

Four-dimensions and spinor helicity

The formalism

Future directions