Classical and quantum double copy of back-reaction
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Springer
Received: June 1, 2020 Accepted: August 17, 2020 Published: September 30, 2020
Tim Adamoa and Anton Ildertonb a
School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom b Centre for Mathematical Sciences, University of Plymouth, Kirkby Place, Plymouth PL4 8AA, United Kingdom
E-mail: [email protected], [email protected] 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. Keywords: Scattering Amplitudes, Classical Theories of Gravity, Nonperturbative Effects ArXiv ePrint: 2005.05807
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)200
JHEP09(2020)200
Classical and quantum double copy of back-reaction
Contents 1
2 Plane wave backgrounds
3
3 Classical colour charge dynamics 3.1 Zeroth order: charge motion in the background 3.2 First order: emission and back-reaction
5 5 7
4 Classical gravitational mass dynamics 4.1 Zeroth order: particle motion in the background 4.2 First order: emission and back-reaction
9 10 11
5 Non-linear Compton scattering 5.1 Gluon emission amplitude 5.2 Graviton emission amplitude
13 14 17
6 Double copy
20
7 Four-dimensions and spinor helicity 7.1 The formalism 7.2 4d non-linear Compton amplitudes
22 23 26
8 Future directions
27
1
Introduction
The double copy is a non-trivial set of relationships between the perturbative scattering amplitudes of gauge theory and gravity, whereby the amplitudes of a gravitational theory can be expressed as the ‘square’ of amplitudes at the same perturbative order and particle number in a gauge theory [1–4]. When this can be made precise, double copy is an extremely powerful statement, since perturbative gravity is based on a non-polynomial Lagrangian with an infinite number of interaction vertices (e.g., the Einstein-Hilbert Lagrangian) whereas the standard perturbation theory of gauge theories is much less complicated. For scattering amplitudes on a trivial background, double copy has been formulated (see [5] for a comprehensive review with references) at tree-level and beyond for a wide array of gravitational theories (the most recent addition to this catalog being massive gravity [6, 7]). A perturbative version of double copy has also been found relating the asymptotic radiation resulting from
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