The convolutional double copy: a case study with a point

Abstract

The double copy relates scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, and a number of approaches have been developed for doing so. One of these involves expressing fields in a variety of (super-)gravity theories in terms of convolutions of gauge fields, including also BRST ghost degrees of freedom that map neatly to their corresponding counterparts in gravity. In this paper, we spell out how to use the convolutional double copy to map gauge and gravity solutions in the manifest Lorenz and de Donder gauges respectively. We then apply this to a particular example, namely the point charge in pure gauge theory. As well as clarifying how to use the convolutional approach, our results provide an alternative point of view on a recent discussion concerning whether point charges map to the Schwarzschild solution, or the more general two-parameter JNW solution, which includes a dilaton field. We confirm the latter.

15 pages

References in corpus (13)

• New Relations for Gauge-Theory Amplitudes
• Black holes and the double copy
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• The Kerr-Schild double copy in curved spacetime
• Yang-Mills origin of gravitational symmetries
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Topology and Wilson lines: global aspects of the double copy
• The Classical Double Copy of a Point Charge
• Extended solutions for the biadjoint scalar field
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• Monopoles, shockwaves and the classical double copy
• Strings, extended objects, and the classical double copy

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• New heavenly double copies
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• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
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• Alternative formulations of the twistor double copy
• Twistor Space Origins of the Newman-Penrose Map
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