The Double Copy of Electric-Magnetic Duality

Abstract

We argue that the complex transformation relating the Schwarzschild to the Taub-NUT metric, introduced by Talbot, is in fact an electric-magnetic duality transformation. We show that at null infinity, the complex transformation is equivalent to a complexified BMS supertranslation, which rotates the supertranslation and the dual (magnetic) supertranslation charges. This can also be seen from the cubic coupling between the classical source and its background, which for Taub-NUT is given by a complex phase rotation acting on gravitational minimal couplings. The same phase rotation generates dyons from electrons at the level of minimally coupled amplitudes, manifesting the double copy relation between the two solutions.

27 pages, 3 figures. v2: typos corrected, references added

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• Topology and Wilson lines: global aspects of the double copy
• Double Copy for Celestial Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Classical observables from coherent-spin amplitudes
• Shifting Spin on the Celestial Sphere
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• Non-perturbative aspects of the self-dual double copy
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• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• The single copy of the gravitational holonomy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Enhanced Ehlers Transformation and the Majumdar-Papapetrou-NUT Spacetime
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Solutions in Nonlinear Electrodynamics and their double copy regular black holes
• Gravitational Wu-Yang Monopoles
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• Electromagnetic Duality and D3-Brane Scattering Amplitudes Beyond Leading Order
• Quantization Conditions and the Double Copy
• Non-locality and gravitoelectromagnetic duality
• The double copy: from optics to quantum gravity
• Waveforms from Amplitudes
• Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
• Next-to-MHV Yang-Mills kinematic algebra
• Hawking radiation from the double copy
• New framework for classical double copies
• The Weyl double copy from twistor space
• Massive Covariant Colour-Kinematics in 3D
• Scattering Amplitudes for Monopoles: Pairwise Little Group and Pairwise Helicity
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• Dual Komar Mass, Torsion and Riemann-Cartan Manifolds
• Electromagnetic duality and central charge from first order formulation
• Quantum point particle approximation of spinning black holes and compact stars
• The Radial Action from Probe Amplitudes to All Orders
• The Kerr-Schild Double Copy in Lifshitz Spacetime