New heavenly double copies

Abstract

The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Plebański's heavenly equation for self-dual gravity. The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation. In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra. As a result, we obtain a double-copy interpretation for hyper-Hermitian manifolds, extending the previously known hyper-Kähler case. We also introduce a double-Moyal deformation of the heavenly equation. The examples where the construction of Lax pairs is possible are manifestly consistent with Ward's conjecture, and suggest that the classical integrability of the gravity-type theory may be guaranteed in general by the integrability of at least one of two gauge-theory-type single copies.

34 pages, 1 figure

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Cited by in corpus (24)

• Classical Solutions and their Double Copy in Split Signature
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Classical double copy at null infinity
• Celestial chiral algebras, colour-kinematics duality and integrability
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• The double copy of the multipole expansion
• Non-perturbative aspects of the self-dual double copy
• Isometries and the double copy
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• The single copy of the gravitational holonomy
• Gravitational dynamics: A novel shift in the Hamiltonian paradigm
• Non-perturbative Double Copy in Flatland
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
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• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• On self-dual Yang-Mills fields on special complex surfaces