The self-dual classical double copy, and the Eguchi-Hanson instanton

Abstract

The double copy is a map from non-abelian gauge theories to gravity, that has been demonstrated both for scattering amplitudes and exact classical solutions. In this study, we reconsider the double copy for exact solutions that are self-dual in either the gauge or gravity theory. In this case, one may formulate a general double copy in terms of a certain differential operator, which generates the gauge and gravity solutions from a harmonic function residing in a biadjoint scalar theory. As an illustration, we examine the single copy of the well-known Eguchi-Hanson instanton in gravity. The gauge field thus obtained represents an abelian-like object whose field is dipole-like at large distances, and which has no magnetic or electric charge.

arXiv comment20 pages, 4 figures. Version 2 has additional references added

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Cited by in corpus (80)

• Observables and amplitudes for spinning particles and black holes
• Double copy for massive quantum particles with spin
• A Twistorial Foundation for the Classical Double Copy
• S-duality and the Double Copy
• The Weyl Double Copy for Gravitational Waves
• Double Copy from Homotopy Algebras
• Classical Solutions and their Double Copy in Split Signature
• Topology and Wilson lines: global aspects of the double copy
• Double Copy for Celestial Amplitudes
• The classical double copy of non-singular black holes
• The Classical Double Copy of a Point Charge
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• The convolutional double copy: a case study with a point
• A double copy for asymptotic symmetries in the self-dual sector
• Ehlers as EM duality in the double copy
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• The Newman-Penrose Map and the Classical Double Copy
• Weyl doubling
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Classical double copy at null infinity
• Monopoles, shockwaves and the classical double copy
• Biadjoint wires
• Strings, extended objects, and the classical double copy
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• New heavenly double copies
• Massive Gravity from Double Copy
• Asymptotic Weyl Double Copy
• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• Loop-Level Double-Copy for Massive Quantum Particles
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Alternative formulations of the twistor double copy
• Twistor Space Origins of the Newman-Penrose Map
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• The double copy of the multipole expansion
• Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor
• Why is the Weyl double copy local in position space?
• Geodesics From Classical Double Copy
• Non-perturbative aspects of the self-dual double copy
• Gauge $\times$ Gauge on Spheres
• Isometries and the double copy
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Shift symmetries, soft limits, and the double copy beyond leading order
• The Weyl double copy in vacuum spacetimes with a cosmological constant
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• More on the Classical Double Copy in Three Spacetime Dimensions
• 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
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Weyl double copy and massless free fields in curved spacetimes
• 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
• Extracting Einstein from the Loop-Level Double-Copy
• Black Hole Horizons from the Double Copy
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Non-thermal production of lepton asymmetry and dark matter in minimal seesaw with right handed neutrino induced Higgs potential
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Classical double copy and higher-spin fields
• Note on the asymptotic structure of Kerr-Schild form
• On symmetries and dynamics of exotic supermultiplets
• Aspects of High Energy Scattering
• The double copy: from optics to quantum gravity
• Compactifying the Kerr-Schild Double Copy
• Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy
• Weyl double copy in type D spacetime in four and five dimensions
• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• Hawking radiation from the double copy
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• A Topological Way of Finding Solutions to Yang-Mills Equation
• Slowly rotating charges from Weyl double copy for Kerr black hole with Chern-Simons correction
• Self-dual gravity via Hitchin's equations
• Notes on self-dual gravity
• Ambitwistor strings and amplitudes in curved backgrounds
• NS-NS Spacetimes from Amplitudes
• The Kerr-Schild Double Copy in Lifshitz Spacetime