Why is the Weyl double copy local in position space?

Abstract

The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space and when this form will break has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. We show that for certain vacuum type-D solutions, the momentum-space, twistor-space and position-space double copies amount to the same thing, and are directly related by integral transforms. Locality in position space is ultimately a consequence of the very special form of momentum-space three-point amplitudes, and we thus confirm suspicions that local position-space double copies are possible only for highly algebraically-special spacetimes.

arXiv comment23 pages plus references, 5 figures

References in corpus (50)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Gravity as the Square of Gauge Theory
• Black holes and the double copy
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• The S-Matrix in Twistor Space
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• The Kerr-Schild double copy in curved spacetime
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Yang-Mills origin of gravitational symmetries
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• Spinning particles, axion radiation, and the classical double copy
• Static BPS black hole in 4d higher-spin gauge theory
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• Bound states and the classical double copy
• Gravity as Gauge Theory Squared: A Ghost Story
• A Twistorial Foundation for the Classical Double Copy
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• The Weyl Double Copy for Gravitational Waves
• Double Copy from Homotopy Algebras
• Classical Solutions and their Double Copy in Split Signature
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• The classical double copy of non-singular black holes
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• The convolutional double copy: a case study with a point
• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
• The Newman-Penrose Map and the Classical Double Copy
• Weyl doubling
• Sources in the Weyl double copy
• Kerr-Schild Double Copy and Complex Worldlines
• Classical double copy at null infinity
• Strings, extended objects, and the classical double copy
• Asymptotic Weyl Double Copy
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Unfolded Description of $Ad{S}_4$ Kerr Black Hole
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• Alternative formulations of the twistor double copy
• Twistor Space Origins of the Newman-Penrose Map
• The double copy of the multipole expansion
• Black Holes in Klein Space
• Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor
• The Weyl double copy in vacuum spacetimes with a cosmological constant
• Weyl double copy and massless free fields in curved spacetimes
• Quantization Conditions and the Double Copy
• BRST Symmetry and the Convolutional Double Copy

Cited by in corpus (14)

• Einstein-Maxwell theory and the Weyl double copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Black Hole Horizons from the Double Copy
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Regularized Weyl double copy
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Asymptotic Weyl double copy in Newman-Penrose formalism
• Compactifying the Kerr-Schild Double Copy
• Gravito-electromagnetism, Kerr-Schild and Weyl double copies; a unified perspective
• Weyl double copy in type D spacetime in four and five dimensions
• Background ambiguity and the Gödel double copy
• Hawking radiation from the double copy
• New framework for classical double copies
• Five dimensional Weyl double copy