Topology and Wilson lines: global aspects of the double copy

Abstract

The Kerr-Schild double copy relates exact solutions of gauge and gravity theories. In all previous examples, the gravity solution is associated with an abelian-like gauge theory object, which linearises the Yang-Mills equations. This appears to be at odds with the double copy for scattering amplitudes, in which the non-abelian nature of the gauge theory plays a crucial role. Furthermore, it is not yet clear whether or not global properties of classical fields - such as non-trivial topology - can be matched between gauge and gravity theories. In this paper, we clarify these issues by explicitly demonstrating how magnetic monopoles associated with arbitrary gauge groups can be double copied to the same solution (the pure NUT metric) in gravity. We further describe how to match up topological information on both sides of the double copy correspondence, independently of the nature of the gauge group. This information is neatly expressed in terms of Wilson line operators, and we argue through specific examples that they provide a useful bridge between the classical double copy and the BCJ double copy for scattering amplitudes.

arXiv comment31 pages, 4 figures. Some minor corrections have been implemented

References in corpus (100)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Gravity as the Square of Gauge Theory
• Black holes and the double copy
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• Observables and amplitudes for spinning particles and black holes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Factorization Properties of Soft Graviton Amplitudes
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Diffeomorphism-invariant observables and their nonlocal algebra
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Pure Gravities via Color-Kinematics Duality for Fundamental Matter
• Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
• Color-Kinematics Duality for QCD Amplitudes
• Double copy for massive quantum particles with spin
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Yang-Mills origin of gravitational symmetries
• Gravitational Radiation from Color-Kinematics Duality
• Colour-Kinematics Duality for One-Loop Rational Amplitudes
• Type D Spacetimes and the Weyl Double Copy
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Spinning particles, axion radiation, and the classical double copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• BCJ duality and the double copy in the soft limit
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• High energy scattering in QCD and cross singularities of Wilson loops
• Bound states and the classical double copy
• Perturbative Gravity from QCD Amplitudes
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• Collinear and Soft Divergences in Perturbative Quantum Gravity
• New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• Gravity as Gauge Theory Squared: A Ghost Story
• The Double Copy of Electric-Magnetic Duality
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Amplitude Relations in Non-linear Sigma Model
• String-inspired BCJ numerators for one-loop MHV amplitudes
• Exact solutions for the biadjoint scalar field
• Evolution equation for gluon Regge trajectory
• New dual gravitational charges
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Eikonal methods applied to gravitational scattering amplitudes
• Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
• S-duality and the Double Copy
• Equivalent D=3 Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Wilson line approach to gravity in the high energy limit
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• The Classical Double Copy of a Point Charge
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Extended solutions for the biadjoint scalar field
• Double-Copy Constructions and Unitarity Cuts
• Are all supergravity theories Yang-Mills squared?
• Twin Supergravities from Yang-Mills Squared
• Ehlers as EM duality in the double copy
• All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
• On the Double Copy for Spinning Matter
• Kerr-Newman from Minimal Coupling
• Kerr-Schild Double Copy and Complex Worldlines
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• Monopoles, shockwaves and the classical double copy
• Soft-collinear gravity
• Biadjoint wires
• Strings, extended objects, and the classical double copy
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction
• Properties of Dual Supertranslation Charges in Asymptotically Flat Spacetimes
• Gravity as the square of Yang-Mills?
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes
• Gravitational multi-NUT solitons, Komar masses and charges
• Conformal Gravity from Gauge Theory
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• Wilson loops in four-dimensional quantum gravity
• Radiation of scalar modes and the classical double copy
• Shift symmetries, soft limits, and the double copy beyond leading order
• Dual-color decompositions at one-loop level in Yang-Mills theory
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
• An Introduction to Webs
• Gravitational Wilson Loop in Discrete Quantum Gravity
• Gravitational Wu-Yang Monopoles
• Color-kinematics duality and dimensional reduction for graviton emission in Regge limit
• The gravitational cusp anomalous dimension from AdS space
• Entanglement and the Double Copy
• On the Quantization of the Gravitational Field

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• A Twistorial Foundation for the Classical Double Copy
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• The classical double copy of non-singular black holes
• The convolutional double copy: a case study with a point
• A double copy for asymptotic symmetries in the self-dual sector
• Classical Yang-Mills observables from amplitudes
• The Newman-Penrose Map and the Classical Double Copy
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• Off-Shell Color-Kinematics Duality for Chern-Simons
• New heavenly double copies
• Asymptotic Weyl Double Copy
• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• 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
• Black Holes in Klein Space
• The double copy of the multipole expansion
• Non-perturbative aspects of the self-dual double copy
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• The single copy of the gravitational holonomy
• More on the Classical Double Copy in Three Spacetime Dimensions
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Black Hole Horizons from the 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
• Quantization Conditions and the Double Copy
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• The double copy: from optics to quantum gravity
• Next-to-MHV Yang-Mills kinematic algebra
• Hawking radiation from the double copy
• The Weyl double copy from twistor space
• Massive Covariant Colour-Kinematics in 3D
• From colored gravity to electromagnetism
• Global shift symmetry on an ADM hypersurface: Toward emergent gravity
• Wilson Lines and Boundary Operators of BCFW Shifts
• Newman-Janis Algorithm from Taub-NUT Instantons
• Extended Field Theories as higher Kaluza-Klein theories
• NS-NS Spacetimes from Amplitudes
• The Kerr-Schild Double Copy in Lifshitz Spacetime