The single copy of the gravitational holonomy

Abstract

The double copy is a well-established relationship between gravity and gauge theories. It relates perturbative scattering amplitudes as well as classical solutions, and recently there has been mounting evidence that it also applies to non-perturbative information. In this paper, we consider the holonomy properties of manifolds in gravity and prescribe a single copy of gravitational holonomy that differs from the holonomy in gauge theory. We discuss specific cases and give examples where the single copy holonomy group is reduced. Our results may prove useful in extending the classical double copy. We also clarify previous misconceptions in the literature regarding gravitational Wilson lines and holonomy.

arXiv comment31 pages, 2 figures

References in corpus (56)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Gravity as the Square of Gauge Theory
• Black holes and the double copy
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Evidence for a New Soft Graviton Theorem
• The Kinematic Algebra From the Self-Dual Sector
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• The classical double copy for Taub-NUT spacetime
• The simplest massive S-matrix: from minimal coupling to Black Holes
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Kerr Black Holes as Elementary Particles
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Factorization Properties of Soft Graviton Amplitudes
• Soft sub-leading divergences in Yang-Mills amplitudes
• 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
• High energy scattering in QCD and cross singularities of Wilson loops
• The Double Copy of Electric-Magnetic Duality
• A Twistorial Foundation for the Classical Double Copy
• The Kinematic Algebras from the Scattering Equations
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• A worldsheet for Kerr
• Exact solutions for the biadjoint scalar field
• 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
• Newtonian Potential in Quantum Regge Gravity
• S-duality and the Double Copy
• Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
• Double Copy from Homotopy Algebras
• Topology and Wilson lines: global aspects of the double copy
• Wilson line approach to gravity in the high energy limit
• Extended solutions for the biadjoint scalar field
• Gravitational radiation from the classical spinning double copy
• Weyl doubling
• Monopoles, shockwaves and the classical double copy
• Biadjoint wires
• From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction
• New heavenly double copies
• Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes
• Kerr-Newman stress-tensor from minimal coupling
• Twistor Space Origins of the Newman-Penrose Map
• Wilson loops in four-dimensional quantum gravity
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Holonomy in the Schwarzschild-Droste Geometry
• Gravitational Wilson Loop and Large Scale Curvature
• Circular holonomy in the Taub-NUT spacetime
• Gravitational Wilson Loop in Discrete Quantum Gravity
• Color-kinematics duality and dimensional reduction for graviton emission in Regge limit
• Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse
• The gravitational cusp anomalous dimension from AdS space
• Holonomy groups of Lorentzian manifolds

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• Non-perturbative aspects of the self-dual double copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Quantization Conditions and the Double Copy
• The Radial Action from Probe Amplitudes to All Orders
• NS-NS Spacetimes from Amplitudes