Scattering on plane waves and the double copy

Abstract

Perturbatively around flat space, the scattering amplitudes of gravity are related to those of Yang-Mills by colour-kinematic duality, under which gravitational amplitudes are obtained as the 'double copy' of the corresponding gauge theory amplitudes. We consider the question of how to extend this relationship to curved scattering backgrounds, focusing on certain 'sandwich' plane waves. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave. This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds. It must also account for new 'tail' terms arising from scattering off the background. These encode a memory effect in the scattering amplitudes, which naturally double copies as well.

39 pages, 1 figure. v2: typos corrected, published version

References in corpus (40)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Gravity as the Square of Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• Black holes and the double copy
• Ambitwistor strings and the scattering equations
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Is N = 8 Supergravity Ultraviolet Finite?
• An electromagnetic analog of gravitational wave memory
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Classical gluon and graviton radiation from the bi-adjoint scalar double copy
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Solvable model of strings in a time-dependent plane-wave background
• The Memory Effect for Plane Gravitational Waves
• Soft Gravitons & the Memory Effect for Plane Gravitational Waves
• Dual Identities inside the Gluon and the Graviton Scattering Amplitudes
• On amplitudes in self-dual sector of Yang-Mills theory
• Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy
• Infra-red divergences in plane wave backgrounds
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Ambitwistor strings at null infinity and subleading soft limits
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• A magic pyramid of supergravities
• Twofold Symmetries of the Pure Gravity Action
• Perturbative gauge theory at null infinity
• Scattering in plane-wave backgrounds: infra-red effects and pole structure
• A Worldsheet Theory for Supergravity
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Gravity as the square of Yang-Mills?
• Caustics and wave propagation in curved spacetimes
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Tails of plane wave spacetimes: Wave-wave scattering in general relativity

Cited by in corpus (88)

• Advances in QED with intense background fields
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Observables and amplitudes for spinning particles and black holes
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Kerr-Schild double copy in curved spacetime
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• Spinning particles, axion radiation, and the classical double copy
• The self-dual classical double copy, and the Eguchi-Hanson instanton
• The Weyl Double Copy for Gravitational Waves
• Screw-symmetric gravitational waves: a double copy of the vortex
• Double Copy from Homotopy Algebras
• Classical Solutions and their Double Copy in Split Signature
• Double Copy for Celestial Amplitudes
• The classical double copy of non-singular black holes
• Gluons and gravitons at one loop from ambitwistor strings
• The Classical Double Copy of a Point Charge
• Extended solutions for the biadjoint scalar field
• Are all supergravity theories Yang-Mills squared?
• Double Copy Relation for AdS
• Gravitational radiation from the classical spinning double copy
• Classical and quantum double copy of back-reaction
• Classical double copy at null infinity
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Plane wave backgrounds and colour-kinematics duality
• Biadjoint wires
• Strings, extended objects, and the classical double copy
• Unraveling conformal gravity amplitudes
• Celestial holography on Kerr-Schild backgrounds
• Celestial double copy from the worldsheet
• Massive Gravity from Double Copy
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• Asymptotic Weyl Double Copy
• Loop-Level Double-Copy for Massive Quantum Particles
• Back-reaction on background fields: a coherent state approach
• MHV scattering of gluons and gravitons in chiral strong fields
• Twistor Space Origins of the Newman-Penrose Map
• Conformal Gravity from Gauge Theory
• Towards Color-Kinematics Duality in Generic Spacetimes
• Graviton scattering in self-dual radiative space-times
• All order gravitational waveforms from scattering amplitudes
• Geodesics From Classical Double Copy
• Isometries and the double copy
• Gauge $\times$ Gauge on Spheres
• The Weyl double copy in vacuum spacetimes with a cosmological constant
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• A Worldline Theory for Supergravity
• 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
• Gluon scattering on self-dual radiative gauge fields
• Exact results for scattering on ultra-short plane wave backgrounds
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• From polarized gravitational waves to analytically solvable electromagnetic beams
• The double copy: gravity from gluons
• Large Gauge Effects and the Structure of Amplitudes
• Gluon helicity flip in a plane wave background
• Extracting Einstein from the Loop-Level Double-Copy
• Black Hole Horizons from the Double Copy
• Ambitwistor string vertex operators on curved backgrounds
• 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
• Niederer's transformation, time-dependent oscillators and polarized gravitational waves
• Classical double copy and higher-spin fields
• The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red
• Wave scattering event shapes at high energies
• One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Flavour-kinematics duality for Goldstone modes
• The double copy: from optics to quantum gravity
• Gauge and Gravity Amplitudes on the Celestial Sphere
• Proportionality of gravitational and electromagnetic radiation by an electron in an intense plane wave
• Quantum probing of null-singularities
• Superintegrable relativistic systems in scalar background fields
• Gravitational wave memory and its effects on particles and fields
• Next-to-MHV Yang-Mills kinematic algebra
• Hawking radiation from the double copy
• Dynamics, quantum states and Compton scattering in nonlinear gravitational waves
• The $L_{\infty }$-algebra of the S-matrix
• The Radial Action from Probe Amplitudes to All Orders
• On Non-Perturbative Unitarity in Gravitational Scattering
• Classical physics from amplitudes on curved backgrounds
• Weyl double copy in Lifshitz spacetimes
• Ambitwistor strings and amplitudes in curved backgrounds
• NS-NS Spacetimes from Amplitudes