Classical and quantum gravitational scattering with Generalized Wilson Lines

Abstract

The all-order structure of scattering amplitudes is greatly simplified by the use of Wilson line operators, describing eikonal emissions from straight lines extending to infinity. A generalization at subleading powers in the eikonal expansion, known as Generalized Wilson Line (GWL), has been proposed some time ago, and has been applied both in QCD phenomenology and in the high energy limits of gravitational amplitudes. In this paper we revisit the construction of the scalar gravitational GWL starting from first principles in the worldline formalism. We identify the correct Hamiltonian that leads to a simple correspondence between the soft expansion and the weak field expansion. This allows us to isolate the terms in the GWL that are relevant in the classical limit. In doing so we devote special care to the regularization of UV divergences that were not discussed in an earlier derivation. We also clarify the relation with a parallel body of work that recently investigated the classical limit of scattering amplitudes in gravity in the worldline formalism.

arXiv comment41 pages, 5 figures; published version: typos corrected, references added, discussion in section 5.2 extended, results unchanged

References in corpus (71)

• An Effective Field Theory of Gravity for Extended Objects
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Black holes and the double copy
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Radiation and the classical double copy for color charges
• Classical black hole scattering from a worldline quantum field theory
• Eikonal Quantum Gravity and Planckian Scattering
• Observables and amplitudes for spinning particles and black holes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Classical and quantum scattering in post-Minkowskian gravity
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Spinning gravitating objects in the effective field theory in the post-Newtonian scheme
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Factorization Properties of Soft Graviton Amplitudes
• Universality of ultra-relativistic gravitational scattering
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Radiation Reaction from Soft Theorems
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Gravitational Radiation from Color-Kinematics Duality
• Light-like Scattering in Quantum Gravity
• Universality in the classical limit of massless gravitational scattering
• High energy scattering in QCD and cross singularities of Wilson loops
• Webs in multiparton scattering using the replica trick
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Non-abelian factorisation for next-to-leading-power threshold logarithms
• Worldline formalism in a gravitational background
• Diagrammatic insights into next-to-soft corrections
• Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Trace Anomalies from Quantum Mechanics
• A worldsheet for Kerr
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Evolution equation for gluon Regge trajectory
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Infrared features of gravitational scattering and radiation in the eikonal approach
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• A new gauge-invariant double copy for heavy-mass effective theory
• The Non-Abelian Exponentiation theorem for multiple Wilson lines
• Wilson line approach to gravity in the high energy limit
• Diagrammatic Exponentiation for Products of Wilson Lines
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• Diagrammatic resummation of leading-logarithmic threshold effects at next-to-leading power
• An $S$-Matrix for Massless Particles
• Loop calculations in quantum-mechanical non-linear sigma models
• High energy scattering in gravity and supergravity
• Infrared Divergences and the Eikonal Exponentiation
• Spin-multipole effects in binary black holes and the test-body limit
• The Subleading Eikonal in Supergravity Theories
• NLO gravitational quartic-in-spin interaction
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• BRST treatment of zero modes for the worldline formalism in curved space
• Asymptotic dynamics on the worldline for spinning particles
• Multiple Gluon Exchange Webs
• Emerging Hawking-like Radiation from Gravitational Bremsstrahlung Beyond the Planck Scale
• Classical Gravitational Self-Energy from Double Copy
• An Introduction to Webs
• Soft Graviton Emission at High and Low Energies in Yukawa and Scalar Theories
• Worldline description of a bi-adjoint scalar and the zeroth copy
• Position-space cuts for Wilson line correlators
• Dimensional Regularization for the Particle Transition Amplitude in Curved Space

Cited by in corpus (8)

• Angular momentum of zero-frequency gravitons
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Light bending from eikonal in worldline quantum field theory
• Quantization Conditions and the Double Copy
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Diamond of Infrared Equivalences in Abelian Gauge Theories
• The need for a nonlocal expansion in general relativity
• Double soft graviton factors from the gravitational Wilson line