Infrared Divergences and the Eikonal Exponentiation

Abstract

The aim of this note is to explore the interplay between the eikonal resummation in impact-parameter space and the exponentiation of infrared divergences in momentum space for gravity amplitudes describing collisions of massive objects. The eikonal governs the classical dynamics relevant to the two-body problem, and its infrared properties are directly linked to the zero-frequency limit of the gravitational wave emission spectrum and to radiation-reaction effects. Combining eikonal and infrared exponentiations it is possible to derive these properties at a given loop order starting from lower-loop data. This is illustrated explicitly in $\mathcal{N}=8$ supergravity and in general relativity by deriving the divergent part of the two-loop eikonal from tree-level and one-loop elastic amplitudes.

22 pages, 3 figures. v2: References updated, published in Phys. Rev. D

References in corpus (9)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Three-Loop Superfiniteness of N=8 Supergravity
• Is N = 8 Supergravity Ultraviolet Finite?
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Classical Gravity from Loop Amplitudes
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes

Cited by in corpus (26)

• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Radiated Angular Momentum and Dissipative Effects in Classical Scattering
• Inelastic Exponentiation and Classical Gravitational Scattering at One Loop
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder
• Radiation reaction for spinning black-hole scattering
• Angular momentum of zero-frequency gravitons
• Classical Double Copy of Worldline Quantum Field Theory
• Exponentiation of the leading eikonal with spin
• Eikonal amplitudes from curved backgrounds
• Light bending from eikonal in worldline quantum field theory
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering
• Observables from the Spinning Eikonal
• Classical and quantum gravitational scattering with Generalized Wilson Lines
• Binary Dynamics from Worldline QFT for Scalar-QED
• Large Gauge Effects and the Structure of Amplitudes
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Exposing the threshold structure of loop integrals
• Quantization Conditions and the Double Copy
• Waveforms from Amplitudes
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Pair creation, backreaction, and resummation in strong fields
• Scrambling and Entangling Spinning Particles
• Double soft graviton factors from the gravitational Wilson line
• Yang-Mills observables: from KMOC to eikonal through EFT