Eikonal amplitudes from curved backgrounds

Abstract

Eikonal exponentiation in QFT describes the emergence of classical physics at long distances in terms of a non-trivial resummation of infinitely many diagrams. Long ago, 't Hooft proposed a beautiful correspondence between ultra-relativistic scalar eikonal scattering and one-to-one scattering in a background shockwave space-time, bypassing the need to resum. In this spirit, we propose here a covariant method for computing one-to-one amplitudes in curved background space-times which gives rise what we conjecture to be a general expression for the eikonal amplitude. We show how the one-to-one scattering amplitude for scalars on any stationary space-time reduces to a boundary term that captures the long-distance behavior of the background and has the structure of an exponentiated eikonal amplitude. In the case of scalar scattering on Schwarzschild, we recover the known results for gravitational scattering of massive scalars in the eikonal regime. For Kerr, we find a remarkable exponentiation of the tree-level amplitude for gravitational scattering between a massive scalar and a massive particle of infinite spin. This amplitude exhibits a Kawai-Lewellen-Tye-like factorization, which we use to evaluate the eikonal amplitude in momentum space, and study its analytic properties.

30 pages, 9 figures. v2: typos corrected, references added; v3: more typos corrected; v4: version accepted for publication

References in corpus (32)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Classical black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• On-shell heavy particle effective theories
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Universality of ultra-relativistic gravitational scattering
• Radiation Reaction from Soft Theorems
• Ionization of Gravitational Atoms
• Universality in the classical limit of massless gravitational scattering
• On an Exponential Representation of the Gravitational S-Matrix
• Classical Gravity from Loop Amplitudes
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• A worldsheet for Kerr
• Classical observables from coherent-spin amplitudes
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• Kerr-Newman from Minimal Coupling
• The Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions
• Infrared Divergences and the Eikonal Exponentiation
• Exponentiation of the leading eikonal with spin
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Quantum imprints of gravitational shockwaves
• Quantum gravity on the black hole horizon
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Invariance of Unruh and Hawking radiation under matter-induced supertranslations
• Black Hole S-matrix for a scalar field
• $2\to 2N$ scattering: Eikonalisation and the Page curve
• Classical gravitational scattering from a gauge-invariant double copy

Cited by in corpus (21)

• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• Scattering Angles in Kerr Metrics
• Celestial holography on Kerr-Schild backgrounds
• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• Bethe-Salpeter equation for classical gravitational bound states
• Graviton scattering in self-dual radiative space-times
• All order gravitational waveforms from scattering amplitudes
• Observables from the Spinning Eikonal
• Gravitational Bound Waveforms from Amplitudes
• Large Gauge Effects and the Structure of Amplitudes
• Wave scattering event shapes at high energies
• Radiation eikonal for post-Minkowskian observables
• Charged test-particle scattering and effective one-body metrics with spin
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection
• Charged particle scattering near the horizon
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Exploring gravitational impulse via quantum Boltzmann equation
• Celestial Regge theory