Infrared Divergences and the Eikonal Exponentiation

TL;DR

This paper investigates how eikonal resummation and infrared divergence exponentiation relate in gravity amplitudes, revealing their connection to classical two-body dynamics and gravitational wave emission.

Contribution

It demonstrates the explicit link between eikonal and infrared exponentiations in gravity, deriving two-loop divergences from lower-loop data in supergravity and general relativity.

Findings

Derived the divergent part of the two-loop eikonal from lower-loop amplitudes.

Established the connection between eikonal resummation and infrared divergences in gravity.

Applied the framework to $ abla$8 supergravity and general relativity.

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.