Abstract
The aim of this article 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.
Highlights
Gravity amplitudes are constrained by two very different kinds of nonperturbative resummations that lead to the exponentiation of certain all-order contributions
The first is the eikonal exponentiation, which captures the classical limit of the scattering amplitude
The systematic study of the eikonal resummation was initiated in the late 1980s [1,2,3,4,5,6], in the context of unitarity restoration in ultrarelativistic scattering, but it has been recently applied in amplitude-based approaches to the two-body problem and gravitational wave emission in general relativity (GR) and in its supersymmetric extensions [7,8,9,10,11,12,13,14,15,16,17,18,19]
Summary
Gravity amplitudes are constrained by two very different kinds of nonperturbative resummations that lead to the exponentiation of certain all-order contributions. The maximally supersymmetric theory, N 1⁄4 8, has been put forward as a potential UV finite theory of gravity in D 1⁄4 4 [46,47,48,49,50], and, especially in the context of the classical limit, it has proved to be a useful theoretical laboratory for developing new calculational tools and tackling conceptual issues in a technically simpler setup compared to GR [9,12,14,16,18,19] Given these two a priori independent exponentiations, it is natural to wonder how they combine to provide constraints for gravity amplitudes. Notations and conventions are collected in Appendix A, while Appendix B contains the explicit evaluation of some useful IR-divergent integrals
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