A tale of two exponentiations in ${\cal N}=8$ supergravity at subleading level

TL;DR

This paper extends the analysis of high-energy massless gravitational scattering in ${ m =8}$ supergravity to the sub-leading level, exploring infrared divergence exponentiation, impact parameter formulation, and testing eikonal predictions at three loops.

Contribution

It provides the first detailed study of sub-leading deflection angles at two loops in ${ m =8}$ supergravity, revealing insights into IR divergence exponentiation and impact parameter factorization.

Findings

IR finite conservative part matches Einstein gravity predictions

Dissipative part remains IR divergent, requiring regularization

Eikonal formulation partially accounts for lower-loop exponentiation, but fails for dissipative parts at all loops

Abstract

High-energy massless gravitational scattering in ${\cal N}=8$ supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in $\epsilon$, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.