# A tale of two exponentiations in ${\cal N}=8$ supergravity

## TL;DR

This paper analyzes the structure of scattering amplitudes in ${
m extbf{N}=8}$ supergravity, revealing the exponentiation pattern at three loops and predicting similar features at higher loops, thus providing consistency checks for future calculations.

## Contribution

It explains the origin of high-energy terms in the three-loop amplitude and predicts their persistence at all higher loops, offering a new understanding of amplitude structure in supergravity.

## Key findings

- Three-loop amplitude expressed as exponentiated one-loop plus a remainder
- High-energy terms originate from unitarity-restoring exponentiation
- Predictions of similar high-energy terms at all higher loop orders

## Abstract

The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for $2\rightarrow 2$ scattering in ${\cal N}=8$ supergravity was presented at three-loop order for the first time. The result can be written in terms of an exponentiated one-loop contribution, modulo a remainder function which is free of infrared singularities, but contains leading terms in the high energy Regge limit. We explain the origin of these terms from a well-known, unitarity-restoring exponentiation of the high-energy gravitational $S$-matrix in impact-parameter space. Furthermore, we predict the existence of similar terms in the remainder function at all higher loop orders. Our results provide a non-trivial cross-check of the recent three-loop calculation, and a necessary consistency constraint for any future calculation at higher loops.