A tale of two exponentiations in [formula omitted] supergravity

Paolo Di Vecchia,Andrés Luna,Stephen G Naculich,Rodolfo Russo,Gabriele Veneziano,Chris D White

doi:10.1016/j.physletb.2019.134927

Abstract

The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for 2→2 scattering in 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.

Highlights

Scattering amplitudes in gauge and gravity theories continue to be intensively studied, due to a wide variety of both formal and phenomenological applications
One of the simplest amplitudes in terms of external multiplicity is that of four-graviton scattering, results for which have been previously calculated at one-loop [6,7,8,9] and two-loop [10,11,12,13] order
We examined the form of the four-graviton scattering amplitude in N = 8 supergravity, which was recently calculated at three-loop order [31]

Summary

Introduction

Scattering amplitudes in gauge and gravity theories continue to be intensively studied, due to a wide variety of both formal and phenomenological applications. The four-graviton scattering amplitude in N = 8 supergravity has been obtained at an impressive three-loop order [31] The authors compared their results with the form of eq (1.2), confirming that the three-loop remainder function is infrared finite. [31], we will use a very well-established property of gravitational scattering in the leading Regge limit, namely that the S-matrix has a certain exponential structure in transverse position (i.e. impact parameter) space, in terms of the so-called eikonal phase This may be expanded in the gravitational coupling constant, before being Fourier transformed to momentum-transfer space order-by-order in perturbation theory. We will use our findings to predict additional terms at higher loops, before forming a conjecture for the leading Regge behaviour of the remainder function at arbitrary order in perturbation theory.

The remainder function up to three-loop order

Impact-parameter exponentiation and the eikonal phase

The three-loop remainder function in the Regge limit

The remainder function to all orders in the Regge limit

Discussion