The Subleading Eikonal in Supergravity Theories

TL;DR

This paper investigates the subleading eikonal contributions in supergravity theories, focusing on elastic and inelastic scattering processes of massless particles off Dp-branes, and introduces novel computational methods validated by classical and geometric analyses.

Contribution

It presents a new method for computing leading and subleading eikonal phases using on-shell vertices, applicable in large impact parameter regimes, and demonstrates their equivalence with traditional Feynman diagram calculations.

Findings

Leading and subleading eikonal depend only on elastic processes.

Inelastic processes modify the eikonal by a multiplicative factor.

Results agree with classical gravitational backreaction and geodesic deflection calculations.

Abstract

In this paper we study the subleading contributions to eikonal scattering in (super)gravity theories with particular emphasis on the role of both elastic and inelastic scattering processes. For concreteness we focus on the scattering of various massless particles off a stack of D$p$-branes in type II supergravity in the limit of large impact parameter $b$. We analyse the relevant field theory Feynman diagrams which naturally give rise to both elastic and inelastic processes. We show that in the case analysed the leading and subleading eikonal only depend on elastic processes, while inelastic processes are captured by a pre-factor multiplying the exponentiated leading and subleading eikonal phase. In addition to the traditional Feynman diagram computations mentioned above, we also present a novel method for computing the amplitudes contributing to the leading and subleading eikonal phases, which, in the large $b$ limit, only involves knowledge of the onshell three and four-point vertices. The two methods are shown to give the same results. Furthermore we derive these results in yet another way, by computing various one-point amplitudes which allow us to extract the classical solution of the gravitational back reaction of the target D$p$-branes. Finally we show how our expressions for the leading and subleading eikonal agree with the calculation of the metric and corresponding deflection angle for massless states moving along geodesics in the relevant curved geometry.