Wilson line approach to gravity in the high energy limit

TL;DR

The paper analyzes the high-energy (Regge) limit of gravitational scattering using a Wilson-line formalism, connecting graviton Reggeization to the soft eikonal phase in a gauge-theory-like language. At one loop, gravity exhibits both an eikonal phase and a Reggeized graviton, with the Regge trajectory linear in $t$ and the eikonal piece proportional to $s$, leading to Regge cuts from their cross-talk. Infrared-finite parts in supergravity carry $M$-dependent double logarithms that may not exponentiate, while two-loop remainders vanish in the strict Regge limit, signaling dominance of the one-loop eikonal exponentiation there for ${\cal N}\ge 4$. The analysis extends to multigraviton (MRK) amplitudes, where the eikonal phase remains leading and Reggeization applies to each $t$-channel ladder, with cross-talk generating Regge-cut structures; overall, the Wilson-line framework unifies Regge behavior in gauge and gravity theories and highlights connections to double-copy ideas and shockwave pictures.

Abstract

We examine the high energy (Regge) limit of gravitational scattering using a Wilson line approach previously used in the context of non-Abelian gauge theories. Our aim is to clarify the nature of the Reggeization of the graviton and the interplay between this Reggeization and the so-called eikonal phase which determines the spectrum of gravitational bound states. Furthermore, we discuss finite corrections to this picture. Our results are of relevance to various supergravity theories, and also help to clarify the relationship between gauge and gravity theories.

Figures (5)

• Figure 1: Particle labels used throughout for $2\rightarrow2$ scattering.
• Figure 2: The Regge limit as two Wilson lines separated by a transverse distance $\vec{z}$.
• Figure 3: One-loop diagrams entering the calculation of the Wilson line vacuum expectation value of eq. (\ref{['Mdef']}).
• Figure 4: Diagrams contributing to the one-loop four-graviton amplitude in ${\cal N}=8$ supergravity.
• Figure 5: A general $L$-parton scattering process in the MRK limit, consisting of strongly ordered rapidities in the final state. Here $T_{t_i}$ is a quadratic Casimir operator associated with a given strut of the ladder.