Four-point Amplitudes in N=8 Supergravity and Wilson Loops

TL;DR

This paper explores the structure of four-point amplitudes in N=8 supergravity, confirming exponentiation of infrared divergences, analyzing transcendentality, and relating Wilson loops to physical amplitudes.

Contribution

It investigates Wilson loop techniques in N=8 supergravity and establishes their connection to scattering amplitudes, extending methods from N=4 super Yang-Mills theory.

Findings

Infrared divergences exponentiate in two-loop four-point amplitudes.

Finite parts of amplitudes show uniform transcendentality.

Wilson loops with metric relate closely to supergravity amplitudes.

Abstract

Prompted by recent progress in the study of N=4 super Yang-Mills amplitudes, and evidence that similar approaches might be relevant to N=8 supergravity, we investigate possible iterative structures and applications of Wilson loop techniques in maximal supergravity. We first consider the two-loop, four-point MHV scattering amplitude in N=8 supergravity, confirming that the infrared divergent parts exponentiate, and we give the explicit expression which represents the failure for this to occur for the finite part. We observe that each term in the expansion of the one- and two-loop amplitudes in the dimensional regularisation parameter epsilon has a uniform degree of transcendentality. We then turn to consider Wilson loops in supergravity, showing that a natural definition of the loop, involving the Christoffel connection, fails to reproduce the one-loop amplitude. An alternative expression, which involves the metric explicitly, is shown to have a close relationship with the physical amplitude. We find that in a gauge in which the cusp diagrams vanish, the remaining diagrams for this Wilson loop correctly generate the full one-loop, four-point N=8 supergravity amplitude.