Four-point amplitudes in [formula omitted] supergravity and Wilson loops

Abstract

Prompted by recent progress in the study of N = 4 super Yang–Mills amplitudes, and evidence that similar approaches are 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 ϵ 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.