A Surprise in the Amplitude/Wilson Loop Duality

TL;DR

This paper demonstrates that the duality between MHV scattering amplitudes and lightlike polygon Wilson loops persists at two loops through order epsilon in dimensional regularization, revealing an unexpected robustness of this conjectured equality.

Contribution

The paper provides explicit two-loop calculations showing the amplitude/Wilson loop duality holds beyond previous expectations, including at order epsilon in dimensional regularization.

Findings

Duality holds at two loops through order epsilon.

Equality persists for four- and five-particle amplitudes.

Unanticipated robustness of the amplitude/Wilson loop duality.

Abstract

One of the many remarkable features of MHV scattering amplitudes is their conjectured equality to lightlike polygon Wilson loops, which apparently holds at all orders in perturbation theory as well as non-perturbatively. This duality is usually expressed in terms of purely four-dimensional quantities obtained by appropriate subtraction of the IR and UV divergences from amplitudes and Wilson loops respectively. In this paper we demonstrate, by explicit calculation, the completely unanticipated fact that the equality continues to hold at two loops through order epsilon in dimensional regularization for both the four-particle amplitude and the (parity-even part of the) five-particle amplitude.