The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude

TL;DR

This paper tests the gluon scattering amplitude/Wilson loop duality in N=4 super Yang-Mills theory by evaluating a hexagonal Wilson loop at two loops and comparing it to the BDS conjecture, revealing discrepancies that challenge the duality.

Contribution

The study provides a two-loop calculation of the hexagon Wilson loop and demonstrates deviations from the BDS conjecture for six-gluon amplitudes, questioning the duality's validity.

Findings

The finite parts match in the collinear limit.

Differences appear as a non-trivial function of conformal variables.

Results suggest the BDS conjecture or duality fails at two loops.

Abstract

As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate the hexagonal light-like Wilson loop at two loops in N=4 super Yang-Mills theory. We compare its finite part to the Bern-Dixon-Smirnov (BDS) conjecture for the finite part of the six-gluon amplitude. We find that the two expressions have the same behavior in the collinear limit, but they differ by a non-trivial function of the three (dual) conformally invariant variables. This implies that either the BDS conjecture or the gluon amplitude/Wilson loop duality fails for the six-gluon amplitude, starting from two loops. Our results are in qualitative agreement with the analysis of Alday and Maldacena of scattering amplitudes with infinitely many external gluons.