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

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

2007-12-26

arxiv.org/abs/0712.4138v2

Phys.Lett.B662:456-460,2008

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, 3 figures; typos corrected

Scientific paper

10.1016/j.physletb.2008.03.032

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.

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