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

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