We consider the proposed new duality between n-gluon scattering amplitudes and light-like Wilson loops with n cusps in the N=4 super- Yang-Mills theory. This duality was established at strong coupling by Alday and Maldacena. We discuss its validity at weak coupling. We show that the Wilson loop satisfies anomalous conformal Ward identities which unambiguously fix the form of the amplitude for n=4,5 but leave room for an arbitrary function of conformal invariants for n $geq$ 6. We reprot on recent two-loop calculation for the hexagon Wilson loop and the matching 6-gluon amplitude, which indicate that the BDS conjecture fails for n $geq$ 6.

LAPTH (Annecy)