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The MHV scattering amplitudes in planar N=4 SYM are dual to bosoniclight-like Wilson loops. We explore various proposals for extending thisduality to generic non-MHV amplitudes. The corresponding dual object shouldhave the same symmetries as the scattering amplitudes and be invariant to allloops under the chiral half of the N=4 superconformal symmetry. We analyze therecently introduced supersymmetric extensions of the light-like Wilson loop(formulated in Minkowski space-time) and demonstrate that they have therequired symmetry properties at the classical level only, up to termsproportional to field equations of motion. At the quantum level, due to thespecific light-cone singularities of the Wilson loop, the equations of motionproduce a nontrivial finite contribution which breaks some of the classicalsymmetries. As a result, the quantum corrections violate the chiralsupersymmetry already at one loop, thus invalidating the conjectured dualitybetween Wilson loops and non-MHV scattering amplitudes. We compute thecorresponding anomaly to one loop and solve the supersymmetric Ward identity tofind the complete expression for the rectangular Wilson loop at leading orderin the coupling constant. We also demonstrate that this result is consistentwith conformal Ward identities by independently evaluating correspondingone-loop conformal anomaly.

Are scattering amplitudes dual to super Wilson loops?