  The MHV scattering amplitudes in planar N=4 SYM are dual to bosonic
light-like Wilson loops. We explore various proposals for extending this
duality to generic non-MHV amplitudes. The corresponding dual object should
have the same symmetries as the scattering amplitudes and be invariant to all
loops under the chiral half of the N=4 superconformal symmetry. We analyze the
recently introduced supersymmetric extensions of the light-like Wilson loop
(formulated in Minkowski space-time) and demonstrate that they have the
required symmetry properties at the classical level only, up to terms
proportional to field equations of motion. At the quantum level, due to the
specific light-cone singularities of the Wilson loop, the equations of motion
produce a nontrivial finite contribution which breaks some of the classical
symmetries. As a result, the quantum corrections violate the chiral
supersymmetry already at one loop, thus invalidating the conjectured duality
between Wilson loops and non-MHV scattering amplitudes. We compute the
corresponding anomaly to one loop and solve the supersymmetric Ward identity to
find the complete expression for the rectangular Wilson loop at leading order
in the coupling constant. We also demonstrate that this result is consistent
with conformal Ward identities by independently evaluating corresponding
one-loop conformal anomaly.
