  The computation of n-point planar amplitudes in N=4 SYM at strong coupling is
known to be reduced to the search for solutions of the integrable 2d SO(4,2)
sigma-model with growing asymptotics on the world-sheet and to the study of
their Whitham deformations induced by an epsilon-regularization, which breaks
both integrability and SO(4,2) symmetry. A multi-parameter (moduli) family of
such solutions is constructed for n=4. They all correspond to the same s and t
and some are related by SO(4,2) transformations. Nevertheless, they lead to
different regularized areas, whose minimum is the Alday-Maldacena solution. A
brief review of results on n-point amplitudes is also provided, with special
emphasis on the underlying equivalence of the above regularized minimal area in
AdS and a double contour integral along the same boundary, two purely geometric
quantities.
