  Alday-Maldacena conjecture is that the area A_P of the minimal surface in
AdS_5 space with a boundary P, located in Euclidean space at infinity of AdS_5,
coincides with a double integral D_P along P, the Abelian Wilson average in an
auxiliary dual model. The boundary P is a polygon formed by momenta of n
external light-like particles in N=4 SYM theory, and in a certain n=infty limit
it can be substituted by an arbitrary smooth curve (wavy circle). The
Alday-Maldacena conjecture is known to be violated for n>5, when it fails to be
supported by the peculiar global conformal invariance, however, the structure
of deviations remains obscure. The case of wavy lines can appear more
convenient for analysis of these deviations due to the systematic method
developed in arXiv:0803.1547 for (perturbative) evaluation of minimal areas,
which is not yet available in the presence of angles at finite n. We correct a
mistake in that paper and explicitly evaluate the h^2\bar h^2 terms, where the
first deviation from the Alday-Maldacena duality arises for the wavy circle.
