  We study the divergences of Wilson loops for a contour with a cusp of zero
opening angle, combined with a nonzero discontinuity of its curvature. The
analysis is performed in lowest order, both for weak and strong coupling. Such
a spike contributes a leading divergent term proportional to the inverse of the
square root of the cutoff times the jump of the curvature. As nextleading term
appears a logarithmic one in the supersymmetric case, but it is absent in QCD.
The strong coupling result, obtained from minimal surfaces in AdS via
holography, can be used also for applications to entanglement entropy in
(2+1)-dimensional CFT's.
