  In this note we consider minimal surfaces in three dimensional anti-de Sitter
space that end at the AdS boundary on a polygon given by a sequence of null
segments. The problem can be reduced to a certain generalized Sinh-Gordon
equation and to SU(2) Hitchin equations. The mathematical problem to be solved
arises also in the context of the moduli space of certain three dimensional
supersymmetric theories. We can use explicit results available in the
literature in order to find the explicit answer for the area of a surface that
ends on a eight-sided null Wilson loop. Via the gauge/gravity duality this can
also be interpreted as a certain eight-gluon scattering amplitude at strong
coupling for a special kinematic configuration.
