  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. We describe in detail the mathematical problem that
needs to be solved. This problem is mathematically the same as the one studied
by Gaiotto, Moore and Neitzke in the context of the moduli space of certain
supersymmetric theories. Using their results we can find the explicit answer
for the area of a surface that ends on an eight-sided polygon. Via the
gauge/gravity duality this can also be interpreted as a certain eight-gluon
scattering amplitude at strong coupling. In addition, we give fairly explicit
solutions for regular polygons.
