Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling

Understand

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.