Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space

Details Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space

2009-04-03

arxiv.org/abs/0904.0663v2

JHEP 0911:082,2009

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1088/1126-6708/2009/11/082

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.

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