Series Solution and Minimal Surfaces in AdS

Details Series Solution and Minimal Surfaces in AdS Series Solution and Minimal Surfaces in AdS

2009-11-05

arxiv.org/abs/0911.1107v3

JHEP 1003:028,2010

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, no figures; references added, one note added

Scientific paper

10.1007/JHEP03(2010)028

According to the Alday-Maldacena program the strong coupling limit of Super Yang-Mills scattering amplitudes is given by minimal area surfaces in AdS spacetime with a boundary consisting of a momentum space polygon. The string equations in AdS systematically reduce to coupled Toda type equations whose Euclidean classical solutions are then of direct relevance. While in the simplest case of AdS_3 exact solutions were known from earlier studies of the sinh-Gordon equation, there exist at present no similar exact forms for the generalized Toda equations related to AdS_d with d>=4. In this paper we develop a series method for the solution to those equations and evaluate their contribution to the finite piece of the worldsheet area. For the known sinh-Gordon case the method is seen to give results in excellent agreement with the exact answer.

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