Series solution and minimal surfaces in AdS

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 who...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2010; no. 3
Main Authors Jevicki, Antal, Jin, Kewang
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.03.2010
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Elementary Particles
Exact solutions
High energy physics
Mathematical analysis
Minimal surfaces
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
AdS-CFT Correspondence
Integrable Field Theories
Bosonic Strings
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Summary: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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2010)028