Series Solution and Minimal Surfaces in AdS

Abstract

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.

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

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Cited by in corpus (9)

• Thermodynamic Bubble Ansatz
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• Space-like minimal surfaces in AdS x S
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• Some comments on spacelike minimal surfaces with null polygonal boundaries in $Ad{S}_m$
• Minimal surfaces in AdS space and Integrable systems
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• AdS String: Classical Solutions and Moduli Dynamics
• Novel aspects of integrability for NLSMs in symmetric spaces