Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle

Abstract

We further develop the formalism of arXiv:0712.0159 for approximate solution of Nambu-Goto (NG) equations with polygon conditions in AdS backgrounds, needed in modern studies of the string/gauge duality. Inscribed circle condition is preserved, which leaves only one unknown function y_0(y_1,y_2) to solve for, what considerably simplifies our presentation. The problem is to find a delicate balance -- if not exact match -- between two different structures: NG equation -- a non-linear deformation of Laplace equation with solutions non-linearly deviating from holomorphic functions, -- and the boundary ring, associated with polygons made from null segments in Minkovski space. We provide more details about the theory of these structures and suggest an extended class of functions to be used at the next stage of Alday-Maldacena program: evaluation of regularized NG actions.

45 pages

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Cited by in corpus (15)

• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Moduli Dynamics of AdS_3 Strings
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
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• Constant mean curvature surfaces in AdS_3
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
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• Analogue of the identity Log Det = Trace Log for resultants
• Series Solution and Minimal Surfaces in AdS
• Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• Deviation from Alday-Maldacena Duality For Wavy Circle
• Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R^{1,2}
• A short review on TBA equation and scattering amplitude/Wilson loop duality