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

Understand

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.