Constant mean curvature surfaces in AdS3

Abstract

We construct constant mean curvature surfaces of the general finite-gap type in AdS3. The special case with zero mean curvature gives minimal surfaces relevant for the study of Wilson loops and gluon scattering amplitudes in N =4 super Yang-Mills. We also analyze properties of the finite-gap solutions including asymptotic behavior and the degenerate (soliton) limit, and discuss possible solutions with null boundaries. © 2010 SISSA.