Constant mean curvature surfaces in AdS_3

TL;DR

This paper constructs and analyzes finite-gap constant mean curvature surfaces in AdS_3, including minimal surfaces relevant for gauge theory amplitudes, exploring their properties and special limits.

Contribution

It introduces a general finite-gap construction for constant mean curvature surfaces in AdS_3, including minimal surfaces and their properties.

Findings

Finite-gap solutions exhibit specific asymptotic behaviors.

Degenerate limits correspond to soliton solutions.

Potential solutions with null boundaries are discussed.

Abstract

We construct constant mean curvature surfaces of the general finite-gap type in AdS_3. 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.