Vacuum type space-like string surfaces in AdS_3 x S^3

TL;DR

This paper classifies all space-like minimal surfaces in AdS_3 x S^3 with constant induced metrics, analyzing their boundary behaviors and calculating their regularized areas for specific scattering configurations.

Contribution

It provides a complete classification of space-like minimal surfaces in AdS_3 x S^3 with constant induced metrics, using group theory and Pohlmeyer reduction methods.

Findings

Most surfaces are parameterized by four real parameters.

Different classes exhibit distinct boundary behaviors.

Calculated regularized areas for four-point scattering configurations.

Abstract

We construct and classify all space-like minimal surfaces in AdS_3 x S^3 which globally admit coordinates with constant induced metric on both factors. Up to O(2,2) x O(4) transformations all these surfaces, except one class, are parameterized by four real parameters. The classes of surfaces correspond to different regions in this parameter space and show quite different boundary behavior. Our analysis uses a direct construction of the string coordinates via a group theoretical treatment based on the map of AdS_3 x S^3 to SL(2,R) x SU(2). This is complemented by a cross check via standard Pohlmeyer reduction. After embedding in AdS_5 x S^5 we calculate the regularized area for solutions with a boundary spanned by a four point scattering s-channel momenta configuration.