Space-like minimal surfaces in AdS × S

Abstract

We present a four parameter family of classical string solutions in AdS 3 ×S 3, which end along a light-like tetragon at the boundary of AdS 3 and carry angular momentum along two cycles on the sphere. The string surfaces are space-like and their projections on AdS 3 and on S 3 have constant mean curvature. The construction is based on the Pohlmeyer reduction of the related sigma model. After embedding in AdS 5 × S 5, we calculate the regularized area and analyze conserved charges. Comments on possible relations to scattering amplitudes are presented. We also sketch time-like versions of our solutions.