Space-like minimal surfaces in AdS x S

TL;DR

This paper constructs a family of classical space-like string solutions in AdS_3 x S^3 with specific boundary conditions and conserved charges, using Pohlmeyer reduction, and discusses their potential relation to scattering amplitudes.

Contribution

It introduces a new four-parameter family of classical string solutions in AdS_3 x S^3 with boundary tetragon and angular momentum, based on Pohlmeyer reduction.

Findings

Calculated regularized area of solutions

Analyzed conserved charges and symmetries

Discussed potential links to scattering amplitudes

Abstract

We present a four parameter family of classical string solutions in AdS_3 x 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 x 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.