Some comments on spacelike minimal surfaces with null polygonal boundaries in AdS m

Abstract

We discuss some geometrical issues related to spacelike minimal surfaces in AdS m with null polygonal boundaries at conformal infinity. In particular for AdS 4, two holomorphic input functions for the Pohlmeyer reduced system are identified. This system contains two coupled differential equations for two functions $ \alpha \left( {z,\bar z} \right) $ and $ \beta \left( {z,\bar z} \right) $ , related to curvature and torsion of the surface. Furthermore, we conjecture that, for a polynomial choice of the two holomorphic functions, the relative positions of their zeros encode the conformal invariant data of the boundary null 2n-gon.