Some comments on spacelike minimal surfaces with null polygonal boundaries in $AdS_m$

Details Some comments on spacelike minimal surfaces with null polygonal boundaries in $AdS_m$ Some comments on spacelike minimal surfaces with null polygonal boundaries in $AdS_m$

2009-10-06

arxiv.org/abs/0910.0934v2

JHEP 1002:013,2010

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, a note and references added, version to appear in JHEP

Scientific paper

10.1007/JHEP02(2010)013

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 $\alpha (z,\bar z)$ and $\beta (z,\bar z)$, 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.

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