On spacelike and timelike minimal surfaces in $AdS_n$

Details On spacelike and timelike minimal surfaces in $AdS_n$ On spacelike and timelike minimal surfaces in $AdS_n$

2009-03-05

arxiv.org/abs/0903.0977v3

JHEP 0905:048,2009

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, typo in eq.(11) corrected

Scientific paper

10.1088/1126-6708/2009/05/048

We discuss timelike and spacelike minimal surfaces in $AdS_n$ using a Pohlmeyer type reduction. The differential equations for the reduced system are derived in a parallel treatment of both type of surfaces, with emphasis on their characteristic differences. In the timelike case we find a formulation corresponding to a complete gauge fixing of the torsion. In the spacelike case we derive three sets of equations, related to different parameterizations enforced by the Lorentzian signature of the metric in normal space. On the basis of these equations, we prove that there are no flat spacelike minimal surfaces in $AdS_n, n\geq 4$ beyond the four cusp surfaces used in the Alday-Maldacena conjecture. Furthermore, we give a parameterization of flat timelike minimal surfaces in $AdS_5$ in terms of two chiral fields.

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