Abstract
For the asymptotic string solution in AdS3 which is represented by the AdS3 Poincaré coordinates and yields the planar multi-gluon scattering amplitude at strong coupling in arXiv:0904.0663, we express it by the AdS4 Poincaré coordinates and demonstrate that the hexagonal and octagonal Wilson loops surrounding the string surfaces take closed contours consisting of null vectors in R1,2 owing to the relations of Stokes matrices. For the tetragonal Wilson loop we construct a string solution characterized by two parameters by solving the auxiliary linear problems and demanding a reality condition, and analyze the asymptotic behavior of the solution in R1,2. The freedoms of two parameters are related with some conformal SO(2,4) transformations.
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