Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R¹,²

الأصل · EN

For the asymptotic string solution in AdS₃ which is represented by the AdS₃ Poincare coordinates and yields the planar multi-gluon scattering amplitude at strong coupling in arXiv:0904.0663, we express it by the AdS₄ Poincare 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.