Abstract
We use the string sigma model action in AdS5×S5 to reconstruct the open string solution ending on the Wilson loop in S3×R parametrized by a geometric angle in S3 and an angle in flavor space. Under the interchange of the world sheet space and time coordinates and the T-duality transformation with the radial inversion, the static open string configuration associated with the BPS Wilson loop with two equal angle parameters becomes a long open spinning string configuration which is produced by taking the special limit of equal two frequencies for the folded spinning closed string with two spins in AdS5×S5.
Highlights
IntroductionThrough the T-duality along the boundary directions of Lorentzian AdS5 in the Poincare coordinates together with the radial inversion z → 1/z [32, 33, 34] and the interchange of space and time coordinates of the Minkowski world sheet, the world sheet of small closed string is related with the open string surface ending on wavy line representing small-velocity “quark” trajectory at the boundary
The AdS/CFT correspondence [1] has more and more revealed the deep relations between the N = 4 super Yang-Mills (SYM) theory and the string theory in AdS5 × S5
The lower supersymmetric Wilson loops on a two-sphere S2 embedded into the R4 spacetime have been analyzed by finding the corresponding open string solutions as well as by reducing a purely perturbative calculation in the soluble bosonic 2d Yang-Mills on the sphere [14, 15, 16, 17]
Summary
Through the T-duality along the boundary directions of Lorentzian AdS5 in the Poincare coordinates together with the radial inversion z → 1/z [32, 33, 34] and the interchange of space and time coordinates of the Minkowski world sheet, the world sheet of small closed string is related with the open string surface ending on wavy line representing small-velocity “quark” trajectory at the boundary. This open string solution corresponds to the small-wave open string solution in [35] which ends on a time-like near BPS Wilson loop differing by small fluctuations from a straight line.
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