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Wilson loops and gluon scattering amplitudes in the AdS/CFT correspondence

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Grosse Wiesmann, C. (2009). Wilson loops and gluon scattering amplitudes in the AdS/CFT correspondence. Diploma Thesis, Humboldt University, Berlin.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-F3EE-0
This thesis deals with different aspects of the Wilson loop operator in the AdS/CFT correspondence. In the context of the recently proposed duality between light-like polygonal Wilson loops and planar MHV gluon scattering amplitudes in N = 4 super Yang-Mills theory, we propose a regularisation of the Wilson loop in order to match off-shell scattering amplitudes. The thus regularised Wilson loop is explicitly shown to match the dual off-shell 4-gluon amplitude to 1-loop order in Feynman gauge. The leading divergent terms, related to the cusp anomalous dimension, are shown to be gauge invariant. In a second part, the properties of Wilson loops along several specific contours in Minkowski space are examined. Light-like tangents along the contour can lead to divergences. We show that while smooth curves remain finite, curves with a discontinuity in the second derivative in a point with light-like tangent are divergent. We compute these divergences and define a corresponding anomalous dimension, in analogy to the cusp anomalous dimension. Furthermore, we point out thatWilson loops with straight extended light-like segments are divergent and construct a coupling of the locally supersymmetric Wilson loop to the scalars, that makes it finite. Finally, we compute the Minkowskian rectangular Wilson loop and compare it to the Euclidean one.