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Abstract:
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.
