Publication : t14/147

Abstract:
Abstract This thesis aims at providing better understanding of the perturbative expansion of gauge theories with and without supersymmetry. At tree level, the BCFW recursion relations are analyzed with respect to their validity for general o-shell objects in Yang-Mills theory, which is a signicant step away from their established zone of applicability. Unphysical poles constitute a new potential problem in addition to the boundary behavior issue, common to the on-shell case as well. For an innite family of massive fermion currents, both obstacles are shown to be avoided under certain conditions, which provides a natural recursion relation. At one loop, scattering amplitudes can be calculated from unitarity cuts through their expansion into known scalar integrals with free coecients. A powerful method to obtain these coecients, namely spinor integration, is discussed and rederived in a somewhat novel form. It is then used to compute analytically the in- nite series of one-loop gluon amplitudes in N = 1 super-Yang-Mills theory with exactly three negative helicities. The nal part of this thesis concerns the intriguing relationship between gluon and graviton scattering amplitudes, which involves a beautiful duality between the color and kinematic content of gauge theories. This BCJ duality is extended to include particles in the fundamental representation of the gauge group, which is shown to relieve the restriction of the BCJ construction to factorizable gravities and thus give access to amplitudes in generic (super-)gravity theories.

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