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AbstractAbstract
[en] In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in N=4 super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result. We also investigate the properties of the corresponding remainder functions. Moreover, we extend on-shell diagrams, a Grassmannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of the stress-tensor supermultiplet as an example. In the second part, we study the β- and the γ_i-deformation, which were respectively shown to be the most general supersymmetric and non-supersymmetric field-theory deformations of N=4 super Yang-Mills theory that are integrable at the level of the asymptotic Bethe ansatz. For these theories, a new kind of finite-size effect occurs, which we call prewrapping and which emerges from double-trace structures that are required in the deformed Lagrangians. While the β-deformation is conformal when the double-trace couplings are at their non-trivial IR fixed points, the γ_i-deformation has running double-trace couplings without fixed points, which break conformal invariance even in the planar theory. Nevertheless, the γ_i-deformation allows for highly non-trivial field-theoretic tests of integrability at arbitrarily high loop orders.
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12 Feb 2016; 174 p; Diss. (Dr.rer.nat.)
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