On Observables in Supersymmetric Gauge Theories
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There has been great progress in recent years in the understanding of the mathematical structure of scattering amplitudes in Quantum Field Theory as well as the development of powerful methods for their calculation, particularly in the arena of N = 4 Super Yang-Mills where hidden and manifest symmetries lead to striking simplifications. In this thesis, we will discuss the extensions of such methods away from the case of on-shell amplitudes in conformal N = 4. After introducing the necessary mathematical background and physical setting, we consider in Chapter Three the form factors of BPS operators in N = 4 Super Yang- Mills. These objects have several physical applications, and share many properties with scattering amplitudes. However, they are off-shell, which makes them a natural starting point to set out in the direction of correlation functions. After demonstrating the computation of form factors by BCFW recursion and unitarity based methods, we go on to show how the scalar form factor can be supersymmetrised to encompass the full stress-tensor multiplet. In Chapter Four, we discuss the Sudakov form factor in ABJM Theory. This object, which first appears at two loops and controls the IR divergences of the theory, is computed by generalised unitarity. In particular, we note that the maximal transcendentality of three dimensional integrals is related to particular triple cuts. Finally, in Chapter Five we consider massive amplitudes on the Coulomb Branch of N = 4 at one loop. Here we find that vertex cut conditions inherited from the embedding of the theory in String Theory lead to a restricted class of massive integrals.
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