On-shell Methods in Three and Six Dimensions
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In the past few years, on-shell analytic methods have played a pivotal role in gauge theory calculations. Since the initial success of these methods in Standard Model physics, considerable activity has led to development and application in supersymmetric gauge theories. In particular, the maximally supersymmetric super Yang-Mills theory received much attention after the discovery of holographic dualities. Here, the spinor helicity formalism and on-shell superspace is described initially for four dimensions. The framework of general unitarity is shown to be a useful tool for calculating loop corrections of scattering amplitudes. Once the foundation is laid, application in three and six dimensions is explored. In six dimensions the case of interest is a theory with (1,1) supersymmetry which captures the dynamics of five-branes in string theory. In this setup the one-loop superamplitude with four and five external particles is calculated and checked for consistency. In three dimensions, the supersymmetric gauge theory that is supposed to describe the dynamics of M2-branes is considered. This particular theory is also related to M-theory via the holographic duality. The goal was to explore and determine the infra-red divergences of the theory. This was achieved by calculating the Sudakov form factor at two loops.
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