Maximally Supersymmetric Theories In Light-cone Superspace

Reduced supersymmetric field theories retain a great deal of information regarding their higher-dimensional progenitors. In this dissertation, we describe how the ( N = 4, d = 4) SuperYang-Mills theory may be 'oxidized' into its parent theory, the fully ten- dimensional N = 1 Yang- Mills. Remarkably, this is achieved by adding a single term to the four-dimensional transverse space derivatives. We work in light-cone superspace which is entirely free of auxiliary fields. Very similar in structure to ( N = 4, d = 4) Yang-Mills is the maximally supersymmetric ( N = 8, d = 4) Supergravity. This theory is obtained by reduction from eleven-dimensional N = 1 Supergravity. We show that this four-dimensional Supergravity theory may be restored to eleven dimensions in a very similar fashion