In Chapter 1, we combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a formalism for computing one-loop amplitudes in dimensionally regularized Quantum Chromodynamics (QCD). We illustrate the procedure through various examples, including a next-to-leading order QCD correction to a Higgs process in the large top-quark mass limit.

In Chapter 2, we review the duality between color and kinematics and give our general procedure for extracting ultraviolet divergences in preparation for the following chapters.

In Chapter 3, we construct a form of the one-loop four-point amplitude in pure Yang-Mills, valid in any dimension, that makes the conjectured duality between color and kinematics manifest. We also describe a two-loop example. We then use these to obtain gravity integrands for a theory containing a graviton, dilaton and antisymmetric tensor, with which we study the ultraviolet structure at one and two loops.

In Chapters 4-6, we use the duality between color and kinematics to study the ultraviolet properties of half-maximal supergravity with and without matter. At one and two loops, we link cancellations to forbidden color tensors in pure Yang-Mills. Principal results for the pure theory (without matter) are the finiteness at two loops in D=5 and at three loops in D=4. These results are unexpected based on standard symmetry arguments. We also show that both cases are divergent when matter is included, which contradicts the conjectured existence of a superspace formalism used to explain the finite results in the pure theory.