Scattering Amplitudes in Supersymmetric Quantum Chromodynamics and Gravity

Abstract: Quantum field theory is a theoretical framework for the description of nature in terms of fundamental particles, fields and their interactions. In the quantum regime, elementary scattering processes are observables in many experiments and studied in theoretical physics. The theoretical understanding of scattering amplitudes is often based on a perturbative analysis in powers of the coupling strength of the fundamental forces. Whereas the computation of scattering amplitudes has been dominated by Feynman diagram constructions for a long time, new methods have lead to a multitude of novel results in the last 20-30 years. Thereafter discoveries of new representations, dualities and construction methods have enormously increased our understanding of the mathematical structure of scattering amplitudes.In this thesis we focus on a particular structure of gauge theory amplitudes known as the color-kinematics duality. Closely tied to this duality is the double copy construction of gravitational amplitudes, and a set of identities among basic building blocks of the gauge theory, the BCJ identities. Using methods developed for the study of this duality, we obtain new results for scattering amplitudes in non-maximal supersymmetric Yang-Mills coupled to massless fundamental matter at one and two loops. We immediately construct amplitudes in supergravity theories via the double copy. Furthermore, we include methods and results for the integration of gauge theory amplitudes and the ultraviolet structure of supergravity amplitudes.In a second part we present ideas related to the identification of basic building blocks that underlie the construction of  scattering amplitudes. A decomposition of gauge theory amplitudes into color- and kinematic-dependent contributions exposes a set of primitive objects. Relations among these objects allow us to identify a minimal set of independent kinematic building blocks.