Novel Structures in Scattering Amplitudes and Other Boundary Correlators

Abstract

In this dissertation, I discuss some novel structures found in the computation of scattering amplitudes and other boundary correlators. First, I describe the connection between singularities of planar amplitudes in N = 4 super-Yang-Mills and the boundary structure of the positive kinematic region in kinematic space. I use wall-crossing to study different compactifications of the positive kinematic region and illustrate how algebraic coordinate transformations emerge from infinite sequences of rational coordinate transformations. Second, I shift to studying the double copy, an algorithm for computing scattering amplitudes in uncolored theories, such as gravity, using planar amplitudes in colored theories, such as Yang-Mills. I extend the double copy algorithm to include higher derivative corrections in the input and output amplitudes. In particular, I develop an algorithm termed the Kawai-Lewellen-Tye bootstrap to systematically determine the space of effective field theories (EFT) that can be double-copied and study how the higher derivative operators map under the double copy. Finally, I conclude by studying how these amplitude structures generalize to boundary correlators in anti-de Sitter space (AdS). I use the differential representation, where the AdS boundary correlator is represented as a collection of (non-local) differential operators acting on a contact diagram, to generalize color-kinematics duality and certain techniques for evaluating higher loop Feynman diagrams to AdS.