Scattering and Gravitational Effective Field Theory

Citation

Shah, Nabha Niranjan (2024) Scattering and Gravitational Effective Field Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/z5r7-rr17. https://resolver.caltech.edu/CaltechTHESIS:06042024-060925080

Abstract

Advances in the methodologies developed in quantum field theory and in the scattering amplitudes program have led to their application to questions pertaining to the classical physics of gravitationally interacting binary systems. The perturbative and relativistic nature of the quantum field theoretic setup is perfectly suited for obtaining results in an expansion in the gravitational constant, also known as the post-Minkowskian (PM) expansion. However, there are several practical scenarios where the gravitational waves produced by the inspiral or interaction of two massive bodies arise from dynamics in the strong field regime and the PM expansion breaks down. Extreme mass ratio inspirals, where a lighter body interacts with a much heavier black hole, are examples of such systems.

In contrast, classical solutions, such as the Schwarzschild metric, and the geodesic trajectories of test bodies traversing in these nontrivial backgrounds encode information to all orders in the gravitational constant. In fact, these solutions can be viewed as the summation of certain infinite sets of Feynman diagrams from the perspective of point particle effective field theory (EFT). Alternatively, metrics and related geodesic trajectories can be seen as performing enormous simplifications of the tensor structures arising in these equivalent sets of Feynman integrals. We describe how the all order in PM information present in classical solutions can be utilized to simplify PM calculations in point particle EFT and set up a systematic framework for studying the classical dynamics of binary systems as an expansion in their mass ratio.

We also delve into questions about the origin and scope of validity of color-kinematics duality and the double copy relation, which can be used to generate amplitudes of one theory from another. For example, graviton amplitudes can be obtained from gluon amplitudes. Unveiling the underlying structure that gives rise to these relations would not only deepen our understanding of the properties of these theories but could also serve in streamlining their application to computations of practical interest such as those showing up in the study of the gravitational two-body problem using field theory techniques. Specifically, we analyze a toy system in two dimensions where we find a Lagrangian-level manifestation of the duality in a classical equivalent of the nonlinear sigma model. We unpack the implications of an off-shell formulation of the color-kinematics duality and double copy in order to understand the possible wider implications for these relations in other theories.

Thesis Files