Scattering Amplitudes and QFT Insight (Final Scientific Report)
The calculation of scattering amplitudes provides an invariant window into the physical dynamic content of relativistic quantum field theory. Yet with traditional methods, for empirically relevant theories, these calculations scale with a factorial complexity in external particles and precision. If we aspire to collapse the theoretical uncertainty obscuring new physics hidden at all scales from the microscopic probed at high energy colliders to the largest effective field theory in the universe governing the evolution of large scale structure, this complexity challenge necessitates new ideas and methods in calculation. Novel approaches like the color-kinematics duality and the associated double-copy construction have drastically simplified the situation, relating both gauge and gravity theory predictions to a much smaller kernel of invariant kinematic data. This project supporting research by the PI's Amplitudes and Insights group at Northwestern University looked to push insight deep into both the IR and the UV by establishing how novel structures must constrain the predictions of counterterms in both gauge and gravity theories, setting the groundwork to exploring the high energy behavior of particular gravity theories via constituent gauge-theory calculations, and confronting fundamental challenges at the interface between QFT amplitudes analysis and next generation gravitational wave science as well as well as inflationary and large scale structure cosmology.