Calculation of Graviton Scattering Amplitudes using String-Based Methods

TL;DR

The paper tackles the computational bottleneck of perturbative gravity by importing string-based amplitude techniques and a supersymmetric decomposition to streamline one-loop four-graviton calculations with arbitrary loop content. It derives gravity-specific rules that reflect a double-copy relationship with gauge theories and applies them to obtain explicit helicity amplitudes, showcasing significant cancellations and reduced polynomial degrees. The authors validate their results through unitarity constraints (Cutkosky rules), demonstrating UV finiteness for external-graviton amplitudes and characteristic IR structure, thereby illustrating the practical power of string-inspired methods in gravitational perturbation theory. Overall, the work emphasizes the utility of string-based formalisms and supersymmetric organization in rendering gravity amplitude calculations more tractable and reveals consistency with established theoretical expectations.

Abstract

Techniques based upon the string organisation of amplitudes may be used to simplify field theory calculations. We apply these techniques to perturbative gravity and calculate all one-loop amplitudes for four-graviton scattering with arbitrary internal particle content. Decomposing the amplitudes into contributions arising from supersymmetric multiplets greatly simplifies these calculations. We also discuss how unitarity may be used to constrain the amplitudes.