Generalized Wilson lines and the gravitational scattering of spinning bodies

Abstract

A generalization of Wilson line operators at subleading power in the soft expansion has been recently introduced as an efficient building block of gravitational scattering amplitudes for non-spinning objects. The classical limit in this picture corresponds to the strict Regge limit, where the Post-Minkowskian (PM) expansion corresponds to the soft expansion, interpreted as a sum over correlations of soft emissions. Building on the well-studied worldline model with ${\cal N}=1$ supersymmetry, in this work we extend the generalized Wilson line (GWL) approach to the case of spinning gravitating bodies. Specifically, at the quantum level we derive from first-principles a representation for the spin $1/2$ GWL that is relevant for the all-order factorization of next-to-soft gravitons with fermionic matter, thus generalizing the exponentiation of single-emission next-to-soft theorems. At the classical level, we identity the suitable generalization of Wilson line operators that enables the generation of classical spin observables at linear order in spin. Thanks to the crucial role played by the soft expansion, the map from Grassmann variables to classical spin is manifest. We also comment on the relation between the GWL approach and the Worldline Quantum Field Theory as well as the Heavy Mass Effective Theory formalism. We validate the approach by rederiving known results in the conservative sector at 2PM order.