Higher-Spin Effects in Black Hole and Neutron Star Binary Dynamics: Worldline Supersymmetry beyond Minimal Coupling

The inclusion of spin effects in the binary dynamics for black holes and neutron stars is crucial for the computation of gravitational wave observables. Worldline supersymmetric models have been shown to be particularly efficient at this task up to quadratic order in spin, but progress at higher orders has been hampered by no-go theorems. In this Letter, we propose a novel approach to overcome this problem by extending the supersymmetry beyond minimal coupling. We demonstrate the potential of this approach by computing an "all-order-in-spin," "linear in curvature," manifestly supersymmetric Hamiltonian, as well as a "cubic-order-in-spin" Hamiltonian in arbitrary spacetime dimensions. In doing so, we identify a criterion that uniquely determines the Kerr geometry in terms of worldline supersymmetry. Equipped with these Hamiltonians, we demonstrate the exponentiation of three-point and Compton amplitudes using the recently proposed generalized Wilson line approach.