Scattering of spinning compact objects from a worldline EFT

We study the EFT of a spinning compact object and show that with appropriate gauge fixing, computations become amenable to worldline quantum field theory techniques. We use the resulting action to compute Compton and one-loop scattering amplitudes at fourth order in spin. By matching these amplitdes to solutions of the Teukolsky equations, we fix the values of Wilson coefficients appearing in the EFT such that it reproduces Kerr black hole scattering. We keep track of the spin supplementary condition throughout our computations and discuss alternative ways to ensure its preservation.