Kerr worldline-QFT action from Compton amplitude to infinite spin orders

We develop a quadratic-in-Riemann worldline action for a Kerr black hole at infinite spin orders by matching to a proposed tree-level Kerr Compton amplitude, originally obtained from higher-spin QFT considerations. A worldline action is an effective theory, and as such the tree-level matching needs to be corrected by loop effects, including UV counter terms, renormalization, and higher-order matching to general relativity. However, we anticipate that many features of the Wilson coefficients of the proposed tree-level action will remain unchanged even after a loop-level matching. While the worldline action is given in closed form, it contains an infinite number of quadratic-in-Riemann operators $R^2$, even for the same-helicity sector. We argue that in the same-helicity sector the $R^2$ operators have no intrinsic meaning, as they merely remove unwanted terms produced by the linear-in-Riemann operators, which are well-established in the literature. The opposite-helicity sector is somewhat more complicated, it contains both $R^2$ operators that removes unwanted terms, and $R^2$ operators that add new needed terms to the Compton amplitude. We discuss and classify all independent $R^2$ operators that can feature in the worldline action.