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

TL;DR

This paper constructs a worldline action for Kerr black holes at infinite spin orders by matching to a Kerr Compton amplitude, addressing loop corrections and classifying quadratic Riemann operators.

Contribution

It introduces a closed-form worldline action for Kerr black holes at infinite spin orders, incorporating an infinite set of quadratic Riemann operators and analyzing their roles.

Findings

The worldline action matches the Kerr Compton amplitude at tree level.

In the same-helicity sector, R^2 operators only remove unwanted terms.

The opposite-helicity sector contains R^2 operators that add or remove terms.

Abstract

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.