BRST methods for constructing quartic actions for spinning black holes

TL;DR

The paper develops a BRST-based framework to construct gauge-invariant quartic interactions between reducible massive and massless higher-spin fields, with the aim of modeling Kerr black hole scattering in a Post Minkowskian setting. Starting from BRST-invariant cubic vertices, it derives defining equations for off-shell quartic vertices (W, U, X) that enforce gauge invariance and associativity at order $g^2$, and shows that a formal nonlocal solution exists while local solutions arise in specific low-spin cases. It then specializes to on-shell vertices, yielding simplified equations and demonstrating the existence of local on-shell quartic vertices in a spin-1 1-1-2 setup when the cubic-graviton coupling is suitably fixed (ratio $g_2/g=1$). The work provides explicit off-shell results for the 1-1-1 quartic vertex and analyzes locality conditions, offering a path toward higher-spin quartic interactions relevant for black-hole physics and potential numerical implementations. Overall, the BRST construction links cubic and quartic interactions in a gauge-consistent way and maps out when locality can be maintained in physically interesting configurations.

Abstract

We develop a systematic approach to the computation of gauge invariant quartic interactions between reducible massive and massless higher spin fields. Extending the BRST formulation of existing cubic results, we obtain a single constraint for each off-shell quartic vertex that ensures both the gauge invariance of the Lagrangian and associativity of the gauge transformations at quartic order. A solution to these equations is presented. The general equation is then reduced to an on-shell version to reduce complexity. We find example solutions for the off-shell and on-shell quartic vertices in low spin examples relevant to the problem of black hole scattering.