BRST methods for constructing quartic actions for spinning black holes

TL;DR

This paper introduces a systematic BRST-based method to construct gauge-invariant quartic interactions for higher spin fields, with applications to black hole scattering.

Contribution

It extends BRST formulations from cubic to quartic interactions, providing a unified constraint approach and explicit solutions for low-spin cases.

Findings

Derived a single constraint for gauge invariance at quartic order.

Provided explicit solutions for low-spin quartic vertices.

Applied results to black hole scattering scenarios.

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.