On Killing tensors and cubic vertices in higher-spin gauge theories

TL;DR

This paper reviews the use of antifield-BRST formalism to identify all local Killing tensors and classify consistent non-Abelian interactions in higher-spin gauge theories in flat spacetime.

Contribution

It provides a systematic method to compute Killing tensor fields and classifies all consistent deformations of spin-three actions under locality and Poincare invariance.

Findings

All on-shell local Killing tensor fields are computed.

All non-trivial consistent deformations of spin-three actions are classified.

Comparison with lower-spin cases highlights unique features.

Abstract

The problem of determining all consistent non-Abelian local interactions is reviewed in flat space-time. The antifield-BRST formulation of the free theory is an efficient tool to address this problem. Firstly, it allows to compute all on-shell local Killing tensor fields, which are important because of their deep relationship with higher-spin algebras. Secondly, under the sole assumptions of locality and Poincare invariance, all non-trivial consistent deformations of a sum of spin-three quadratic actions deforming the Abelian gauge algebra were determined. They are compared with lower-spin cases.