A note on higher-derivative actions for free higher-spin fields

TL;DR

This paper explores higher-derivative free higher-spin field theories, constructing new actions with various symmetries and demonstrating their relation to known conformal actions in four dimensions.

Contribution

It introduces generalized higher-derivative actions with Einstein-like, Maxwell-like, and Weyl-like symmetries, extending previous two-derivative formulations.

Findings

Constructed less-constrained Einstein-like and Maxwell-like higher-derivative actions.

Developed Weyl-like actions with constrained Weyl symmetries in a factorized form.

Identified the highest-derivative Weyl-like action with the Fradkin-Tseytlin conformal higher-spin action in four dimensions.

Abstract

Higher-derivative theories of free higher-spin fields are investigated focusing on their symmetries. Generalizing familiar two-derivative constrained formulations, we first construct less-constrained Einstein-like and Maxwell-like higher-derivative actions. Then, we construct Weyl-like actions - the actions admitting constrained Weyl symmetries - with different numbers of derivatives. They are presented in a factorized form making use of Einstein-like and Maxwell-like tensors. The last (highest-derivative) member of the hierarchy of the Weyl-like actions coincides with the Fradkin-Tseytlin conformal higher-spin action in four dimensions.