All actions for free massive higher-spin fields

TL;DR

This paper explores a unified family of actions for massive higher-spin fields in four dimensions, generalizing known models like Proca and Fierz-Pauli, and extends the framework to fermionic fields.

Contribution

It introduces a discrete family of second-order actions parametrized by spin-tensor types, unifying various approaches for massive higher-spin fields and their fermionic counterparts.

Findings

Identifies a family of actions interpolating between known formulations.

Generalizes Proca and Fierz-Pauli actions to all spins.

Extends the framework to fermionic higher-spin fields.

Abstract

Massive higher-spin states/fields appear in the effective description of various systems from hadrons and nuclei to black holes, whenever the point-particle approximation is justified, as well as in the bottom-up approaches to the quantum gravity problem. In four dimensions the actions for massive higher-spin fields utilize either the Singh-Hagen/Zinoviev set of auxiliary fields or a single chiral field, which is an $sl(2,\mathbb{C})$ spin-tensor of type $(2s,0)$, generalizing the Chalmers-Siegel approach. We show that these two actions are on the opposite ends of a discrete family of actions where the physical field is a spin-tensor of type $(s+k,s-k)$. The $(2s-1,1)$- and $(2s-2,2)$-cases generalize the Proca and the Fierz-Pauli actions, respectively, to all spins. A similar family of second-order actions exists for fermionic higher-spin fields.