Massive and massless higher spinning particles in odd dimensions

TL;DR

This paper develops a framework for describing massive and massless higher spin particles in odd dimensions through dimensional reduction, establishing their equations of motion, geometric formulations, and consistency in curved spacetimes like (A)dS.

Contribution

It introduces a novel method to obtain massive higher spin actions in odd dimensions from massless models with extended supersymmetry, and analyzes their properties in curved backgrounds.

Findings

Dimensional reduction yields consistent massive higher spin actions in odd dimensions.

Massless limit produces higher spin multiplets with geometric field equations.

Models remain consistent on (A)dS backgrounds with nonlinear but first class gauge algebras.

Abstract

We study actions for massive bosonic particles of higher spins by dimensionally reducing an action for massless particles. For the latter we take a model with a SO(N) extended local supersymmetry on the worldline, that is known to describe massless (conformal) particles of higher spins in flat spacetimes of even dimensions. Dimensional reduction produces an action for massive spinning particles in odd dimensions. The field equations that emerge in a quantization a la Dirac are shown to be equivalent to the Fierz-Pauli ones. The massless limit generates a multiplet of massless states with higher spins, whose first quantized field equations have a geometric form with fields belonging to various types of Young tableaux. These geometric equations can be partially integrated to show their equivalence with the standard Fronsdal-Labastida equations. We covariantize our model to check whether an extension to curved spacetimes can be achieved. Restricting to (A)dS spaces, we find that the worldline gauge algebra becomes nonlinear, but remains first class. This guarantees consistency on such backgrounds. A light cone analysis confirms the presence of the expected propagating degrees of freedom. A covariant analysis is worked out explicitly for the massive case, which is seen to give rise to the Fierz-Pauli equations extended to (A)dS spaces. It is worth noting that in D=3 the massless limit of our model when N goes to infinity has the same field content of the Vasiliev's theory that accommodates each spin exactly once.