A spin-4 analog of 3D massive gravity

TL;DR

This paper introduces a ghost-free, gauge-invariant higher-order action in 3D for a spin-4 field, propagating massive modes and extending concepts from massive gravity theories to higher spins.

Contribution

It presents the first 6th-order, ghost-free, gauge-invariant action for a spin-4 field in 3D, extending massive gravity models to higher spins with new topologically massive analogs.

Findings

Propagates two parity-interchanged massive spin-4 modes.

Provides ghost-free higher-order actions for spin-4 and topologically massive analogs.

Extends the framework of massive gravity to higher-spin fields.

Abstract

A 6th-order, but ghost-free, gauge-invariant action is found for a 4th-rank symmetric tensor potential in a three-dimensional (3D) Minkowski spacetime. It propagates two massive modes of spin 4 that are interchanged by parity, and is thus a spin-4 analog of linearized "new massive gravity". Also found are ghost-free spin-4 analogs of linearized "topologically massive gravity" and "new topologically massive gravity", of 5th- and 8th-order respectively.