Unitarity of higher derivative spin-3 models

TL;DR

This paper investigates the unitarity of higher derivative spin-3 models in various dimensions, revealing they are only physically consistent in 2+1 dimensions, similar to the behavior observed in spin-2 models like NMG.

Contribution

It extends the analysis of unitarity from spin-2 to spin-3 models, demonstrating dimension-dependent unitarity constraints analogous to those in NMG.

Findings

Higher derivative spin-3 models are unitary only in 2+1 dimensions.

Unitarity restrictions mirror those found in spin-2 NMG models.

Models are non-unitary in higher dimensions due to massless modes.

Abstract

The fourth order in derivatives New Massive Gravity model NMG, describes a massive spin-2 particle in $D=2+1$. At the linearized level a proof of unitarity necessarily implies that the generalization to higher dimensions includes non-unitary massless spin-2 modes. The linearized version of NMG is dual to the Fierz-Pauli model FP. Here we examine the unitarity of higher derivative spin-3 models, analogues to the NMG, dual to the Singh-Hagen model SH. We find that the same kind of restriction on the dimension of the space also happens in this case, and the models are physical only in $D=2+1$.