Unitarity of higher derivative spin-3 models

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.

Duality and unitarity of massive spin-3/2 models in $$D=2+1$$

“…So, in order to have a hermitian result one needs to take in account the complex global factor. 2 Similar conclusions were also obtained for the case of higher derivative massive spin-3 particles in D = 2+1 in [13].…”