The particle content of the Singh-Hagen model (SH) in D dimensions is revisited. We suggest a complete set of spin-projection operators acting on totally symmetric rank-3 fields. We give a general expression for the propagator and determine the coefficients of the SH model confirming previous results of the literature. Adding totally symmetric source terms we provide an unitarity analysis in D dimensions. * eliasleite@feg.unesp.br † rapsb −

Here we present the "soldering" of opposite helicity states of a spin-3 particle, in D = 2 + 1, into one parity doublet. The starting points may be either the sixth-or the fifth-order (in derivatives) spin-3 self-dual models of opposite helicities. The high number of derivatives avoids the use of auxiliary fields which has been so far an obstacle for a successful soldering procedure. The resulting doublet model is a new Lagrangian with six orders in derivatives and no auxiliary field. It may be regarded as a spin-3 analogue of the linearized "New Massive Gravity". We check its particle content via a gauge invariant and Lorentz covariant analysis of the analytic structure of the twopoint amplitude with the help of spin-3 analogues of the Barnes and Rivers projection operators. The particle content is alternatively confirmed in a specific non-covariant gauge by a decomposition in helicity variables. The soldered model is ghost free and contains two physical states as expected for a parity doublet. *

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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.

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