Unitarity of Singh-Hagen Model in D Dimensions

Abstract

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 −

New class of ghost- and tachyon-free metric affine gravities

“…For a three-index tensor that is antisymmetric in one pair of indices, the spin projectors were given in [28,43]. The spin projectors for totally symmetric three-tensors have been given also in [44]. To the best of our knowledge, the spin projectors for a general three-index tensor have not been given in the literature.…”

Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories

“…Having recognized the relevance of lagrangian theories with multiple fields entangled in quadratic mixing, we recap now the efficient approach based on projector operators [11,15,[19][20][21][22][23][24][25] to assess the nature of their particle spectrum. In what follows we will, when stating general properties of the action, hide the index structure and consider a index-less superfield formalism as in Φ = {φ µνρ , φ µν , φ µ , φ}, considering field contractions in the intuitive form…”

“…which describe completeness of the projectors, orthogonality and hermitianicity of the operators 4 . The task of computing the explicit form of these operators, for the set of rank-2 and rank-3 fields has been only recently completed [15,19]. This paper's original contribution is to provide the missing operators to study the mixing between all the fields up to rank-3, including the scalar-tensor and vector-tensor transition operators.…”

“…The latter case is paradigmatic of the use of many different fields with quadratic mixing and simultaneous transformation under gauge symmetry. It has received an increasing attention in the last years and has required the computation of projectors operators up to spin-3, an operation fully completed only recently [15,19]. When moving to higher-spin the simultaneous presence of many fields, possibly in an auxiliary role, is mandatory to provide the propagation of the wanted states.…”

“…More promising, similarly to case of the non-linear sigma model, symmetries might help constraining the form of the UV terms and provide predictive models. Surprisingly, while geometric theories of gravity have attracted most of the use of the method in question, almost none attention has been turned towards Lorentz invariant higher-spin propagation involving multiple fields, one notable exception being the study of Singh model in [19]. A possible reason to justify such lacking can be tracked to the missing operators needed to express the mixing terms involving all the fields.…”