Duality and unitarity of massive spin-3/2 models in $$D=2+1$$ D = 2
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Duality and unitarity of massive spin-3/2 models in D =2+1 E. L. Mendonçaa
, H. L. de Oliveira b , P. H. F. Nogueirac
UNESP - Campus de Guaratinguetá - DFQ, Av. Dr. Ariberto Pereira da Cunha, 333, Guaratinguetá, SP CEP 12516-410, Brazil Received: 12 May 2020 / Accepted: 5 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we provide a triple master action interpolating among three self-dual descriptions of massive spin-3/2 particles in D = 2 + 1 dimensions. Such result generalizes a master action previously suggested in the literature. We also show that, surprisingly a shorthand notation in terms of differential operators applied in the bosonic cases of spins 2 and 3 can also be defined to the fermionic case. With the help of projection operators, we have also obtained the propagator and analyzed unitarity in D dimensions of a second-order spin-3/2 doublet model. Once we demonstrate that this doublet model is free of ghosts, we provide a master action interpolating such model with a fourth-order theory which has several similarities with the spin-2 linearized New Massive Gravity theory.
1 Introduction The seminal work by Deser et al. [1] provides a dynamically and topologically nontrivial theory for gravity in three dimensions. The model describes a single massive spin-2 excitation, and even being of third order in derivatives it is free of ghosts. It is usually called the Topologically Massive Gravity TMG. It is remarkable that in the linearized level one can demonstrate that, through the generalized soldering procedure [2] one can joint opposite helicities + 2 and − 2 in a unique doublet model, which consists of the linearized version of the so-called New Massive Gravity NMG [3]. Supersymetric extensions of TMG and NMG also exists [4] and the fermionic actions are closely related to the bosonic ones regarding their invariances and order in derivatives. The introduction of a field strength f μ (ψ) = μνα ∂ ν ψ α , where ψ α is a two component Majorana vector-spinor, allow us the use of the dynamically trivial first-order Chern–Simons like term, which is called the Rarita–Schwinger term μνα ψ¯ μ ∂ ν ψ α in three dimensions. One can demonstrate that, starting with the first order in derivatives model suggested in [5] one can interpolate it with a second-order model given by [6]. Such procedure is possible thanks to the construction of a master action. Here, we suggest a generalization of such master action, which consists of a triple master action, interpolating the first two models with a third order
a e-mail: [email protected] (corresponding author) b e-mail: [email protected] c e-mail: [email protected]
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in derivatives model also describing the single massive spin-3/2 particle in D = 2 + 1. This third-order action is precisely the fermionic part of the suspersymetric extension of TMG obtained by [4]. Those models describing single exci
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