Parity singlets and doublets of massive spin-3 particles in D = 2 + 1 via Noether gauge embedding

  • D. DalmaziEmail author
  • E. L. Mendonça
  • A. L. R. dos Santos
Regular Article


Here we demonstrate that the sixth-order (in derivatives) spin-3 self-dual model can be obtained from the fifth-order self-dual model via a Noether Gauge Embedding (NGE) of longitudinal Weyl transformations \( \eta_{(\mu\nu} \partial_{\alpha)} \Phi\) . In the case of doublet models we can show that the massive spin-3 Singh-Hagen theory is dual to a fourth- and to a sixth-order theory, via a double round of the NGE procedure by imposing traceless longitudinal (reparametrization-like) symmetries \( \partial_{(\mu} \tilde{\xi}_{\nu\alpha)}\) in the first round and transverse Weyl transformations \( \eta_{(\mu\nu}\psi^T_{\alpha)}\) in the second one. Our procedure automatically furnishes the dual maps between the corresponding fields. Contrary to the spin-2 case where an extra (Weyl) symmetry shows up in the highest-order term, in the spin-3 case only the required symmetries by the NGE procedure appear in the sixth-order doublet model. Consequently, the absence of ghosts still demands an auxiliary scalar field.


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© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.UNESP - Campus de GuaratinguetáGuaratinguetáBrazil
  2. 2.Instituto Tecnológico de AeronáuticaSão José dos CamposBrazil

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