Eur. Phys. J. Plus (2019) 134: 387
https://doi.org/10.1140/epjp/i2019-12762-3

Regular Article

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

¹ UNESP - Campus de Guaratinguetá, DFQ CEP 12516-410, Guaratinguetá, SP, Brazil
² Instituto Tecnológico de Aeronáutica, DCTA CEP 12228-900, São José dos Campos, SP, Brazil

^* e-mail: denis.dalmazi@unesp.br

Received: 9 January 2019
Accepted: 15 May 2019
Published online: 12 August 2019

Abstract

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 . 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 in the first round and transverse Weyl transformations 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.