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

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 $ \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.