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

摘要

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 derivative(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 derivative((mu)(xi) over tilde (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.