Higher derivative massive spin-3 models in D=2+1

We find new higher derivative models describing a parity doublet of massive spin-3 modes in D=2+1 dimensions. One of them is of fourth order in derivatives while the other one is of sixth order. They are complete, in the sense that they contain the auxiliary scalar field required to remove spurious degrees of freedom. Both of them are obtained through the master action technique starting with the usual (second-order) spin-3 Singh-Hagen model, which guarantees that they are ghost free. The fourth- and sixth-order terms are both invariant under (transverse) Weyl transformations, quite similarly to the fourth-order K-term of the new massive gravity. The sixth-order term slightly differs from the product of the Schouten by the Einstein tensor, both of third order in derivatives. It is also possible to write down the fourth-order term as a product of a Schouten-like by an Einstein-like tensor (both of second order in derivatives) in close analogy with the K-term.