Higher derivative massive spin-3 models inD=2+1

Abstract

We find new higher derivative models describing a parity doublet of massive spin-3 modes in D ¼ 2 þ 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 sixthorder 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.

Soldering spin-3 opposite helicities in D=2+1

“…This has indicated us that such model is the highest self-consistent description of a parity doublet of helicities +2 and −2. Analogously, we have seen here that the sixth order doublet model (20) is obtained by the generalized soldering of the fifth or sixth order self-dual models. Thus, we expect (20) to be the highest spin-3 doublet model.…”

“…Analogously, we have seen here that the sixth order doublet model (20) is obtained by the generalized soldering of the fifth or sixth order self-dual models. Thus, we expect (20) to be the highest spin-3 doublet model. Another reason to believe that the top order in derivatives is 2s again is the fact that in the master action approach, in order to derive a dual (j + 1)-th order model from a lower j-th order model it is necessary that the highest derivative term has no particle content, like a topological theory.…”

“…Replacing the currents (25) in (26) and defining the invariant combination h µνα = κf µνα − g µνα we obtain exactly the same doublet model we have found in (20).…”

Master actions for massive spin-3 particles in D = 2 + 1

“…The Fierz-Pauli conditions can be obtained from the equations of motion derived from (22), demonstrations can be found in [6,7]. By adding mixing terms without particle content we aim to construct a master action from (22).…”

“…Then we get the mixing terms decoupled. Since they have no particle content, see (11) and (12), we end up with the content of the first-order self-dual model (22). So by the derivatives with respect to the sources we find the following identity:…”