Massive spin-2 particle from a rank-2 tensor

Here we obtain all possible second-order theories for a rank-2 tensor which describe a massive spin-2 particle. We start with a general second-order Lagrangian with ten real parameters. The absence of lower-spin modes and the existence of two local field redefinitions leads us to only one free parameter. The solutions are split into three one-parameter classes according to the local symmetries of the massless limit. In the class which contains the usual massive Fierz-Pauli theory, the subset of spin-1 massless symmetries is maximal. In another class where the subset of spin-0 symmetries is maximal, the massless theory is invariant under Weyl transformations and the mass term does not need to fit into the form of the Fierz-Pauli mass term. In the remaining third class neither the spin-1 nor the spin-0 symmetry is maximal and we have a new family of spin-2 massive theories. © 2013 American Physical Society.