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Here we show that in arbitrary dimensions $D\ge 3$ there are two families ofsecond order Lagrangians describing massive "spin-2" particles via anonsymmetric rank-2 tensor. They differ from the usual Fierz-Pauli theory ingeneral. At zero mass one of the families is Weyl invariant. Such masslesstheory has no particle content in $D=3$ and gives rise, via master action, to adual higher order (in derivatives) description of massive spin-2 particles in$D=3$ where both the second and the fourth order terms are Weyl invariant,contrary to the linearized New Massive Gravity. However, only the fourth orderterm is invariant under arbitrary antisymmetric shifts. Consequently, theantisymmetric part of the tensor $e_{[\mu\nu]}$ propagates at large momentum as$1/p^2$ instead of $1/p^4$. So, the same kind of obstacle for therenormalizability of the New Massive Gravity reappears in this nonsymmetrichigher order description of massive spin-2 particles.

Massive "spin-2" theories in arbitrary $D \ge 3$ dimensions