A note on linearized "New Massive Gravity" in arbitrary dimensions

By means of a triple master action we deduce here a linearized version of the "New Massive Gravity" (NMG) in arbitrary dimensions. The theory contains a 4th-order and a 2nd-order term in derivatives. The 4th-order term is invariant under a generalized Weyl symmetry. The action is formulated in terms of a traceless $η^{μν}Ω_{μνρ}=0$ mixed symmetry tensor $Ω_{μνρ}=-Ω_{μρν}$ and corresponds to the massive Fierz-Pauli action with the replacement $e_{μν}=\p^ρΩ_{μνρ}$. The linearized 3D and 4D NMG theories are recovered via the invertible maps $Ω_{μνρ} = ε_{νρ}^{\quadβ}h_{βμ} $ and $Ω_{μνρ} = ε_{νρ}^{\quad γδ}T_{[γδ]μ} $ respectively. The properties $h_{μν}=h_{νμ}$ and $T_{[[γδ]μ]}=0$ follow from the traceless restriction. The equations of motion of the linearized NMG theory can be written as zero "curvature" conditions $\p_νT_{ρμ} - \p_ρT_{νμ}=0$ in arbitrary dimensions.