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 eta(mu nu)Omega(mu nu rho) = 0 mixed symmetry tensor Omega(mu nu rho) = -Omega(mu rho nu) and corresponds to the massive Fierz-Pauli action with the replacement e(mu nu) = partial derivative(rho)Omega(mu nu rho). The linearized 3D and 4D NMG theories are recovered via the invertible maps Omega(mu nu rho) = epsilon(beta)(nu rho)h(beta mu) and Omega mu nu rho = epsilon T-gamma delta(nu rho)[gamma delta]mu respectively. The properties h(mu nu) = h(nu mu) and T-[[gamma delta]mu] = 0 follow from the traceless restriction. The equations of motion of the linearized NMG theory can be written as zero "curvature'' conditions partial derivative T-nu(rho mu) - partial derivative T-rho(nu mu) = 0 in arbitrary dimensions. DOI: 10.1103/PhysRevD.87.085021