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

Abstract

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 $e_{μν}=\p^ρΩ_{μνρ}$. The linearized 3D and 4D NMG theories are recovered via the invertible maps ${\Omega }_{\mu \nu \rho }={\epsilon }_{\nu \rho }^{\beta }{h}_{\beta \mu }$ and ${\Omega }_{\mu \nu \rho }={\epsilon }_{\nu \rho }^{\gamma \delta }{T}_{[\gamma \delta ]\mu }$ 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 $\p_νT_{ρμ} - \p_ρT_{νμ}=0$ in arbitrary dimensions.

15 pages, no figures, few typos fixed, one more reference

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Cited by in corpus (10)

• Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space
• Thin-Shells and Thin-Shell Wormholes in New Massive Gravity
• A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields
• Interparticle potential energy for D-dimensional electromagnetic models from the corresponding scalar ones
• Master actions for massive spin-3 particles in D=2+1
• Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1
• Simple prescription for computing the nonrelativistic interparticle potential energy related to dual models
• Hamiltonian analysis and positivity of a new massive spin-2 model
• Duality as a Method to Derive a Gauge Invariant Massive Electrodynamics and New Interactions
• First Order Actions for New Massive Dual Gravities