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

References in corpus (4)

• Resummation of Massive Gravity
• Massive Gravity in Three Dimensions
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Dimensional reduction as a method to obtain dual theories for massive spin two in arbitray dimensions

Cited by in corpus (1)

• Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1