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

TL;DR

This paper derives a linearized form of New Massive Gravity in any dimension using a master action approach, revealing a theory with higher derivatives and generalized Weyl symmetry, connecting to Fierz-Pauli and specific tensor mappings.

Contribution

It introduces a novel linearized NMG formulation in arbitrary dimensions, employing a mixed symmetry tensor and revealing new symmetry properties and connections to known massive gravity models.

Findings

Linearized NMG formulated in arbitrary dimensions.

The theory includes a 4th-order invariant under generalized Weyl symmetry.

Equations of motion expressed as zero curvature conditions.

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 $e_{\mu\nu}=\p^{\rho}\Omega_{\mu\nu\rho}$. The linearized 3D and 4D NMG theories are recovered via the invertible maps $\Omega_{\mu\nu\rho} = \epsilon_{\nu\rho}^{\quad\beta}h_{\beta\mu} $ and $\Omega_{\mu\nu\rho} = \epsilon_{\nu\rho}^{\quad \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 $\p_{\nu}T_{\rho\mu} - \p_{\rho}T_{\nu\mu}=0$ in arbitrary dimensions.