Dual Massive Gravity

Abstract

The linearized massive gravity in three dimensions, over any maximally symmetric background, is known to be presented in a self-dual form as a first order equation which encodes not only the massive Klein-Gordon type field equation but also the supplementary transverse-traceless conditions. We generalize this construction to higher dimensions. The appropriate dual description in d dimensions, additionally to a (non-symmetric) tensor field $h_{\mu \nu }$, involves an extra rank-(d-1) field equivalently represented by the torsion rank-3 tensor. The symmetry condition for $h_{\mu \nu }$ arises on-shell as a consequence of the field equations. The action principle of the dual theory is formulated. The focus has been made on four dimensions. Solving one of the fields in terms of the other and putting back in the action one obtains two other equivalent formulations of the theory in which the action is quadratic in derivatives. In one of these representations the theory is formulated entirely in terms of a rank-2 non-symmetric tensor $h_{\mu \nu }$. This quadratic theory is not identical to the Fierz-Pauli theory and contains the coupling between the symmetric and antisymmetric parts of $h_{\mu \nu }$. Nevertheless, the only singularity in the propagator is the same as in the Fierz-Pauli theory so that only the massive spin-2 particle is propagating. In the other representation, the theory is formulated in terms of the torsion rank-3 tensor only. We analyze the conditions which follow from the field equations and show that they restrict to 5 degrees of freedom thus producing an alternative description to the massive spin-2 particle. A generalization to higher dimensions is suggested.

14 pages; v2: modifications in Appendix, more references added

References in corpus (9)

• Resummation of Massive Gravity
• Infrared-modified gravities and massive gravitons
• Interacting Spin-2 Fields
• Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation
• The recovery of General Relativity in massive gravity via the Vainshtein mechanism
• Frame-like gauge invariant formulation for massive high spin particles
• Massive Gravity: Resolving the Puzzles
• Massive Gravity: Exorcising the Ghost
• Duality for massive spin two theories in arbitrary dimensions

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• Higher-derivative massive actions from dimensional reduction
• Massive spin-2 particle from a rank-2 tensor
• Massive "spin-2" theories in arbitrary $D\ge 3$ dimensions
• Nonuniqueness of the Fierz-Pauli mass term for a nonsymmetic tensor
• Massive spin-2 particles in a curved background via a nonsymmetric tensor
• A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields
• Dualities Among Massive, Partially Massless and Shift Symmetric Fields on (A)dS
• Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion
• Partially massless theory in three dimensions and self-dual massive gravity
• Absence of the Higuchi bound in a family of alternative linear massive spin-2 models