
TL;DR
This paper generalizes the self-dual formulation of linearized massive gravity from three to higher dimensions, introducing dual descriptions involving tensor fields and analyzing their properties to describe massive spin-2 particles.
Contribution
It extends the dual formulation of massive gravity to higher dimensions, incorporating additional tensor fields and formulating equivalent quadratic actions, including in four dimensions.
Findings
The dual theories propagate only massive spin-2 particles.
The quadratic formulations are equivalent to the original theory.
The approach is generalized to higher dimensions.
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 , involves an extra rank-(d-1) field equivalently represented by the torsion rank-3 tensor. The symmetry condition for 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…
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