Abstract
A sixth-order, but ghost-free, gauge-invariant action is found for a fourth-rank symmetric tensor potential in a three-dimensional (3D) Minkowski spacetime. It propagates two massive modes of spin 4 that are interchanged by parity and is thus a spin-4 analog of linearized ‘new massive gravity’. Also found are ghost-free spin-4 analogs of linearized ‘topologically massive gravity’ and ‘new topologically massive gravity’, of fifth and eighth order, respectively.
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