A 6th-order, but ghost-free, gauge-invariant action is found for a 4th-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 5th- and 8th-order respectively.
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