We investigate in which sense, at the linearized level, one can extend the 3D topologically massive gravity theory beyond three dimensions. We show that, for each k=1,2,3... a free topologically massive gauge theory in 4k-1 dimensions can be defined
describing a massive spin-2 particle provided one uses a non-standard representation of the massive spin-2 state which makes use of a two-column Young tableau where each column is of height 2k-1. We work out the case of k=2, i.e. 7D, and show, by canonical analysis, that the model describes, unitarily, 35 massive spin-2 degrees of freedom. The issue of interactions is discussed and compared with the three-dimensional situation.
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 an
alog 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.
