On topologically massive spin-2 gauge theories beyond three dimensions

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,⋯ afreetopologicallymassivegaugetheoryin4k−1dimensionscanbedefined 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.