Tensor Galileons as Lovelock theories

We construct novel Galileon interactions involving a single two-column mixed-symmetry tensor of arbitrary degree in flat spacetime of arbitrary dimensions. These vertices combine into theories that are formally analogous to the linearized Lovelock theory of Gravity. The simplest example is a cubic vertex involving a 2-form gauge field that is nontrivial in five dimensions or higher, being the analogue of the linearized Gauss-Bonnet term. We show that, except for the case of equal-length tensors, these theories are distinct from the already known p-form and tensor Galileons.

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