Non-Abelian Tensors with Consistent Interactions

We present a systematic method for constructing consistent interactions for a tensor field of an arbitrary rank in the adjoint representation of an arbitrary gauge group in any space-time dimensions. This method is inspired by the dimensional reduction of Scherk-Schwarz, modifying field strengths with certain Chern-Simons forms, together with modified tensorial gauge transformations. In order to define a consistent field strength of a r-rank tensor B_{\mu_1…\mu_r}^I in the adjoint representation, we need the multiplet (B_{\mu_1…\mu_r}^I, B_{\mu_1…\mu_{r-1}}^{I J}, …, B_\mu^{I_1…I_r}, B^{I_1… I_{r+1}}). The usual problem of consistency of the tensor field equations is circumvented in this formulation.