Non-Abelian Tensors with Consistent Interactions

Abstract

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_{μ_1...μ_r}^I in the adjoint representation, we need the multiplet (B_{μ_1...μ_r}^I, B_{μ_1...μ_{r-1}}^{I J}, ..., B_μ^{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.