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 Bμ1...μrI in the adjoint representation, we need the multiplet (Bμ1...μrI, Bμ1...μr-1I J, ..., BμI1...Ir, BI1... Ir+1). The usual problem of consistency of the tensor field equations is circumvented in this formulation.
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