The Doublet Extension of Tensor Gauge Potentials and a Reassessment of the Non-Abelian Topological Mass Mechanism

A well-defined local non-Abelian gauge connection involving a rank-p gauge B-field was introduced a decade ago. This was achieved by introducing doublet groups and doublet-assembled connections that can act on a doublet of matter fields, and so, standard gauging procedures and minimal substitutions are applicable. We provide here a summarized version of this formalism. We also build up doublet-extended gauge-invariant actions for bosonic and fermionic matter fields, and discuss the appearance of novel topological quantities in these doublet-type gauge models. A partner action for higher-spin fields appears in the doublet version of the fermionic matter sector. As an application of the proposed formalism, a gauge-invariant Chern-Simons action in four dimensions is built up; a second order quadratic Yang-Mills type action can also be defined in this doublet framework, but we show that they can only be invariant under a Lie subgroup of our extended gauge symmetry. We finally carry out the task of studying the topological mass generation mechanism in the simplest model combining these actions into a non-Abelian generalization of the Cremmer-Scherk-Kalb-Ramond theory that we also show to be power-counting renormalizable.