A 3-form gauge potential in 5D in connection with a possible dark sector of 4D-electrodynamics

Abstract

We here propose a 5-dimensional Abelian gauge model based on the mixing between a U(1) potential and an Abelian 3-form field by means of a topological mass term. An extended covariant derivative is introduced to minimally couple a Dirac field to the U(1) potential, while this same covariant derivative non-minimally couples the 3-form field to the charged fermion. A number of properties are discussed in 5D; in particular, the appearance of a topological fermionic current. A 4-dimensional reduced version of the model is investigated and, in addition to the U(1) electric- and magnetic-sort of fields, there emerges an extra set of electric- and magnetic-like fields which contribute a negative pressure and may be identified as a possible fraction of dark energy. The role of the topological fermionic current is also contemplated upon dimensional reduction from 5D to 4D. Other issues we present in 4 space-time dimensions are the emergence of a pseudo-scalar massive particle, an extra massive neutral gauge boson, which we interpret as a kind of paraphoton, and the calculation of spin- and velocity-dependent interparticle potentials associated to the exchange of the intermediate bosonic fields of the model.