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) electricand 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.

Effective theories and non-minimal couplings in low-dimensional systems

“…Our motivation is based on a line of works in the literature in which a higher-dimensional scenario plays an important role in the description of the reduced system. For instance, we mention the theoretical proposal of the topological superconductor [42]; a possible dark sector from five-dimensional Electrodynamics coupled to 3-form gauge field [43]; new interactions and spin-dependent contributions introduced through dimensional reduction [44,45] and effects of boundary conditions on reduced field theories [46]. Within this point of view, we consider a fermionic field non-minimally coupled to an external electromagnetic field.…”

The bosonized version of the Schwinger model in four dimensions: A blueprint for confinement?

“…with α = − 1 48 and β = σ 6 , where the parameter β has mass dimension. This model was considered in [25], and the main motivation to consider this model is based on the possible connection with dark energy. However, we shall start from the five-dimensional spacetime model…”

“…with the additional presence of a mass term m C for the Abelian 3-form field; this explicit mass term makes a difference: if it were not introduced, the model could be reduced to nothing but a Proca-type model in (4 + 1) dimensions. Next, we perform its dimensional reduction along the lines of [25,26]:…”

Topologically massive spin-1 particles and spin-dependent potentials

“…A massive spin-1 particle can also be described through a gauge-invariant formulation: a vector and a tensor fields connected by a mixing topological mass term [27]. Both the vector A μ and the tensor B μν are gauge fields described by the following Lagrangean:…”

“…The Proca vector field transforms under the 1 2 , 1 2 -representation of the Lorentz group and its Lagrangean is the simplest extension leading to a massive intermediate vector boson, but it is not the only one. A massive spin-1 particle can also be described through a gaugeinvariant formulation: a vector and a tensor fields connected by a mixing topological mass term [23]. Both the vector A µ and the tensor B µν are gauge fields described by the following Lagrangean:…”