Fermionic vacuum polarization induced by a non-Abelian vortex

Abstract

In this paper, we analyze the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy–momentum tensor associated with an iso-spin-[Formula: see text] charged massive fermionic field induced by the presence of a [Formula: see text] vortex, taking into account the effect of the conical geometry produced by this object. We consider the vortex as an idealized topological defect, i.e. very thin, straight and carrying a magnetic flux running along its core. Besides the direct coupling of the fermionic field with the iso-vector gauge field, we also admit the coupling with the scalar sector of the non-Abelian vortex system, expressed as a vector in the three-dimensional iso-space. Due to this interaction, the FC is expressed as the sum of two contributions associated with the two different effective masses for the [Formula: see text] fermionic components of the iso-spin operator, [Formula: see text]. The VEV of the energy tensor also presents a similar structure. The vacuum energy density is equal to the radial and axial stresses. As to the azimuthal one, it is expressed in terms of the radial derivative of energy density. Regarding the magnetic flux, both the FC and the VEV of the energy–momentum tensor can be positive or negative. Another interesting consequence of the interaction with the bosonic sector, the FC and VEV of the energy–momentum tensor, presents different intensity for different values of the ratio between the scalar coupling constant and the mass of the fermionic field. This is a new feature presented by the system.