Fermionic vacuum polarization induced by a non-Abelian vortex

In this paper, we analyze the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy-momentum tensor associated with an isospin-$1/2$ charged massive fermionic field induced by the presence of a $SU(2)$ 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 isospace. Due to this interaction, the FC is expressed as the sum of two contributions associated with the two different effective masses for the $\pm 1/2$ fermionic components of the isospin operator, $\tau^3/2$. 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 to 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, present 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 that the system presents.