Fermionic vacuum polarization induced by a non-Abelian vortex

TL;DR

This paper investigates how a non-Abelian vortex influences fermionic vacuum polarization, revealing the effects of conical geometry, magnetic flux, and scalar coupling on fermionic condensates and energy-momentum tensor expectations.

Contribution

It introduces a detailed analysis of fermionic vacuum polarization induced by a non-Abelian vortex, considering scalar and gauge interactions, and highlights new effects related to scalar coupling ratios.

Findings

Fermionic condensate depends on magnetic flux and scalar coupling.

Vacuum energy density equals radial and axial stresses.

Different scalar coupling ratios affect fermionic and energy-momentum tensor intensities.

Abstract

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.