Fermionic current induced by magnetic flux in compactified cosmic string spacetime

TL;DR

This paper studies how magnetic flux and compactification of a cosmic string spacetime induce fermionic currents, providing explicit formulas and analyzing their behavior near the string and at large distances.

Contribution

It offers a comprehensive analysis of fermionic current densities in a compactified cosmic string spacetime, including new closed-form expressions and the effects of magnetic flux and boundary conditions.

Findings

The azimuthal current decomposes into uncompactified and compactification-induced parts.

The axial current arises due to compactification and quasiperiodicity, with specific flux periodicity properties.

Currents are finite on the string's axis and exhibit characteristic asymptotic behaviors.

Abstract

In this paper, we investigate the fermionic current densities induced by a magnetic flux running along the idealized cosmic string in a four-dimensional spacetime, admitting that the coordinate along the string's axis is compactified. In order to develop this investigation we construct the complete set of fermionic mode functions obeying a general quasiperiodicity condition along the compactified dimension. The vacuum expectation value of the azimuthal current density is decomposed into two parts. The first one corresponds to the uncompactified cosmic string geometry and the second one is the correction induced by the compactification. For the first part we provide a closed expression which includes various special cases previously discussed in the literature. The second part is an odd periodic function of the magnetic flux along the string axis with the period equal to the flux quantum and it is an even function of the magnetic flux enclosed by the string axis. The compactification of the cosmic string axis in combination with the quasiperiodicity condition leads to the nonzero axial current density. The latter is an even periodic function of the magnetic flux along the string axis and an odd periodic function of the magnetic flux enclosed by the string axis. The axial current density vanishes for untwisted and twisted fields in the absence of the magnetic flux enclosed by the string axis. The asymptotic behavior of the vacuum fermionic current is investigated near the string and at large distances from it. In particular, the topological part of the azimuthal current and the axial current are finite on the string's axis.