Azimuthal fermionic current in the cosmic string spacetime induced by a magnetic tube

TL;DR

This paper investigates how different magnetic field configurations confined in a finite-radius tube induce azimuthal fermionic currents in the spacetime around a cosmic string, revealing both flux-dependent and core-dependent effects.

Contribution

It provides a detailed analysis of the vacuum azimuthal fermionic current in cosmic string spacetime for three magnetic field configurations, including explicit wave-functions and flux dependence.

Findings

Induced current decomposes into zero-thickness and core-induced parts.

Zero-thickness part depends only on fractional magnetic flux.

Core-induced part depends on total magnetic flux and is generally non-periodic.

Abstract

In this paper, we analyze the vacuum azimuthal fermionic current induced by a magnetic field confined in a cylindrical tube of finite radius $a$, in the cosmic string spacetime. Three distinct configurations for the magnetic field are taken into account: (i) a cylindrical shell of radius $a$, (ii) a magnetic field proportional to $1/r$ and (iii) a constant magnetic field. In these three cases, the axis of the infinitely long tube of radius $a$ coincides with the cosmic string; moreover, we only develop this analysis for the region outside the tube. In order to do that, we explicitly construct the corresponding complete set of normalized wave-functions. We show that in the region outside the tube, the induced current is decomposed into a part corresponding to a zero-thickness magnetic flux in addition to a core-induced contribution. The latter presents specific form depending on the magnetic field configuration considered. The zero-thickness contribution depends only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one. As to the core-induced contribution, it depends on the total magnetic flux inside the tube, and consequently, in general, it is not a periodic function of the flux.