Induced vacuum current and magnetic field in the background of a cosmic string

TL;DR

This paper investigates how vacuum polarization around a cosmic string induces a circulating current and magnetic field, analyzing their dependence on string properties and space dimensions, with implications for magnetic flux confinement.

Contribution

It demonstrates the induction of vacuum currents and magnetic fields in the cosmic string background, extending the analysis to higher dimensions and exploring their dependence on physical parameters.

Findings

A vacuum current circulates around the string.

A magnetic field is induced along the string.

The current and magnetic field decrease exponentially with distance.

Abstract

Vacuum polarization effects in the cosmic string background are considered. We find that a current is induced in the vacuum of the quantized massive scalar field and that the current circulates around the string which is generalized to a $(d-2)$-brane in locally flat $(d+1)$-dimensional space-time. As a consequence of the Maxwell equation, a magnetic field strength is also induced in the vacuum and is directed along the cosmic string. The dependence of the current and the field strength on the string flux and tension is comprehensively analyzed. Both the current and the field strength are holomorphic functions of the space dimension, decreasing exponentially with the distance from the string. In the case of $d=3$ we show that, due to the vacuum polarization, the cosmic string is enclosed in a tube of the magnetic flux lines if the mass of the quantized field is less than the inverse of the transverse size of the string core.