Induced fermionic current densities by magnetic flux in higher dimensional cosmic string spacetime

TL;DR

This paper investigates how magnetic flux in higher-dimensional cosmic string spacetimes induces fermionic current densities, providing explicit expressions for various dimensions and field masses, enhancing understanding of quantum effects in such geometries.

Contribution

It derives a general fermionic propagator applicable to multiple dimensions and analyzes induced currents for both massless and massive fields in higher-dimensional cosmic string backgrounds.

Findings

Explicit formulas for induced fermionic currents in 3 and 4 dimensions for massless fields.

Results for massive fields across dimensions 2 to 5, considering cosmic string parameters.

Qualitative insights into fermionic current behavior in higher-dimensional cosmic string spacetimes.

Abstract

In this paper we analyse the vacuum fluctuations of quantum fermionic current densities, $<j^A(x)>$, induced by a magnetic flux running along the core of the conical space produced by the presence of cosmic string, in a $(1+d)-$dimensional bulk, for $2\leq d\leq 5$. In order to develop this investigation we construct an expression for the fermionic propagator, which can be applied for those different dimensions of the spacetime. Two specific analysis for the induced current densities are presented: $(i)$ for massless fields in three and four dimensions, and $(ii)$ for massive fields in all dimensions considered. In the latter specific values for the parameters which codify the presence of the cosmic string and the fractional part of the ratio of the magnetic flux by the quantum one are considered. Although being a very special situation and somewhat unnatural, the corresponding analysis of induced fermionic current densities under this circumstance may shed light on the qualitative behavior of these quantities in a more general situation.