Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time

TL;DR

This paper studies how a composite topological defect in higher-dimensional space-time influences vacuum polarization effects of a massless fermion field, revealing the role of magnetic flux and conical geometry in quantum field behavior.

Contribution

It provides explicit calculations of vacuum polarization effects caused by a composite defect with magnetic flux in higher dimensions, including the impact of conical structures and flux quantization.

Findings

Vacuum energy-momentum tensor depends on fractional magnetic flux.

Effects are exponentially suppressed for large solid angle deficits.

The study extends understanding of quantum fields in complex topological backgrounds.

Abstract

We investigate the vacuum polarization effects associated with a charged massless spin-1/2 field in a higher-dimensional space-time, induced by a composite topological defect. The defect is constituted by a global monopole living on a three-brane and two-dimensional conical space transverse to the latter. In addition, we assume the presence of an extra magnetic flux along the core of the conical space. The heat kernel and the Feynman Green function are presented in the form of a sum of two terms. The first one corresponds to the contribution coming from the bulk with global monopole in the absence of conical structure of the orthogonal two-space, and the second one is induced by this structure and the magnetic flux. We explicitly evaluate the part in the vacuum expectation value of the energy-momentum tensor induced by the flux carrying conical structure. As in pure cosmic string geometries, only the fractional part of the ratio of the magnetic flux to flux quantum leads to non-trivial effects. The vacuum energy-momentum tensor is an even function of this parameter. We show that for strong gravitational fields corresponding to large values of the solid angle deficit, the effects induced by the conical structure and flux are exponentially suppressed.