Topological Casimir effect in compactified cosmic string spacetime

TL;DR

This paper studies how the topology of a cosmic string spacetime with a compact dimension affects quantum vacuum properties, revealing enhanced vacuum polarization effects and deriving formulas for the Casimir energy.

Contribution

It provides a detailed analysis of vacuum expectation values in a cosmic string spacetime with a compact dimension, including effects of topology, boundary conditions, and gauge fields.

Findings

Vacuum polarization effects are enhanced by the cosmic string topology.

A simple formula for the topological Casimir energy is derived.

Vacuum expectation values depend periodically on the gauge field component.

Abstract

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling in the generalized cosmic string geometry with a compact dimension along its axis. The boundary condition along the compactified dimension is taken in general form with an arbitrary phase. The vacuum expectation values are 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. The asymptotic behavior of the vacuum expectation values of the field squared, energy density and stresses are investigated near the string and at large distances. We show that the nontrivial topology due to the cosmic string enhances the vacuum polarization effects induced by the compactness of spatial dimension for both the field squared and the vacuum energy density. A simple formula is given for the part of the integrated topological Casimir energy induced by the planar angle deficit. The results are generalized for a charged scalar field in the presence of a constant gauge field. In this case, the vacuum expectation values are periodic functions of the component of the vector potential along the compact dimension.