# Vacuum polarization in high-dimensional AdS spacetime in the presence of a cosmic string and compactified extra dimension

## TL;DR

This paper investigates vacuum polarization effects of a charged scalar field in high-dimensional anti-de Sitter space with a cosmic string and a compactified extra dimension, revealing how magnetic fluxes influence quantum vacuum properties.

## Contribution

It provides a detailed analysis of vacuum expectation values in a complex geometric setup, including the effects of compactification and magnetic fluxes, extending previous models to higher dimensions.

## Key findings

- VEVs decompose into cosmic string and compactification contributions.
- Vacuum polarization depends on the fractional magnetic flux due to Aharonov-Bohm effect.
- Compactification effects vanish as the extra dimension becomes infinite.

## Abstract

In this paper, we analyze the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a charged and massive scalar quantum field in a generalized $(D+1)$-dimensional anti-de Sitter space in the presence of a cosmic string, admitting a magnetic flux running along the string's core. In addition we admit that an extra coordinate is compactified to a circle and presents a magnetic flux running along its center. This compactification is implemented by imposing a quasiperiodic condition on the field with an arbitrary phase. The calculation of the VEVs of the field squared and the energy-moment tensor, are developed by using positive-energy Wightman function. The latter is construct by the mode sum over the complete set of normalized bosonic wavefunctions. Due to the compactification, the Wightman function is presented as the sum of two distinct contributions. The first one corresponding to the idealized cosmic string, and the second is induced by the compactification. The latter goes to zero for an infinite length of the compactification. As a consequence of the general structure of the Wightman function, both VEVs present also this decomposition. Moreover, due to the Aharanov-Bohm type of interaction between the field with the magnetic fluxes, the VEVs depend on the fractional part of the ration between the total flux and the quantum one.