Vacuum polarization for compactified $QED_{4+1}$ in a magnetic flux background

TL;DR

This paper calculates one-loop quantum effects in a five-dimensional QED model with a compactified extra dimension and magnetic flux, revealing parity-breaking effects in the effective four-dimensional theory.

Contribution

It provides an exact evaluation of the vacuum polarization tensor and parity-breaking terms in a compactified higher-dimensional QED with magnetic flux.

Findings

Derived the vacuum polarization tensor in the presence of magnetic flux

Identified parity-breaking contributions in the effective 4D theory

Presented exact results for one-loop effects in a non-trivial gauge vacuum

Abstract

We evaluate one-loop effects for $QED_{4+1}$ compactified to ${\bf R}^4 \times S^1$, in a non-trivial vacuum for the gauge field, such that a non-vanishing magnetic flux is encircled along the extra dimension. We obtain the vacuum polarization tensor and evaluate the exact parity breaking term, presenting the results from the point of view of the effective 3+1 dimensional theory.