Vacuum polarization for compactified QED₄₊₁ in a magnetic flux background

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.