CP Violation from 5-dimensional QED

It has been shown that QED in (1+4)-dimensional space-time, with the fifth dimension compactified on a circle, leads to CP violation (CPV). Depending on fermionic boundary conditions, CPV may be either explicit (through the Scherk--Schwarz mechanism), or spontaneous (via the Hosotani mechanism). The fifth component of the gauge field acquires (at the one-loop level) a non-zero vacuum expectation value. In the presence of two fermionic fields, this leads to spontaneous CPV in the case of CP-symmetric boundary conditions. Phenomenological consequences are illustrated by a calculation of the electric dipole moment for the fermionic zero-modes