Vacuum Polarization of Twisted Scalars in a Non-simply Connected Space-time and Its Effects

The vacuum polarization the due to twisted scalar fields is investigated in a non-simply connected space-time. It is found that some photon modes acquire an imaginary topological mass, thus traveling at a superluminal speed. Topological bi-refringence is expected for photons propagating perpendicularly to the compactification direction. The effect of a topological photon mass on the static properties of electromagnetic fields is also considered for the cases of both twisted and untwisted scalar fields. Our result shows that in the untwisted case the magnetic field is screened along the radial direction for massive photon modes while in the twisted case no screening occurs and the magnetic fields merely oscillate.