Photon propagation in space–time with a compactified spatial dimension

The one-loop effects of vacuum polarization induced by untwisted fermions in QED in a nonsimply connected space–time with topology S1×R3 are investigated. It is found that photon propagation in this system is anisotropic, appearing several massive photon modes and a superluminal transverse mode. For small compactification radius a, the superluminal velocity increases logarithmically with a. At low energies the photon masses lead to an effective confinement of the gauge fields into a (2+1)-dimensional manifold transverse to the compactified direction. The system shows a topologically induced directional superconductivity.