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 $S^{1}\times R^{3}$ 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.