  Parity violating superconductors can support a low-dimension local
interaction that becomes, upon condensation, a purely spatial Chern-Simons
term. Solutions to the resulting generalized London equations can be obtained
from solutions of the ordinary London equations with a complex penetration
depth, and suggest several remarkable physical phenomena. The problem of flux
exclusion by a sphere brings in an anapole moment, the problem of
current-carrying wires brings in an azimuthal magnetic field, and the problem
of vortices brings in currents along the vortices. We demonstrate that
interactions of this kind, together with a conceptually related dimensionally
reduced Chern-Simons interaction, can arise from physically plausible
microscopic interactions.
