  The effects of anomalies in high density QCD are striking. We consider a
direct application of one of these effects, namely topological currents, on the
physics of neutron stars. All the elements required for topological currents
are present in neutron stars: degenerate matter, large magnetic fields, and
P-parity violating processes. These conditions lead to the creation of vector
currents capable of carrying momentum and inducing magnetic fields. We estimate
the size of these currents for many representative states of dense matter in
the neutron star and argue that they could be responsible for the large proper
motion of neutron stars (kicks), the toroidal magnetic field and finite
magnetic helicity needed for stability of the poloidal field, and the
resolution of the conflict between type-II superconductivity and precession.
Though these observational effects appear unrelated, they likely originate from
the same physics -- they are all P-odd phenomena that stem from a topological
current generated by parity violation.
