  Recently an effective Lagrangian for the interactions of photons,
Nambu-Goldstone bosons and superfluid phonons in dense quark matter has been
derived using anomaly matching arguments. In this paper we illuminate the
nature of certain anomalous terms in this Lagrangian by an explicit microscopic
calculation. We also generalize the corresponding construction to introduce the
axion field. We derive an anomalous axion effective Lagrangian describing the
interactions of axions with photons and superfluid phonons in the dense matter
background. This effective Lagrangian, among other things, implies that an
axion current will be induced in the presence of magnetic field. We speculate
that this current may be responsible for the explanation of neutron star kicks.
