Axion electrodynamics and nonrelativistic photons in nuclear and quark matter

We argue that the effective theory for electromagnetic fields in spatially varying meson condensations in dense nuclear and quark matter is given by the axion electrodynamics. We show that one of the helicity states of photons there has the nonrelativistic gapless dispersion relation $\omega \sim k^2$ at small momentum, while the other is gapped. This “nonrelativistic photon” may also be realized at the interface between topological and trivial insulators in condensed matter systems.