Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly

The chiral anomaly of massless fermions at zero temperature defines arelativistic quantum superfluid. The anomaly implies correlated fermion/anti-fermion pair excitations of the Fermi-Dirac sea that propagate as gapless Chiral Density Waves (CDWs), i.e. an axion-like acoustic mode. This collective boson is a U(1) chiral phase field which is gapless as a result of a novel and non-trivial realization of Goldstone?s theorem extended to the case of anomalous symmetry breaking. In QED_4 this collective Goldstone mode appears as a massless pole in the axial anomaly triangle diagram, and is responsible for the macroscopic non-dissipative currents of the Chiral Magnetic and Chiral Separation Effects. The effect of electromagnetic interactions, finite fermion mass and possible realizations in Weyl materials will be briefly discussed.