Quantum anomalies in dense matter

We consider the effects of quantum anomalies involving the baryon current for high-density matter. In the effective Lagrangian, the anomaly terms describe the interaction of three light fields: the electromagnetic photons $A_{\mu }$, neutral light Nambu-Goldstone bosons ($\pi$, $\eta$, ${\eta }^{\prime }$), and the superfluid phonon. The anomaly induced interactions lead to a number of interesting phenomena which may have phenomenological consequences observable in neutron stars.