Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions

We derive effective actions for parity-violating fluids in both $(3+1)$ and $(2+1)$ dimensions, including those with anomalies. As a corollary we confirm the most general constitutive relations for such systems derived previously using other methods. We discuss in detail connections between parity-odd transport and underlying discrete symmetries. In (3+1) dimensions we elucidate connections between anomalous transport coefficients and global anomalies, and clarify a previous puzzle concerning transports and local gravitational anomalies.