Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions

TL;DR

This paper derives effective actions for parity-violating fluids with anomalies in various dimensions, confirming general constitutive relations and exploring the links between discrete symmetries, anomalies, and transport phenomena.

Contribution

It provides a unified derivation of effective actions for anomalous fluids and clarifies the relationship between anomalies, symmetries, and transport coefficients.

Findings

Confirmed the most general constitutive relations for parity-violating fluids.

Established connections between anomalous transport coefficients and global anomalies.

Clarified the role of local gravitational anomalies in transport phenomena.

Abstract

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.