Effective field theory for hydrodynamics: Wess-Zumino term and anomalies in two spacetime dimensions

TL;DR

This paper constructs a non-dissipative EFT for relativistic fluids in $(1+1)$ dimensions that incorporates quantum anomalies through a Wess-Zumino term added to the fluid Lagrangian. The authors derive the modified constitutive relations, show that the anomaly produces a novel propagating mode (the one-and-a-halfth sound) even without external fields, and verify the results with a standard hydrodynamic derivation. They also discuss unitarity- and CPT-based bounds on the anomaly coefficient and explore the implications for generalizations to higher dimensions and topology. Overall, the work provides a field-theoretic, anomaly-aware framework for hydrodynamics in low dimensions with clear predictions for the spectrum and transport corrections, potentially informing condensed-matter realizations and guiding extensions to more realistic, higher-dimensional settings.

Abstract

We develop the formalism that incorporates quantum anomalies in the effective field theory of non-dissipative fluids. We consider the effect of adding a Wess-Zumino-like term to the low-energy effective action to account for anomalies. In this paper we restrict to two spacetime dimensions. We find modifications to the constitutive relations for the current and the stress-energy tensor, and, more interestingly, half a new propagating mode (one-and-a-halfth sound): a left- or right-moving wave with propagation speed that goes to zero with the anomaly coefficient. Unlike for the chiral magnetic wave in four dimensions, this mode propagates even in the absence of external fields. We check our results against a more standard, purely hydrodynamical derivation. Unitarity of the effective field theory suggests an upper bound on the anomaly coefficient in hydrodynamics.