Effective actions for anomalous hydrodynamics

TL;DR

The paper builds an effective field theory for non-dissipative fluids that faithfully encodes quantum flavour anomalies and their impact on hydrodynamic transport. It constructs an anomalous action from transgression forms using a background gauge field and a hydrodynamic shadow field, and introduces a novel Schwinger-Keldysh cross-term to realize correct anomaly inflow and Ward identities out of equilibrium. The authors generalize the construction to all even dimensions and non-abelian symmetries, linking to equilibrium partition functions and a holographic horizon interpretation. This framework clarifies how to implement anomaly-induced transport in real-time dynamics and opens paths to exploring out-of-equilibrium anomaly phenomena in strongly coupled systems.

Abstract

We argue that an effective field theory of local fluid elements captures the constraints on hydrodynamic transport stemming from the presence of quantum anomalies in the underlying microscopic theory. Focussing on global current anomalies for an arbitrary flavour group, we derive the anomalous constitutive relations in arbitrary even dimensions. We demonstrate that our results agree with the constraints on anomaly governed transport derived hitherto using a local version of the second law of thermodynamics. The construction crucially uses the anomaly inflow mechanism and involves a novel thermofield double construction. In particular, we show that the anomalous Ward identities necessitate non-trivial interaction between the two parts of the Schwinger-Keldysh contour.

Figures (3)

• Figure 1: The heuristic picture of anomalous effective actions suggested by the Schwinger-Keldysh thermofield double construction, illustrated holographically using the eternal black hole in AdS.
• Figure 2: Illustration of the anomaly inflow mechanism. The bulk theory in ${\mathcal{M}}_{2n+1}$ is the Hall insulator theory, and on the boundary we have the physical theory with the anomaly. The Hall current $\bm{J}_{_H}$ propagates in the bulk and its inflow shows up as anomaly in the boundary theory. Coupling to the Hall insulator corrects the physical current $\bm{J}_\text{cons}$ by a Bardeen-Zumino contribution $\bm{J}_{_{BZ}}$. The consistent boundary current $\bm{J}_\text{cons}$ together with the Bardeen-Zumino term $\bm{J}_{_{BZ}}$ gives the total current $\bm{J}_\text{cov}$ which transforms covariantly.
• Figure 3: Complex time Keldysh contour for systems out of equilibrium in Schwinger-Keldysh formalism.