Chiral Anomaly in Euler Fluid and Beltrami Flow

TL;DR

This paper reveals that the chiral anomaly, known from quantum field theories, is inherently linked to the classical fluid dynamics of Beltrami flows, leading to equilibrium electric currents.

Contribution

It demonstrates that the chiral anomaly is a fundamental aspect of classical fluid kinematics, specifically in Beltrami flows, connecting quantum anomalies with classical fluid behavior.

Findings

Beltrami flows exhibit the chiral anomaly similar to Dirac fermions.

Chiral anomaly in fluids leads to equilibrium electric currents.

The anomaly is an intrinsic property of perfect classical fluids.

Abstract

We show that the chiral anomaly of quantum field theories with Dirac fermions subject to an axial background field is an inherent property of kinematics of a perfect classical fluid. Celebrated Beltrami flows (stationary solutions of Euler equations with extensive helicity) exhibit the chiral anomaly equivalent to that known for Dirac fermions. A prominent effect of the chiral anomaly is the transport electric current at equilibrium. We show that it is also a property of Beltrami flows.