Quantization of Hydrodynamics: Rotating Superfluid and Gravitational Anomaly

Understand

We present a consistent scheme of quantization of chiral flows (flows with extensive vorticity) in ideal hydrodynamics in two dimensions.

• Chiral flows occur in rotating superfluid, rotating turbulence and also in electronic systems in the magnetic field in the regime of a fractional Hall effect.
• The quantization is based on a geometric relation of chiral flows to two-dimensional quantum gravity and is implemented by the gravitational anomaly.
• The effect of the gravitational anomaly violates the major property of classical hydrodynamics, the Helmholtz law: vortices are no longer frozen into the flow.