Challenges in Solving Chiral Hydrodynamics

TL;DR

This paper demonstrates that ideal chiral hydrodynamics derived from kinetic theory is inherently acausal and ill-posed, but proposes a frame choice that restores causality and properly incorporates the chiral anomaly.

Contribution

It identifies fundamental issues in ideal chiral hydrodynamics and introduces a frame choice that yields a causal, well-posed theory consistent with the chiral anomaly.

Findings

Ideal chiral hydrodynamics is acausal and ill-posed.

A different frame choice fixes causality and well-posedness.

Vorticity is constrained by the anomaly coefficient.

Abstract

We prove that ideal chiral hydrodynamics, as derived from chiral kinetic theory, is acausal and its initial-value problem is ill-posed both in the linearized case around a local equilibrium solution and also in the full nonlinear regime. Therefore, such theory cannot be used to determine how the chiral anomaly affects the hydrodynamic evolution. We show that these fundamental issues can be fixed by using different definitions (frames) for the hydrodynamic fields. This leads to a causal theory of ideal chiral hydrodynamics where the vorticity strength is constrained by the coefficient that encodes the anomaly.