Challenges in Solving Chiral Hydrodynamics

Understand

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.