The anomalous transport of axial charge: topological vs non-topological fluctuations

Axial charge imbalance is an essential ingredient in novel effects associated with chiral anomaly such as chiral magnetic effects (CME). In a non-Abelian plasma with chiral fermions, local axial charge can be generated a) by topological fluctuations which would create domains with non-zero winding number b) by conventional non-topological thermal fluctuations. We provide a holographic evaluations of medium's response to dynamically generated axial charge density in hydrodynamic limit and examine if medium's response depends on the microscopic origins of axial charge imbalance. We show a local domain with non-zero winding number would induce a non-dissipative axial current due to chiral anomaly. We illustrate holographically that a local axial charge imbalance would be damped out with the damping rate related to Chern-Simon diffusive constant. By computing chiral magnetic current in the presence of dynamically generated axial charge density, we found that the ratio of CME current over the axial charge density is independent of the origin of axial charge imbalance in low frequency and momentum limit. Finally, a stochastic hydrodynamic equation of the axial charge is formulated by including both types of fluctuations.