Notes on chiral hydrodynamics within effective theory approach

TL;DR

The paper develops an effective-field-theory framework for chiral hydrodynamics with chemical potentials $\mu$ and $\mu_5$, showing that the leading $\mu^2$-dependent contributions to chiral transport (e.g., via vorticity $\omega^\mu$ and magnetic field $B^\mu$) are fixed by the chiral anomaly and agree with thermodynamic analyses. However, higher-order terms (notably $\mu^3$) generically depend on infrared regularization, leading to discrepancies with purely thermodynamic results unless additional hydrodynamic assumptions are imposed. The work discusses how anomalies can be realized in the hydrodynamic regime through effective theory, and proposes the idea of hydrodynamic bosonic excitations (a hydrodynamic pion) saturating the anomaly, with potential two-component or superfluid-like behavior. Overall, the study highlights IR sensitivity in higher-order transport coefficients and frames relativistic hydrodynamics as a context where chiral symmetries can be realized and matched in novel ways, possibly even above the deconfinement transition.

Abstract

We address the issue of evaluating chiral effects (such as the newly discovered chiral separation) in hydrodynamic approximation. The main tool we use is effective theory which defines interaction in terms of chemical potentials $μ,μ_5$. In the lowest order in $μ,μ_5$ we reproduce recent results based on thermodynamic considerations. In higher orders the results depend on details of infrared cutoff. Another point of our interest is an alternative way of the anomaly matching through introduction of effective scalar fields arising in the hydrodynamic approximation.