Relativistic Hydrodynamics with General Anomalous Charges

TL;DR

This work develops a relativistic hydrodynamic framework for gauge theories with triangle anomalies, integrating global and gauged as well as abelian and non-abelian currents, and introduces a gradient-expansion parameter $\varepsilon$ to derive leading viscous corrections. It extends Son:2009tf by providing gauge-covariant currents in the presence of external fields, and by deriving explicit anomaly-driven transport coefficients $\xi_a$, $\xi^{(B)}_{ab}$, $\tilde{\xi}$, and $\tilde{\xi}^{(B)}_a$ expressed through the symmetric anomaly tensor $C_{abc}$ with integration constants $\beta_a$ and $\gamma$. The first-order constitutive relations couple the stress-energy tensor, currents, and entropy current with viscosities, conductivities, and vorticity/magnetic-field terms, enforcing positivity of entropy production and yielding precise formulas for the anomaly-induced coefficients. The paper also discusses how dynamical gauge-field-induced non-conservation $\Phi_a$ can modify the hydrodynamic equations, arguing under controlled assumptions that the leading transport structure remains unaffected while providing a framework to include small non-conservation effects.

Abstract

We consider the hydrodynamic regime of gauge theories with general triangle anomalies, where the participating currents may be global or gauged, abelian or non-abelian. We generalize the argument of arXiv:0906.5044, and construct at the viscous order the stress-energy tensor, the charge currents and the entropy current.