Causal and stable first-order chiral hydrodynamics

TL;DR

This paper establishes the necessary and sufficient conditions for causality and stability in first-order relativistic chiral hydrodynamics, providing a foundational framework for consistent viscous chiral fluid theories.

Contribution

It derives the first comprehensive set of inequalities ensuring causality and stability in viscous chiral hydrodynamics, applicable to generic hydrodynamic frames.

Findings

Causality requires absence of vorticity-induced heat flux.

The inequalities define a hypervolume of consistent transport parameters.

Causality depends on three key combinations of parameters.

Abstract

We derive the set of inequalities that is necessary and sufficient for nonlinear causality and linear stability of first-order relativistic hydrodynamics with either a $U(1)_V$ conserved current or a $U(1)_A$ current with a chiral anomaly or both. Our results apply to generic hydrodynamic frames in which no relations among the transport parameters are imposed. Furthermore, our analysis yields, to the best of our knowledge, the first theory of viscous chiral hydrodynamics proven to be causal and stable. We find that causality demands the absence of vorticity-induced heat flux, forcing a departure from the thermodynamic frame in the chiral case. The inequalities for causality and stability define a hypervolume in the space of transport parameters, wherein each point corresponds to a consistent formulation. Notably, causality is determined by just three combinations of transport parameters. We present our results in a form amenable to numerical hydrodynamic simulations.