Parity-Violating Hydrodynamics in 2+1 Dimensions

TL;DR

This work develops a comprehensive framework for first-order relativistic hydrodynamics in 2+1 dimensions with parity violation, identifying parity-odd transport coefficients such as the Hall viscosity $\tilde{\eta}$ and a dissipationless Hall term $\tilde{\sigma}$, along with thermodynamic response parameters $\tilde{\chi}_B$, $\tilde{\chi}_{\Omega}$, $\tilde{\chi}_E$, and $\tilde{\chi}_T$. By combining entropy-production constraints with linear-response analysis, the authors express the parity-odd couplings in terms of two thermodynamic functions ${\mathcal{M}_B}(T,\mu)$ and ${\mathcal{M}_\Omega}(T,\mu)$ and an additional function $f_\Omega(T)$, and show that in equilibrium $\tilde{\chi}_B=\partial P/\partial B$ and $\tilde{\chi}_{\Omega}=\partial P/\partial \Omega$, with $P$ the pressure. The paper further substantiates these results via a holographic model in AdS/CFT, demonstrating that ${\mathcal{M}_B}=\partial P/\partial B$ and ${\mathcal{M}_\Omega}=\partial P/\partial \Omega$ and yielding explicit expressions for transport coefficients such as $\tilde{\sigma}$ and $\tilde{\chi}_E$, while $\tilde{\eta}$ vanishes at leading order. Collectively, the findings provide a robust, testable framework for magnetovortical responses and anomalous Hall-type transport in 2+1D fluids, with concrete holographic predictions and a clear thermodynamic interpretation of the parity-odd sector.

Abstract

We study relativistic hydrodynamics of normal fluids in two spatial dimensions. When the microscopic theory breaks parity, extra transport coefficients appear in the hydrodynamic regime, including the Hall viscosity, and the anomalous Hall conductivity. In this work we classify all the transport coefficients in first order hydrodynamics. We then use properties of response functions and the positivity of entropy production to restrict the possible coefficients in the constitutive relations. All the parity-breaking transport coefficients are dissipationless, and some of them are related to the thermodynamic response to an external magnetic field and to vorticity. In addition, we give a holographic example of a strongly interacting relativistic fluid where the parity-violating transport coefficients are computable.