Effective field theory for fluids: Hall viscosity from a Wess-Zumino-Witten term

TL;DR

The paper develops an effective field theory for a relativistic fluid in (2+1) dimensions that includes Hall viscosity through a Wess-Zumino-Witten term. The authors show that the Hall viscosity contribution to the stress tensor arises as a genuine geometric response, with $\Delta T_{\mu\nu}$ proportional to $-\eta_H\, u^\alpha \varepsilon_{\alpha\beta(\mu}\, {\sigma_{\nu)}}^{\beta}$ and $\eta_H = 2\,s\,f$, where $f$ is a function of comoving variables ($n/s$ or $n'$ depending on the formulation). Using both the standard EFT with fluid scalars and Friedman's (identical-conservation) formulation, they demonstrate how a WZW term yields a Hall response that cannot be removed by field redefinitions, thereby providing a principled action-based account of Hall viscosity in (2+1)D fluids. The work highlights the constraints on $\eta_H$ (namely a homogeneous degree-one form in the comoving densities) and discusses limitations, including the potential need for Schwinger-Keldysh formalisms to capture more general or higher-dimensional anomalous transport.

Abstract

We propose an effective action that describe a relativistic fluid with Hall viscosity. The construction involves a Wess-Zumino-Witten term that exists only in (2+1) spacetime dimensions. We note that this formalism can accommodate only a Hall viscosity which is a homogeneous function of the entropy and particle number densities of degree one.