Comments on Hall transport from effective actions

TL;DR

This paper investigates parity-odd transport phenomena in 2+1D charged fluids, deriving a specific class of non-dissipative fluids from an effective action and analyzing their Hall viscosity and conductivity.

Contribution

It identifies a two-parameter family of non-dissipative fluids derivable from an effective action, contrasting with a four-parameter family from entropy analysis, and links transport coefficients to thermodynamic functions.

Findings

Hall viscosity is predicted to vanish.

Hall conductivity is generally non-zero and depends on thermodynamic data.

Effective action approach clarifies the structure of non-dissipative fluids.

Abstract

We consider parity-odd transport in 2+1 dimensional charged fluids restricting attention to the class of non-dissipative fluids. We show that there is a two parameter family of such non-dissipative fluids which can be derived from an effective action, in contradistinction with a four parameter family that can be derived from an entropy current analysis. The effective action approach allows us to extract the adiabatic transport data, in particular the Hall viscosity and Hall conductivity amongst others, in terms of the thermodynamic functions that enter as 'coupling constants'. Curiously, we find that Hall viscosity is forced to vanish, whilst the Hall conductivity is generically a non-vanishing function of thermodynamic data determined in terms of the hydrodynamic couplings.