Comments on Hall transport from effective actions

TL;DR

This paper investigates parity-odd transport in 2+1 dimensional charged fluids under non-dissipative constraints, comparing an effective action formulation with entropy-current analyses. It shows that the effective action yields a two-parameter family of non-dissipative fluids, with Hall conductivity generally nonzero but Hall viscosity vanishing, while the entropy-current approach allows a four-parameter family. The results demonstrate that the effective action imposes stronger constraints than the second-law framework and clarifies how Hall transport data is encoded in thermodynamic conjugates to background vorticity and magnetic field. The work also discusses potential extensions, such as torsion, and the puzzling absence of Hall viscosity in this approach.

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.