Comments on Hall transport from effective actions

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.

19 pages. v2: added refs and comments on connections with torsion. v3: typos fixed, published version. v4: added comment on Legendre transform

References in corpus (5)

• Nonlinear Fluid Dynamics from Gravity
• Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Non-dissipative hydrodynamics: Effective actions versus entropy current
• Spontaneous Generation of Angular Momentum in Holographic Theories

Cited by in corpus (12)

• Adiabatic hydrodynamics: The eightfold way to dissipation
• Effective actions for anomalous hydrodynamics
• Effective Action for Relativistic Hydrodynamics: Fluctuations, Dissipation, and Entropy Inflow
• Phenomenology of non-relativistic parity-violating hydrodynamics in 2+1 dimensions
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Effective field theory for fluids: Hall viscosity from a Wess-Zumino-Witten term
• Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasi-particles
• Ward Identities for Hall Transport
• Parity odd equilibrium partition function in 2+1 dimensions
• Chiral Torsional Effects in Anomalous Fluids in Thermal Equilibrium
• Hall Viscosity and Angular Momentum in Gapless Holographic Models
• Torsional response of relativistic fermions in $2+1$ dimensions