Leading order magnetic field dependence of conductivities in anomalous hydrodynamics

Abstract

We show that literature results claimed for the magnetic field dependence of the longitudinal conductivity in anomalous first-order hydrodynamics are frame dependent at this derivative order. In particular, we focus on $(3+1)$-dimensional hydrodynamics in the presence of a constant $\mathcal{O}(\partial )$ magnetic field with a $U(1)$ chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. In particular, magnetic field dependent terms that were previously found in the literature only enter the non-zero frequency thermoelectric conductivities through explicitly frame dependent pieces indicating that they are not physical. This issue can be avoided entirely by incorporating the magnetic field into the fluid's equilibrium state.

V2: Several Clarifications added, title changed, Version to appear on Physical review D

References in corpus (6)

• Gravitational Anomaly and Transport
• Chiral Magnetic conductivity
• Chiral anomaly and local polarization effect from quantum kinetic approach
• Relativistic Hydrodynamics with General Anomalous Charges
• Chiral hydrodynamics in strong external magnetic fields
• Temperature in relativistic fluids

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• Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory
• Restoring time-reversal covariance in relaxed hydrodynamics
• Chiral Anomalous Magnetohydrodynamics in action: effective field theory and holography
• Dissipative electrically driven fluids
• The Hamiltonian mechanics of exotic particles