On the frame dependence of conductivities in anomalous hydrodynamics
Résumé
It is becoming clear that different choices of hydrodynamic frame can have non-trivial consequences for the structure of hydrodynamics. Previous discussions have focused on the changes of the causal and thermodynamic properties of a fluid due to a frame change; here we show that previously discovered results in anomalous hydrodynamics are frame dependent. In particular, we focus on $(3+1)$-dimensional hydrodynamics in the presence of a constant ${\cal O}(\partial)$ magnetic field with a $U(1)$ chiral anomaly and show that, for constitutive relations up to and including order one in derivatives, the anomaly only enters the non-zero frequency thermoelectric conductivities through explicitly frame dependent terms. This issue arises due to an inappropriate derivative counting and can be avoided entirely by incorporating the magnetic field into the fluid's equilibrium state.