Leading order magnetic field dependence of conductivities in anomalous hydrodynamics

https://arxiv.org/abs/2212.09761

In four dimensions, fermions can have chiral anomalies. These lead to some rather interesting effects, such as large negative magnetoresistivity. This  effect had been explored in the past. As per usual, the DC conductivities of this translation invariant system were infinite. However, it was argued in that paper that it was necessary to have charge, energy and momentum relaxation to produce a system with finite DC conductivity. This was quite odd as charge loss is certainly not apparent in the kinds of materials that these theories were developed to describe (e.g. Weyl semimetals).  I challenged this viewpoint in a later paper. Moreover, other studies drew rather strange conclusions that seemed to suggest working in different hydrodynamic frames gave different results for the DC conductivity.

This latter point, the target of this paper, is rather odd as observables must be independent of the hydrodynamic frame (it is an arbitrary choice after all). I showed that previous results concerning the contribution of the magnetic field to the DC conductivity were entirely frame dependent. When the magnetic field is treated as order one in derivatives, as was often done, it was possible to redefine away the contribution of the anomaly to the DC conductivity; meaning that it was a frame choice artifact. With a magnetic field that is order zero in derivatives, there is no frame ambiguity as the magnetic field is part of the thermodynamics. This gave a unique procedure to identify a preferential result as one takes a limit where the order zero magnetic field becomes order one in derivatives.