Magneto-transport in an anomalous fluid with weakly broken symmetries, in weak and strong regime

We consider a general system with weakly broken time and translation symmetries. We assume the system also possesses a $U(1)$ symmetry which is not only weakly broken, but is anomalous. We use the second order chiral quasi-hydrodynamics to compute the magneto-conductivities in the system in the presence of a weak magnetic field. Analogous to electrical and thermoelectric conductivities, it turns out that the thermal conductivity is identified with a coefficient which depends on the mixed gauge-gravitational anomaly. By applying our general formulas to a free system of Weyl fermions at low temperature limit $T\ll \mu$, we find that our system is Onsager reciprocal if the relaxation in all energy, momentum and charge channels occurs at the same rate. In the high temperature limit $T\gg \mu$, we consider a strongly coupled $SU(N_c)$ gauge theory with $N_c\gg1$ in the hydrodynamic limit. Its gravity dual is a magnetized charged brane to which, we apply our formulas and compute the conductivities. On the way, we show that analogous to the weak regime, an energy cut-off emerges to regulate the thermodynamic quantities. From this gravity background we also find the coefficients of chiral magnetic effect in agreement with the well-known result of the Son-Surowka.