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

Abstract

We consider a fluid with weakly broken time and translation symmetries. We assume the fluid 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 of this fluid in the presence of a weak magnetic field. Analogous to the electrical and thermoelectric conductivities, it turns out that the thermal conductivity depends on the coefficient of mixed gauge-gravitational anomaly. Our results can be applied to the hydrodynamic regime of every arbitrary system, once the thermodynamics of that system is known. By applying them to a free system of Weyl fermions at low temperature limit T ≪ μ, we find that our fluid is Onsager reciprocal if the relaxation in all energy, momentum and charge channels occurs at the same rate. In the high temperature limit T ≫ μ, we consider a strongly coupled SU(Nc) gauge theory with Nc ≫ 1. Its holographic dual in thermal equilibrium is a magnetized charged brane from which, we compute the thermodynamic quantities and subsequently evaluate the conductivities in gauge theory. On the way, we show that analogous to the weak regime in the system of Weyl fermions, an energy cutoff emerges to regulate the thermodynamic quantities in the strong regime of boundary gauge theory. From this gravity background we also find the coefficients of chiral magnetic effect in agreement with the well-known result of Son-Surowka.