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 (N c ) gauge theory with N c ≫ 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. * abbasi@ipm.ir † armin.ghazi@physics.

Quantum chaos, pole-skipping and hydrodynamics in a holographic system with chiral anomaly

“…The unevaluated integral functions found in [23] can be evaluated analytically in some regimes. In [24], all these functions have been computed in a double expansion over B/T 2 and µ/T . In the current paper we follow [24] and work in the same limit.…”

“…In [24], all these functions have been computed in a double expansion over B/T 2 and µ/T . In the current paper we follow [24] and work in the same limit. 8 Here, however, we do not rewrite the explicit expressions of functions (2.7) evaluated in [24].…”

“…In the current paper we follow [24] and work in the same limit. 8 Here, however, we do not rewrite the explicit expressions of functions (2.7) evaluated in [24]. In order to study the chaos, we only need to know the near horizon limit of the mentioned correction functions.…”

“…In the absence of magnetic field location of horizon is the root of f 0 and is given by r h = πT . However, as discussed in [24], since f 0 gets a magnetic correction, the outer horizon and consequently both the Hawking temperature and the chemical potential of the solution have to be corrected as well. Considering the double expansion discussed above, the corrected outer horizon, is found to be as…”

“…However, the metric functions in [23] are given as some un-evaluated integrals. In order to work with them, we adapt the doubly expanded metric functions over B/T 2 and µ/T , found in [24]. So, whatever we find in this paper will be analytic and will be given in a double expansion over these two dimensionless parameters.…”