Hydrodynamics from charged black branes

Abstract

Abstract:We extend the recent work on fluid-gravity correspondence to charged blackbranes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.

Effective actions for anomalous hydrodynamics

“…The essential point, which forms the main focus of this investigation, is that quantum anomalies, which conventionally are discussed in the context of non-thermal observables, influence equilibrium thermodynamics and near-equilibrium hydrodynamical behaviour in an essential manner. The effects of pure flavour anomalies were recently first noticed in holographic computations of charged fluids using the fluid/gravity correspondence [3,4], where their origins could be traced to gauge Chern-Simons terms in the dual supergravity theory. 1 Whilst surprising at first sight, it was quickly realized in [9] that consistency with a local version of the second law of thermodynamics in near-equilibrium situations necessitates that a part of the hydrodynamical transport is controlled directly by the quantum flavour anomaly.…”

“…In fact, all the dependence on the fluid element variables has been packaged into the hydrodynamic velocity 1-form u and the chemical potential µ appearing inÂ. 4 The subscript of M 2n+1 denotes that the integral is over a manifold which is one dimension higher than the manifold in which the fluid lives. Here, we have found it useful to employ the anomaly inflow mechanism [53] (we refer the reader to the appendices of [30] for a recent review), i.e., viewing our anomalous field theory in d = 2n dimensions as the boundary dynamics of a bulk topological theory (in 2n + 1 dimensions), to guide us in writing covariant effective actions.…”

Chiral drag force

“…This work has been generalized in many directions since then. We will in particular need the modifications of the spacetime metric that describe a flowing, hydrodynamic, plasma in which there are gradients of the fluid properties as a function of space and time [8][9][10]. The corresponding modifications of the drag force were worked out to leading order in the fluid gradients in ref.…”

“…To compute the drag force on a heavy quark moving through the strongly coupled plasma of N = 4 SYM theory with a nonzero chemical potential and with spatial and temporal gradients in the fluid velocity, temperature and chemical potential we need to start with the perturbations to the dual gravitational theory that correspond to hydrodynamic flow [9,10]. We shall present the corresponding 4+1-dimensional bulk metric in this section, delaying the introduction of the heavy quark that we are interested in to section 3.…”

(Non)-renormalization of the chiral vortical effect coefficient

“…Since the original observations in gauge/gravity duality [1][2][3], it has been shown that the hydrodynamic equations of systems with anomalies necessarily contain additional terms if both the equations of anomalies and the second law of thermodynamics are to be preserved [4]. These new terms lead to two new effects: the chiral magnetic effect (CME) and the chiral vortical effect (CVE), i.e.…”