Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields

Abstract

We present a holographic perspective on momentum transport in strongly coupled, anisotropic non-Abelian plasmas in the presence of strong magnetic fields. We compute the anisotropic heavy quark drag forces and Langevin diffusion coefficients and also the anisotropic shear viscosities for two different holographic models, namely, a top-down deformation of strongly coupled N = 4Super-Yang-Mills (SYM) theory triggered by an external Abelian magnetic field, and a bottomup Einstein-Maxwell-dilaton (EMD) model which is able to provide a quantitative description of lattice QCD thermodynamics with (2 + 1)-flavors at both zero and nonzero magnetic fields. We find that, in general, energy loss and momentum diffusion through strongly coupled anisotropic plasmas are enhanced by a magnetic field being larger in transverse directions than in the direction parallel to the magnetic field. Moreover, the anisotropic shear viscosity coefficient is smaller in the direction of the magnetic field than in the plane perpendicular to the field, which indicates that strongly coupled anisotropic plasmas become closer to the perfect fluid limit along the magnetic field. We also present, in the context of the EMD model, holographic predictions for the entropy density and the crossover critical temperature in a wider region of the (T, B) phase diagram thathas not yet been covered by lattice simulations. Our results for the transport coefficients in the phenomenologically realistic magnetic EMD model could be readily used as inputs in numerical codes for magnetohydrodynamics.

Relativistic magnetohydrodynamics

“…We have also communicated with the authors of ref. [26], and it is our understanding that the Kubo formulas for viscosities in an updated version of ref. [26] will agree with ours.…”

“…Some of the hydrodynamic transport coefficients discussed in this paper were evaluated in holographic models in refs. [26,27]. The full set of transport coefficients for fluids in external magnetic field has not yet been explored holographically.…”

“…Papers [25,26] studied transport coefficients for relativistic fluids subject to an external magnetic field. While this does not correspond to MHD in the sense described in this paper (we define MHD as a theory in which magnetic field or its auxiliary is a dynamical degree of freedom), a fluid in external field is a fundamental building block for MHD.…”

“…Some of our results differ from those in refs. [25,26]: the analysis of thermodynamics, the number of transport coefficients, constraints on transport coefficients imposed by the positivity of entropy production, and some of the Kubo formulas. The details are given in appendix B.…”

“…[26] (abbreviated below as FCRN), the authors considered hydrodynamics with fixed non-dynamical magnetic field, and derived Kubo formulas for transport coefficients that appear in the energy-momentum tensor in the Landau-Lifshitz frame. FCRN use a variational approach to find the retarded functions of the energy-momentum tensor, and appendix B of FCRN overlaps with our section 3.…”