Abstract
We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transport coefficients. Five Onsager relations render 5 more transport coefficients dependent. We uncover four novel transport effects, which are encoded in what we call the shear-induced conductivity, the two expansion-induced longitudinal conductivities and the shear-induced Hall conductivity. Remarkably, the shear-induced Hall conductivity constitutes a novel non-dissipative transport effect. As a demonstration, we compute all transport coefficients explicitly in a strongly coupled quantum fluid via holography.
Highlights
Hydrodynamics is a universal effective field theory description of collective phenomena in systems with many degrees of freedom
The constitutive equations, Kubo formulas, equilibrium generating functionals, as well as symmetry constraints, Onsager relations, and the entropy constraints are derived for a charged fluid subjected to a strong external magnetic field
Hydrodynamic constitutive relations are generated for the energy-momentum tensor, consistent, and covariant charge currents
Summary
Hydrodynamics is a universal effective field theory description of collective phenomena in (quantum) systems with many degrees of freedom. We consider the hydrodynamic description of a (3+1)-dimensional chiral charged thermal fluid subject to a strong external magnetic field. Our main result are the Kubo formulas for the transport coefficients of a charged chiral thermal fluid subject to a strong magnetic field Holographic duals of quantum field theories with a chiral anomaly and subject to weak electromagnetic fields (of first order in the hydrodynamic derivative expansion) have received much attention due to a host of applications that ranges from condensed matter physics to heavy ion collisions. Anisotropic effects not related to magnetic fields have been included in holography in the hydrodynamic approximation [64,65,66,67]
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