Abstract
Hydrodynamics is a theory of long-range excitations controlled by equations of motion that encode the conservation of a set of currents (energy, momentum, charge, etc.) associated with explicitly realized global symmetries. If a system possesses additional weakly broken symmetries, the low-energy hydrodynamic degrees of freedom also couple to a few other "approximately conserved" quantities with parametrically long relaxation times. It is often useful to consider such approximately conserved operators and corresponding new massive modes within the low-energy effective theory, which we refer to as quasihydrodynamics. Examples of quasihydrodynamics are numerous, with the most transparent among them hydrodynamics with weakly broken translational symmetry. Here, we show how a number of other theories, normally not thought of in this context, can also be understood within a broader framework of quasihydrodynamics: in particular, the M\"uller-Israel-Stewart theory and magnetohydrodynamics coupled to dynamical electric fields. While historical formulations of quasihydrodynamic theories were typically highly phenomenological, here, we develop a holographic formalism to systematically derive such theories from a (microscopic) dual gravitational description. Beyond laying out a general holographic algorithm, we show how the M\"uller-Israel-Stewart theory can be understood from a dual higher-derivative gravity theory and magnetohydrodynamics from a dual theory with two-form bulk fields. In the latter example, this allows us to unambiguously demonstrate the existence of dynamical photons in the holographic description of magnetohydrodynamics.
Highlights
The past decade has seen a resurgence of interest in developing a systematic understanding of hydrodynamics as an effective field theory, describing the relaxation of locally conserved quantities towards global equilibrium in terms of long-lived degrees of freedom (d.o.f.)[1,2,3,4,5,6,7,8,9]
We show how a number of other theories, normally not thought of in this context, can be understood within a broader framework of quasihydrodynamics: in particular, the Müller-Israel-Stewart theory and magnetohydrodynamics coupled to dynamical electric fields
We have developed a general framework for discussing linearized hydrodynamic theories with additional approximately conserved currents, which we called quasihydrodynamics
Summary
The past decade has seen a resurgence of interest in developing a systematic understanding of hydrodynamics as an effective field theory, describing the relaxation of locally conserved quantities towards global equilibrium in terms of long-lived (low-energy) degrees of freedom (d.o.f.)[1,2,3,4,5,6,7,8,9]. While from a formal effective field theory point of view such a theory should be viewed with suspicion, standard MHD and its simple phenomenological extensions make a number of extremely successful predictions about the dynamics of complicated astrophysical plasmas and processes in fusion reactors Another classic example of a system with an explicitly broken conservation law is fluid dynamics with weak momentum relaxation [28,33,34]. We point out that—at least within linear response—a large number of well-known phenomenological theories are quasihydrodynamic: these include the momentum-relaxing fluid, and magnetohydrodynamics and plasma physics with dynamical photons, simple models of viscoelasticity, (at least in some cases) the Müller-IsraelStewart (MIS) theory of relativistic hydrodynamics, and (quantum) kinetic theory (in some respects). We show analytically how the quasihydrodynamic limit arises
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