Holography and hydrodynamics with weakly broken symmetries

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 Müller-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 Müller-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.

Zoology of solid & fluid holography — Goldstone modes and phase relaxation

“…We find this observation very interesting and similar to what discussed in [49][50][51]69]. It would be valuable, to show with field theory methods that diffusive Goldstone bosons, like in [53], acquire a small propagating speed (together with a mass and a damping), when EXB is introduced.…”

Holographic plasmon relaxation with and without broken translations

“…Then, we analyze carefully the dispersion relation of the quantum critical plasmons and in particular their possible overdamped nature. We will discover a peculiar transition between a standard plasmon dispersion relation ω 2 = ω 2 p + c 2 k 2 and a propagating sound wave ω = ck which in the intermediate regime displays a k-gap dispersion relation [6,21] 3 . The k-gap simply refers to a dispersion relation of the type:…”

Viscoelastic hydrodynamics and holography

“…At this point, we are not aware of a physical hydrodynamic system with unbroken generalised global symmetries at the boundary as described in [27]. This fact has repercussions to several other constructions studied in [70], where the Goldstone modes of spontaneous broken global symmetries have not been taken into account. We wish to study these constructions more carefully in the near future.…”

“…It would be interesting to consider the case of arbitrary finite relaxation times as in [7] in such a way that deviations away from the hydrodynamic regime are under control. In these situations, the framework of quasi-hydrodynamics will most likely be useful, as in [70].…”