Holography and hydrodynamics with weakly broken symmetries

Grozdanov, Sašo (Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA) ; Lucas, Andrew (Department of Physics, Stanford University, Stanford, California 94305 USA) ; Poovuttikul, Napat (University of Iceland, Science Institute, Dunhaga 3, IS-107, Reykjavik, Iceland)

15 April 2019

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.

Published in: Physical Review D 99 (2019)
Published by: APS
DOI: 10.1103/PhysRevD.99.086012
License: CC-BY-4.0

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