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. Inmore »
- Authors:
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1507180
- Alternate Identifier(s):
- OSTI ID: 1611573; OSTI ID: 1637342
- Grant/Contract Number:
- SC0011090
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Name: Physical Review. D. Journal Volume: 99 Journal Issue: 8; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- Astronomy & Astrophysics; Physics; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; gauge-gravity dualities; quantum fluids & solids; strongly correlated systems; continuous symmetries in condensed matter; effective field theory; string theory techniques in condensed matter
Citation Formats
Grozdanov, Sašo, Lucas, Andrew, and Poovuttikul, Napat. Holography and hydrodynamics with weakly broken symmetries. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.086012.
Grozdanov, Sašo, Lucas, Andrew, & Poovuttikul, Napat. Holography and hydrodynamics with weakly broken symmetries. United States. https://doi.org/10.1103/PhysRevD.99.086012
Grozdanov, Sašo, Lucas, Andrew, and Poovuttikul, Napat. Mon .
"Holography and hydrodynamics with weakly broken symmetries". United States. https://doi.org/10.1103/PhysRevD.99.086012.
@article{osti_1507180,
title = {Holography and hydrodynamics with weakly broken symmetries},
author = {Grozdanov, Sašo and Lucas, Andrew and Poovuttikul, Napat},
abstractNote = {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.},
doi = {10.1103/PhysRevD.99.086012},
journal = {Physical Review. D.},
number = 8,
volume = 99,
place = {United States},
year = {Mon Apr 15 00:00:00 EDT 2019},
month = {Mon Apr 15 00:00:00 EDT 2019}
}
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Figures / Tables:
FIG. 1: A schematic depiction of the ranges of validity of hydrodynamics and quasihydrodynamics for two distinct spectra plotted on the complex frequency ω plane. In the left panel, relaxation times of all nonhydrodynamic modes are comparable and the IR part of the spectrum is dominated by hydrodynamic modes. Theremore »
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