Holography and hydrodynamics with weakly broken symmetries

TL;DR

This paper develops a holographic framework to derive quasihydrodynamic theories, including M"uller-Israel-Stewart and magnetohydrodynamics, from dual gravitational models, providing a systematic understanding of weakly broken symmetries in hydrodynamics.

Contribution

It introduces a holographic formalism to systematically derive quasihydrodynamics from microscopic dual gravitational theories, extending the understanding of weakly broken symmetries.

Findings

Holographic derivation of M"uller-Israel-Stewart theory from higher-derivative gravity

Holographic modeling of magnetohydrodynamics with dynamical photons

Unified framework for quasihydrodynamics 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 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.