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.

We begin the exploration of holographic duals to theories with generalised global (higher-form) symmetries. In particular, we focus on the case of magnetohydrodynamics (MHD) in strongly coupled plasmas by constructing and analysing a holographic dual to a recent, generalised global symmetry-based formulation of dissipative MHD. The simplest holographic dual to the effective theory of MHD that was proposed as a description of plasmas with any equation of state and transport coefficients contains dynamical graviton and two-form gauge field fluctuations in a magnetised black brane background. The dual field theory, which is closely related to the large-N c , N = 4 supersymmetric Yang-Mills theory at (infinitely) strong coupling, is, as we argue, in our setup coupled to a dynamical U (1) gauge field with a renormalisation condition-dependent electromagnetic coupling. After constructing the holographic dictionary for gauge-gravity duals of field theories with higher-form symmetries, we compute the dual equation of state and transport coefficients, and for the first time analyse phenomenology of MHD waves in a strongly interacting, dense plasma with a (holographic) microscopic description. From weak to extremely strong magnetic fields, several predictions for the behaviour of Alfvén and magnetosonic waves are discussed. arXiv:1707.04182v3 [hep-th] 25 Apr 2019 4 We note that the order parameter that distinguishes between a broken and an unbroken magnetic oneform symmetry is an expectation value of the 't Hooft loop operator. When the symmetry is preserved, then the expectation value of the loop operator obeys the area law, WC ∼ exp {−T Area[C]}. On the other hand, in the symmetry broken phase with massless photons, the expectation value obeys the perimeter law,5 Note that at zero temperature, in a plasma with a non-fluctuating temperature field, the symmetry is-4 -The frame choice which leads to this particular form of constitutive relations was specified in Ref. [24]. The thermodynamic relations between ε, p and ρ, which need to be obeyed by the equation of state p(T, µ) are( 1.21) Furthermore, for the theory to be invariant under time-reversal, the Onsager relation implies that ζ(1)× ≡ ζ × . Thus, first-order dissipative corrections to ideal MHD are controlled by seven transport coefficients: η ⊥ , η , ζ ⊥ , ζ , ζ × , r ⊥ and r . Each one can be computed from a set of Kubo formulae presented in [24,27] and reviewed in Appendix A. The transport coefficients should obey the following positive entropy production constraints: η ⊥ ≥ 0, η ≥ 0, r ⊥ ≥ 0, r ≥ 0, ζ ⊥ ≥ 0 and ζ ⊥ ζ ≥ ζ 2 × . In absence of charge conjugation symmetry, the theory has four additional transport coefficients, resulting in total in eleven transport coefficients [27]. The precise connection between the above formalism of MHD using the concept of generalised global symmetries and MHD expressed in terms of electromagnetic fields, which match in the limit of a small magnetic field (compared to the temperature of the plasma), was established in Ref. [27]....

Abstract:We consider the spontaneous breaking of translational symmetry and identify the associated Goldstone mode -a longitudinal phonon -in a holographic model with Bianchi VII helical symmetry. For the first time in holography, we observe the pinning of this mode after introducing a source for explicit breaking compatible with the helical symmetry of our setup. We study the dispersion relation of the resulting pseudo-Goldstone mode, uncovering how its speed and mass gap depend on the amplitude of the source and temperature. In addition, we extract the optical conductivity as a function of frequency, which reveals a metal-insulator transition as a consequence of the pinning.

In this work, we show how states with conserved numbers of dynamical defects (strings, domain walls, etc.) can be understood as possessing generalized global symmetries even when the microscopic origins of these symmetries are unknown. Using this philosophy, we build an effective theory of a 2 þ 1-dimensional fluid state with two perpendicular sets of immersed elastic line defects. When the number of defects is independently conserved in each set, then the state possesses two one-form symmetries. Normally, such viscoelastic states are described as fluids coupled to Goldstone bosons associated with spontaneous breaking of translational symmetry caused by the underlying microscopic structure-the principle feature of which is a transverse sound mode. At the linear, nondissipative level, we verify that our theory, based entirely on symmetry principles, is equivalent to a viscoelastic theory. We then build a simple holographic dual of such a state containing dynamical gravity and two two-form gauge fields, and use it to study its hydrodynamic and higher-energy spectral properties characterized by nonhydrodynamic, gapped modes. Based on the holographic analysis of transverse two-point functions, we study consistency between lowenergy predictions of the bulk theory and the effective boundary theory. Various new features of the holographic dictionary are explained in theories with higher-form symmetries, such as the mixedboundary-condition modification of the quasinormal mode prescription that depends on the running coupling of the boundary double-trace deformations. Furthermore, we examine details of low-and highenergy parts of the spectrum that depend on temperature, line defect densities and the renormalization group scale.