Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics
Yanyan Bu, Michael Lublinsky
备注：
v1: 33 pages, 4 multi-figures; v2: added 6 refs, made a couple of clarifications, to appear in JHEP; v3: corrected sound wave dispersion relation in equation (2.44)
In ref. \cite{1406.7222}, we reported a construction of all order linearized fluid dynamics with strongly coupled $\mathcal{N}=4$ super-Yang-Mills theory as underlying microscopic description. The linearized fluid/gravity correspondence makes it possible to resum all order derivative terms in the fluid stress tensor. Dissipative effects are fully encoded by the shear term and a new one, emerging starting from third order in hydrodynamic derivative expansion. In this work, we provide all computational details omitted in \cite{1406.7222} and present additional results. We derive closed-form linear holographic RG flow-type equations for momenta-dependent transport coefficient functions. Generalized Navier-Stokes equations are shown to emerge from the constraint components of the bulk Einstein equations. We perturbatively solve the RG equations for the viscosity functions, up to third order in derivative expansion, and up to this order compute spectrum of small fluctuations. Finally, we solve the RG equations numerically, thus accounting for all order derivative terms in the boundary stress tensor.
In this paper we study the shear viscosity temperature dependence of $SU(3)$--gluodynamics within lattice simulation. To do so, we measure the correlation functions of energy-momentum tensor in the range of temperatures $T/T_c\in [0.9, 1.5]$. To extract the values of shear viscosity we used two approaches. The first one is to fit the lattice data with some physically motivated ansatz for the spectral function with unknown parameters and then determine shear viscosity. The second approach is to apply the Backus-Gilbert method which allows to extract shear viscosity from the lattice data nonpara…
We consider an effective field theory description of beyond-quasi-particle excitations aiming to associate the transport properties of the system with the spectral density of states. Tuning various properties of the many-particle correlations, we investigate how the robust microscopic features are translated into the macroscopic observables like shear viscosity and entropy density. The liquid-gas crossover is analysed using several examples. A thermal constraint on the fluidity measure, the ratio of shear viscosity to entropy density, is discussed.
In this paper we calculate the ratio of transverse shear viscosity to entropy density for the general anisotropic black brane in Horava-Lifshitz gravity. There is a well-known conjecture that states this ratio should be larger than $\frac{1}{4π}$. The ratio of shear viscosity to entropy density is proportional to the inverse square coupling of quantum thermal field theory,$\frac{η}{s} \sim \frac{1}{λ^2 }$. Especially in QFT with gravity dual the stronger coupling means the shear viscosity per entropy density gets closer to the lower bound of $\frac{1}{4π}$. The KSS bound preserves in the aniso…
We study the shear viscosity in an effective hydrodynamic theory and holographic model where the translational symmetry is broken by massless scalar fields. We identify the shear viscosity, $η$, from the coefficient of the shear tensor in the modified constitutive relation, constructed from thermodynamic quantities, fluid velocity and the scalar fields, which break the translational symmetry explicitly. Our construction of constitutive relation is inspired by those derived from the fluid/gravity correspondence in the weakly disordered limit $m/T \ll 1$. We show that the shear viscosity from th…
The Einstein AdS black brane with a cloud of strings background in context of massive gravity is introduced. There is a momentum dissipation on the boundary because of graviton mass on the bulk. The ratio of shear viscosity to entropy density is calculated for this solution. This value violates the KSS bound if we apply the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of the cloud of strings.
A family of deformed AdS4-Reissner-Nordström black branes, governed by a free parameter, is derived using the ADM formalism, in the context of the membrane paradigm. Their new event horizons, the Hawking temperature and other aspects are scrutinized. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio for the deformed AdS4-Reissner-Nordström metric. The Killing equation is shown to yield new values for the free parameter and the shear viscosity-to-entropy ratio is used to derive a reliable range for tidal charge.
We present a proposal to measure anisotropic shear viscosity in a strongly interacting, ultra-cold, unitary Fermi gas confined in a harmonic trap. We introduce anisotropy in this setup by strongly confining the gas in one of the directions with relatively weak confinement in the remaining directions. This system has a close resemblance to anisotropic strongly coupled field theories studied recently in the context of gauge-gravity duality. Computations in such theories (which have gravity duals) revealed that some of the viscosity components of the anisotropic shear viscosity tensor can be made…
