We consider Kasner space-time describing anisotropic three dimensional expansion of RHIC and LHC fireball and study the generalization of Bjorken's one dimensional expansion by taking into account second order relativistic viscous hydrodynamics. Using time dependent AdS/CFT correspondence, we study the late time behaviour of the Bjorken flow. From the conditions of conformal invariance and energy-momentum conservation, we obtain the explicit expression for the energy density as a function of proper time in terms of Kasner parameters. The proper time dependence of the temperature and entropy have also been obtained in terms of Kasner parameters. We consider Eddington-Finkelstein type coordinates and discuss the gravity dual of the anisotropically expanding fluid in the late time regime.
We review recent developments in holographic hydrodynamics. We start from very basic discussion on hydrodynamic systems and motivate why string theory is an essential tool to deal with these systems when they are strongly coupled. The main purpose of this review article is to understand different holographic techniques to compute transport coefficients (first order and higher order) and their corrections in presence of higher derivative terms in the bulk Lagrangian. We also mention some open challenges in this subject.
We study holographic entanglement entropy in spatially anisotropic field theory. We observe that for the background we consider in this paper, to a good approximation, the holographic entanglement entropy can be decomposed into two terms. One of them is the entanglement entropy of the isotropic field theory at fixed temperature and the other term is only a function of anisotropy parameter. Moreover, for large enough values of anisotropy parameter, our numerical results indicate that the entanglement entropy in the perpendicular direction to anisotropic direction is greater than the parallel ca…
The holographic entanglement entropy (HEE) is investigated for a black hole under the minimal geometric deformation (MGD) procedure, created by gravitational decoupling via an anisotropic fluid, in an AdS/CFT on the brane setup. The respective HEE corrections are computed and confronted to the corresponding corrections for both the standard MGD black holes and the Schwarzschild ones.
We first calculate the jet quenching parameter of an anisotropic plasma with a U(1) chemical potential via the AdS/CFT duality. The effects of charge, anisotropy parameter and quark motion direction on the jet quenching parameter are investigated. We then discuss the situation of anisotropic black brane in the IR region. We study both the jet quenching parameters along the longitudinal direction and transverse plane.
Relativistic fluid hydrodynamics, organized as an effective field theory in the velocity gradients, has zero radius of convergence due to the presence of non-hydrodynamic excitations. Likewise, the theory of elasticity of brittle solids, organized as an effective field theory in the strain gradients, has zero radius of convergence due to the process of the thermal nucleation of cracks. Viscoelastic materials share properties of both fluids and solids. We use holographic gauge theory/gravity correspondence to study all order hydrodynamics of relativistic viscoelastic media.
We study hydrodynamics of four-dimensional non-conformal holographic plasma with non-equal central charges $c\ne a$ at the ultraviolet fixed point. We compute equation of state, the speed of sound waves, transport coefficients (shear and bulk viscosities), and discuss causality. We study the asymptotic character of the hydrodynamic series for the homogeneous and isotropic expansion of the plasma. We perform computations for finite $c-a\ne 0$, but to leading nonvanishing order in the conformal symmetry breaking coupling.
We study causality violation in holographic hydrodynamics in the gauge theory/string theory correspondence, focussing on Gauss-Bonnet gravity. The value of the Gauss-Bonnet coupling is related to the difference between the central charges of the dual conformal gauge theory. We show that, when this difference is sufficiently large, causality is violated both in the second-order truncated theory of hydrodynamics, as well as in the exact theory. We find that the latter provides more stringent constraints, which match precisely those appearing in the CFT analysis of Hofman and Maldacena.
We have examined holographic renormalization group($RG$) flows of the shear viscosities in anisotropic holographic superfluids via their gravity duals, Einstein-SU(2) Yang-Mills system. In anisotropic phase, below the critical temperature $T_c$, the SO(3) isometry(spatial rotation) in the dual gravity system is broken down to the residual SO(2). The shear viscosities in the symmetry broken directions of the conformal fluids defined on $AdS$ boundary present non-universal values which depend on the chemical potential $μ$ and temperature $T$ of the system and also satisfy non-trivial holographic…
We construct an analytic solution of the Einstein-SU(2)-Yang-Mills system as the holographic dual of an anisotropic superfluid near its critical point, up to leading corrections in both the inverse Yang-Mills coupling and a symmetry breaking order parameter. We have also calculated the ratio of shear viscosity to entropy density in this background, and shown that the universality of this ratio is lost in the broken symmetry direction. The ratio displays a scaling behavior near the critical point with critical exponent $β=1$, at the leading order in the double expansion.
Gauge theory/string theory holographic correspondence for ${\cal N}=4$ supersymmetric Yang-Mills theory is well under control in the planar limit, and for large (infinitely large) 't Hooft coupling, $λ\to \infty$. Certain aspects of the correspondence can be extended including ${\cal O}(λ^{-3/2})$ corrections. There are no reliable first principle computations of the ${\cal N}=4$ plasma non-equilibrium properties beyond the stated order. We show extreme sensitivity of the non-hydrodynamic spectra of holographic ${\cal N}=4$ SYM plasma to ${\cal O}(λ^{-3})$ corrections, challenging any conclusi…
We use the complexity = action (CA) conjecture to study the full-time dependence of holographic complexity in anisotropic black branes. We find that the time behaviour of holographic complexity of anisotropic systems shares a lot of similarities with the behaviour observed in isotropic systems. In particular, the holographic complexity remains constant for some initial period, and then it starts to change so that the complexity growth rate violates the Lloyd's bound at initial times, and approaches this bound from above at later times. Compared with isotropic systems at the same temperature, t…
In the context of the gauge/gravity duality, using the proposed candidate $c$-function, which is derived from the entanglement entropy of a strip-shaped region, we investigate the RG flow for $d+1$-dimensional quantum field theories with broken Lorentz and rotational symmetries in the IR, but preserved conformal invariance in the UV boundary. We examine conditions of monotonicity of the $c$-function for holographic anisotropic theories dual to the Einstein gravity via the constraints imposed by the null energy conditions. We consider near UV and IR behaviors and identify the sufficient conditi…
We employ the holographic approach to study the thermalization in the quenched strongly-coupled field theories with very general anisotropic scalings including Lifshitz and hyperscaling violating fixed points. The holographic dual is a Vaidya-like time-dependent geometry where the asymptotic metric has general anisotropic scaling isometries. We find the Ryu-Takanayagi extremal surface and use it to calculate the time-dependent entanglement entropy between a strip region with width $2R$ and its outside region. In the special case with an isotropic metric, we also explore the entanglement entrop…
We consider gravity duals to d+1 dimensional quantum critical points with anisotropic scaling. The primary motivation comes from strongly correlated electron systems in condensed matter theory but the main focus of the present paper is on the gravity models in their own right. Physics at finite temperature and fixed charge density is described in terms of charged black branes. Some exact solutions are known and can be used to obtain a maximally extended spacetime geometry, which has a null curvature singularity inside a single non-degenerate horizon, but generic black brane solutions in the mo…
In the previous paper we studied the transport coefficients of Quark-Gluon Plasma in finite temperature and finite density in vector and tensor modes. In this paper, we extend it to the scalar modes. We work out the decoupling problem and hydrodynamic analysis for the sound mode in charged AdS black hole and calculate the sound velocity, the charge susceptibility and the electrical conductivity. We find that Einstein relation among the conductivity, the diffusion constant and the susceptibility holds exactly.
We present a five-dimensional twice anisotropic holographic model supported by Einstein-dilaton-three-Maxwell action describing light quarks. The first of the Maxwell fields provides finite chemical potential. The second Maxwell field serves for anisotropy, characterizing spatial anisotropy of the QGP produced in heavy-ion collisions (HIC). The third Maxwell field is related to a magnetic field that appears in HIC. The dependence of the 5-dim black hole solution and confinement/deconfinement phase diagram on this magnetic field is considered. The effect of the inverse magnetic catalyses for li…
We consider five-dimensional gravity coupled to a negative cosmological constant and a single U(1) gauge field, including a general set of four-derivative interactions. In this framework, we construct charged planar AdS black hole solutions perturbatively and consider the thermal and hydrodynamic properties of the plasma in the dual CFT. In particular, we calculate the ratio of shear viscosity to entropy density and argue that the violation of the KSS bound is enhanced in the presence of a chemical potential. We also compute the electrical conductivity and comment on various conjectured bounds…
We study the poles of the retarded Green functions of a holographic superconductor. The model shows a second order phase transition where a charged scalar operator condenses and a U(1) symmetry is spontaneously broken. The poles of the holographic Green functions are the quasinormal modes in an AdS black hole background. We study the spectrum of quasinormal frequencies in the broken phase, where we establish the appearance of a massless or hydrodynamic mode at the critical temperature as expected for a second order phase transition. In the broken phase we find the pole representing second soun…
We study second-order hydrodynamic transport in strongly coupled non-conformal field theories with holographic gravity duals in asymptotically anti-de Sitter space. We first derive new Kubo formulae for five second-order transport coefficients in non-conformal fluids in $(3+1)$ dimensions. We then apply them to holographic RG flows induced by scalar operators of dimension $Δ=3$. For general background solutions of the dual bulk geometry, we find explicit expressions for the five transport coefficients at infinite coupling and show that a specific combination, $\tilde{H}=2ητ_π-2(κ-κ^*)-λ_2$, al…
We present a five-dimensional fully anisotropic holographic model for heavy quarks supported by Einstein-dilaton-three-Maxwell action; one of the Maxwell fields is related to an external magnetic field. Influence of the external magnetic field on the 5-dim black hole solution and the confinement/deconfinement phase diagram is considered. The effect of the inverse magnetic catalyses is revealed and positions of critical end points are found.
We study the transport coefficients of Quark-Gluon-Plasma in finite temperature and finite baryon density. We use AdS/QCD of charged AdS black hole background with bulk-filling branes identifying the U(1) charge as the baryon number. We calculate the diffusion constant, the shear viscosity and the thermal conductivity to plot their density and temperature dependences. Hydrodynamic relations between those are shown to hold exactly. The diffusion constant and the shear viscosity are decreasing as a function of density for fixed total energy. For fixed temperature, the fluid becomes less diffusib…
We briefly review recent developments of hydrodynamics, its gravitational description and relevance to relativistic heavy ion collisions. We discuss the basics of hydrodynamics, the fluid/gravity correspondence, triangle anomalies and chiral effects, turbulence and its universal structure.
We study the effects of the Chern-Simons term in the hydrodynamics of the five-dimensional Reissner-Nordstrom-AdS background. We work out the decoupling problem of the equations of motion and calculate the retarded Green functions explicitly. We then find that the Chern-Simons term induces the magnetic conductivity caused by the anomaly effect. It is increasing function of temperature running from a non-zero value at zero temperature to the twice the value at infinite temperature.
A Lifshitz black brane at generic dynamical critical exponent $z > 1$, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz p…
We consider the AdS/CFT correspondence in the hydrodynamic regime up to the second order in a derivative expansion. We demonstrate that the fluid conservation equations are equivalent to Einstein's constraint equations projected on different hyper-surfaces. We derive that result for hyper-surfaces of the form r=R(x) up to the first order in a derivative expansion of the metric. At the second order expansion, we introduce the notion of different black hole horizons, and focus on two particular horizon hyper-surfaces: the event horizon and the apparent horizon. We calculate the temperature and e…
We formulate a theory of dissipative hydrodynamics with spontaneously broken translations, describing charge density waves in a clean isotropic electronic crystal. We identify a novel linear transport coefficient, lattice pressure, capturing the effects of background strain and thermal expansion in a crystal. We argue that lattice pressure is a generic feature of systems with spontaneously broken translations and must be accounted for while building and interpreting holographic models. We also provide the first calculation of the coefficients of thermal and chemical expansion in a holographic …
We determine holographically 2-point correlators of gauge invariant operators with large conformal weights and entanglement entropy of strips for a time-dependent anisotropic 5-dimensional asymptotically anti-de Sitter spacetime. At the early stage of evolution where geodesics and extremal surfaces can extend beyond the apparent horizon all observables vary substantially from their thermal value, but thermalize rapidly. At late times we recover quasi-normal ringing of correlators and holographic entanglement entropy around their thermal values, as expected on general grounds. We check the beha…
We discuss recent work showing that in certain cases the membrane paradigm equations governing the dynamics of black hole horizons can be recast as relativistic conservation law equations. In the context of gauge/gravity dualities, these equations are interpreted as defining the viscous hydrodynamics of a holographically dual relativistic field theory. Using this approach, one can derive the viscous transport coefficients and the form of the entropy current for field theories dual to gravity plus matter fields.
We present new anisotropic black brane solutions in 5D Einstein-dilaton-two-Maxwell system. The anisotropic background is specified by an arbitrary dynamical exponent $ν$, a nontrivial warp factor, a non-zero dilaton field, a non-zero time component of the first Maxwell field and a non-zero longitudinal magnetic component of the second Maxwell field. The blackening function supports the Van der Waals-like phase transition between small and large black holes for a suitable first Maxwell field charge. The isotropic case corresponding to $ν= 1$ and zero magnetic field reproduces previously known …
The electric conductivity and direct photons emission rate are considered in the holographic theory with two types of anisotropy. The electric conductivity is derived in two different ways, and their equivalence for the twice anisotropic theory is shown. Numerical calculations of the electric conductivity were done for Einstein-dilaton-three-Maxwell holographic model [29]. The dependence of the conductivity on the temperature, the chemical potential, the external magnetic field, and the spatial anisotropy of the heavy-ions collision (HIC) is studied. The electric conductivity jumps near the fi…
In the context of theories with a first order phase transition, we propose a general covariant description of coexisting phases separated by domain walls using an additional order parameter-like degree of freedom. In the case of a holographic Witten model with a confining and deconfined phase, the resulting model extends hydrodynamics and has a simple formulation in terms of a spacetime action with corresponding expressions for the energy-momentum tensor. The proposed description leads to simple analytic profiles of domain walls, including expressions for surface tension density, which agree n…
We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative solution of relativistic Boltzmann equation with relaxation time approximation. We show that our results for second and third order evolution equations reduce to those of one dimensional expansion case under suitable conditions for the anisotropic parameters in Kasner space-time.
We employ methods of gauge/string duality to analyze the Brownian motion and the concomitant Langevin equation of a heavy quark in a strongly coupled, thermal, anisotropic Yang-Mills plasma. We consider fluctuations both along and perpendicular to the direction of anisotropy and study the effects of anisotropy on the drag coefficient, the diffusion constant and the Langevin coefficient for both the directions. We also verify the fluctuation-dissipation theorem for Brownian motion in an anisotropic medium.
We calculate the holographic entanglement entropy (HEE) of the $\mathbb{Z}_k$ orbifold of Lin-Lunin-Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern-Simons level $k$. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and $k$ up to $μ_0^2$-order where $μ_0$ is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the $F$-theorem. Except the multiplication factor and to all orders in $μ_0$, …
Using the gauge/gravity duality we calculate the heavy quark-antiquark potential in a hot, anisotropic and strongly coupled Yang-Mills plasma in (3+1)-dimensions. As the anisotropic medium we take a deformed version of \mathcal{N} = 4 super Yang-Mills theory at finite temperature following a recent work where the dual type IIB supergravity solution is also proposed. We turn on a small value of the anisotropy parameter, for which the gravity dual is known analytically (perturbatively), and compute the velocity-dependent quark-antiquark interaction potential when the pair is moving through the p…
According to the gauge-gravity duality, we systematically study the Schwinger effect and electric instability with anisotropy in a top-down holographic approach. The anisotropic black brane and bubble (soliton) background in IIB supergravity are employed and the dual theories in these backgrounds are expected to be anisotropic theory at finite temperature and anisotropic theory with confinement respectively. Then performing the potential analysis, we find due to the anisotropy, the potential barrier behaves oppositely with parallel and perpendicular electric fields, and this behavior agrees wi…
Einstein-dilaton-$U(2)$ gauge field theory is considered in a spacetime characterised by $α$ and $z$, which are the hyperscaling violation factor and the dynamical critical exponent respectively. We obtain the critical values of chemical potential $μ_c$ that is defined on its boundary dual fluid and derives phase transition from spatially isotropic to anisotropic phase for the various values of the $α$ and $z$. To do so, we first apply Sturm-Liouville theory and estimate the upper bounds of the critical values of the chemical potential. We also employ a numerical method in the ranges of $1 \le…
Energy loss in anisotropic hot dense QGP in external magnetic field is studied within holographic approach. Energy loss is calculated by estimation of behaviour of the spatial Wilson loops using the effective potential technique. We examine the dependence of the effective potential on the spatial Wilson loops orientation in fully anisotropic background. For this purpose we obtain general formulas for the effective potential and study appearance of the effective potential dynamical wall. We consider particular fully anisotropic model [arXiv:2011.07023] supported by Einstein-Dilaton-three-Maxwel…
We show that the correct dual hydrodynamic description of homogeneous holographic models with spontaneously broken translations must include the so-called "strain pressure" -- a novel transport coefficient proposed recently. Taking this new ingredient into account, we investigate the near-equilibrium dynamics of a large class of holographic models and faithfully reproduce all the hydrodynamic modes present in the quasinormal mode spectrum. Moreover, while strain pressure is characteristic of equilibrium configurations which do not minimise the free energy, we argue and show that it also affect…
We investigate an anisotropic model of superconductors in the Einstein-Maxwell-dilaton theory with a charged scalar field. It is found that the critical temperature decreases as the anisotropy becomes large. We then estimate the energy gap of the superconductor, and find that the ratio of the energy gap to the critical temperature increases as the anisotropy increases and so it is larger than that in the isotropic case. We also find that peudogap appears due to the anisotropy.
We propose a candidate $c$-function in arbitrary dimensional quantum field theories with broken Lorentz and rotational symmetry. For holographic theories we derive the necessary and sufficient conditions on the geometric background for these $c$-functions to satisfy the $c$-theorem. We obtain the null energy conditions for anisotropic background to show that do not themselves assure the $c$-theorem. By employing them, we find that is possible to impose conditions on the UV data that are enough to guarantee at least one monotonic $c$-function along the RG flow. These UV conditions can be used a…
We study the breakdown of diffusive hydrodynamics in holographic systems dual to neutral dilatonic black holes with extremal near horizon geometries conformal to AdS$_2\times\,$R$^2$. We find that at low temperatures by tuning the effective gauge coupling constant in the infra-red, the lowest non-hydrodynamic mode, which collides with the charge diffusive mode and sets the scales at which diffusive hydrodynamics break down, could be either an infra-red mode or a slow mode, resulting in different scaling behaviors of the local equilibrium scales. We confirm that the upper bound for the charge d…
We provide a short review of the hydrodynamical properties of a class of strongly coupled thermal gauge theories, coupled to massless fundamental flavor fields, having a dual supergravity description. The analysis is valid for more general classes of nearly conformal holographic plasmas, where the breaking of conformality is driven by marginally (ir)relevant deformations.
We prove that the purely classical gravity dual of Fermi and non-Fermi liquids exist by employing the logarithmic behavior of entanglement entropy to probe Fermi surfaces. For isotropic systems, the logarithmic behavior originates only from UV-IR intermediate regions of the minimal area surface. For anisotropic systems, the surfaces' configuration becomes largely modified by spatial anisotropy and series of solutions exist. By imposing the null energy condition we show that the specific heat behaves as $C\propto T^α$ where $α\leq1$, in both systems. In the end, we also present an effective gra…
We study holographic RG flow of the shear viscosity tensor of anisotropic, strongly coupled N=4 super-Yang-Mills plasma by using its type IIB supergravity dual in anisotropic bulk spacetime. We find that the shear viscosity tensor has three independent components in the anisotropic bulk spacetime away from the boundary, and one of the components has a non-trivial RG flow while the other two have a trivial one. For the component of the shear viscosity tensor with non-trivial RG flow, we derive its RG flow equation, and solve the equation analytically to second order in the anisotropy parameter …
We study viscous hydrodynamics of hot conformal field theory plasma with multiple/non-Abelian symmetries in the framework of AdS/CFT correspondence, using a recently proposed method of directly solving bulk gravity in derivative expansion of local plasma parameters. Our motivation is to better describe the real QCD plasma produced at RHIC, incorporating its U(1)^Nf flavor symmetry as well as SU(2)_I non-Abelian iso-spin symmetry. As concrete examples, we choose to study the STU model for multiple U(1)^3 symmetries, which is a sub-sector of 5D N=4 gauged SUGRA dual to N=4 Super Yang-Mills theor…
In this paper, we extend the work on the AdS/QCD model to quadratic gravity to gain insight into the influence of gravity. We obtain an anisotropic black brane solution to a $5D$ Einstein-Gauss-Bonnet-two Maxwell-dilaton system. The background is specified by an arbitrary exponent, a dilaton field, a time component of the first Maxwell field, and a magnetic component of the second Maxwell field. The system in three cases has been investigated and in each case the effect of the parameter of theory, the anisotropic parameter has been considered. The blackening function supports the thermodynamic…
We consider the AdS$_4$ RN black hole and work out the momentum dependent hydrodynamic analysis for the vector modes. We also perform the spectral function calculation of the dual field theory. As an application, we consider the permittivity and permeability and find that for low frequency regime, the index of refraction is found to be negative, supporting the claim made in ref.\cite{amariti} for AdS$_5$. We also find that at static limit the medium has the zero permeability, a character of the superconductivity .
