We analyze the time evolution of several physical observables, namely the pressure anisotropy, the scalar condensate, the charge density, and also, for the first time, the non-equilibrium entropy for a Bjorken expanding strongly coupled $\mathcal{N}=4$ Supersymmetric Yang-Mills plasma charged under an Abelian $U(1)$ subgroup of the global $SU(4)$ R-symmetry. This represents a far-from-equilibrium, hot and dense strongly coupled quantum fluid with a critical point in its phase diagram. For some sets of initial data preserving all the energy conditions, dynamically driven transient violations of the dominant and the weak energy conditions are observed when the plasma is still far from the hydrodynamic regime. The energy conditions violations get stronger at larger values of the chemical potential to temperature ratio, $μ/T$, indicating that those violations become more relevant as the strongly coupled quantum fluid approaches its critical regime. For some of those energy conditions violations, it is observed a clear correlation with different plateau structures formed in the far from equilibrium entropy, indicating the presence of transient, early time windows where the Bjorken expanding plasma has zero entropy production even while being far from equilibrium. The hydrodynamization of the pressure anisotropy and also the much later thermalization of the scalar condensate are generally found to be delayed, within small relative tolerances, as $μ/T$ is increased towards criticality. The value of $μ/T$ in the medium is enhanced by increasing its initial charge density, and/or also by reducing its initial energy density.
We analytically compute the out-of-equilibrium direct photon production rate and electric conductivity, in a strongly coupled and expanding Bjorken plasma, from holography. Our results are valid at late times where the expanding plasma asymptotes Bjorken hydrodynamics. The out-of-equilibrium rates are substantially harder and larger, early on in the Bjorken expansion phase.
Evolution of spin polarization in the presence of external electric field is studied for collision energies $\sqrt{s_{\rm NN}}=27\,{\rm GeV}$ and $\sqrt{s_{\rm NN}}=200\,{\rm GeV}$. The numerical analysis is done in the perfect-fluid Bjorken-expanding resistive magnetohydrodynamic background and novel results are reported. In particular, we show that the electric field plays a significant role in the competition between expansion and dissipation.
We demonstrate that a Bjorken expanding strongly coupled $\mathcal{N}=4$ Supersymmetric Yang-Mills plasma can display dynamically-driven violations of the dominant and also the weak energy condition during hydrodynamization. In addition, we find that a period of vanishing entropy production in far-from-equilibrium stages induces later violations of the dominant energy condition in the strongly coupled plasma. Such violations cannot occur in a classical description of hydrodynamization and suggest that the inclusion of quantum effects in transport can lead to new phenomena in these regimes, eve…
We use the AdS/CFT correspondence and the holographic softwall model to investigate the Deep Inelastic Scattering (DIS) in the exponentially small $x$ (Bjorken Parameter) regime. We calculate the corresponding structure functions for scalar fields. Using these results we studied the problem of the saturation line in the strong interactions. Our results are consistent with those achieved using other models.
We propose a consistent setup for a holographic dual of Bjorken flow of strongly coupled large-Nc N=4 SYM-theory plasma. We employ Eddington-Finkelstein type coordinates for the dual geometry, and we propose a late-time expansion there. We construct the dual geometry order by order, and we show that the transport coefficients are determined by the regularity of the geometry. We also show that the dual geometry has an apparent horizon hence an event horizon, which covers the singularity at the origin. We prove that the dual geometry is regular at all orders under an appropriate choice of the tr…
In large-$N_c$ conformal field theories with classical holographic duals, inverse coupling constant corrections are obtained by considering higher-derivative terms in the corresponding gravity theory. In this work, we use type IIB supergravity and bottom-up Gauss-Bonnet gravity to study the dynamics of boost-invariant Bjorken hydrodynamics at finite coupling. We analyze the time-dependent decay properties of non-local observables (scalar two-point functions and Wilson loops) probing the different models of Bjorken flow and show that they can be expressed generically in terms of a few field the…
We use gauge/gravity duality to study the dynamics of strongly coupled gauge theories undergoing boost invariant expansion in an arbitrary number of space-time dimensions (D). By keeping the scale of the late-time energy density fixed, we explore the infinite-D limit and study the first few corrections to this expansion. In agreement with other studies, we find that the large-D dynamics are controlled by hydrodynamics and we use our computation to constrain the leading large-D dependence of a certain combination of transport coefficients up to 6-th order in gradients. Going beyond late time ph…
In a system with a Bjorken-flow (BF), considering the inside of a BF as a subsystem for the reason explained in the body text, we compute entanglement entropy appearing in our side holographically . BF consists of many concentrically scattering quark-gluon plasmas created by colliding two masses of hadrons. Our BF is defined in the boundary space in an asymptoticly five-dimensional Anti de-Sitter space with a growing Schwartzshild black hole. %, where its Hawking temperature diminishes with time. In our analysis we can get a parameter prescribing our bulk space-time in terms of the boundary QC…
In this work we use the string/gauge duality within the Softwall Model (SW). In this model a dilaton field is introduced in the action for the fields playing the role of a soft infrared (IR) cutoff. The SW model is very useful as it provides linear Regge trajectories for mesons. Here, using a $10-$dimensional SW model, we calculate the corresponding structure functions for deep inelastic scattering (DIS) in which electrons are scattered off hadrons in a kinematical regime where the hadrons are broken apart, with high virtuality $q$, in the exponentially small $x$ (Bjorken parameter) regime. Ou…
The Crewther-Broadhurst-Kataev (CBK) relation connects the Bjorken function for deep-inelastic sum rules (or the Gross - Llewellyn Smith function) with the Adler function for electron-positron annihilation in QCD; it has been checked to hold up to four loops in perturbation theory. Here we study non-perturbative terms in the CBK relation using a holographic dual theory that is believed to capture properties of QCD. We show that for the large invariant momenta the perturbative CBK relation is exactly satisfied. For the small momenta non-perturbative corrections enter the relation and we calcula…
Based on a holographic far-from-equilibrium calculation of the chiral magnetic effect~(CME) in an expanding quark gluon plasma, we study collisions at various energies. We compute the time evolution of the CME current in the presence of a time-dependent axial charge density and subject to a time-dependent magnetic field. The plasma expansion leads to a dilution of the CME current. We study distinct combinations of how the initial magnetic field and initial axial charge behave with changing initial energy as proposed in previous literature. Most scenarios we consider lead to an increasing time-…
We use the holographic principle to study quark jets with trailing strings in an expanding plasma that asymptotes Bjorken hydrodynamics. We make use of the fact that the trailing string is the locus of the light delay in bulk to obtain the explicit form for quark jets in the expanding plasma. From the trailing string solution we calculate the drag coefficient of a heavy quark in the strongly coupled expanding plasma. The energy scaling of the maximum penetration length of an ultrarelativistic light quark jet using light rays in bulk is estimated.
We consider a gravity dual description of time dependent, strongly interacting large-Nc N=4 SYM. We regard the gauge theory system as a fluid with shear viscosity. Our fluid is expanding in one direction following the Bjorken's picture that is relevant to RHIC experiments. We obtain the dual geometry at the late time that is consistent with dissipative hydrodynamics. We show that the integration constants that cannot be determined by hydrodynamics are given by looking at the horizon of the dual geometry. Relationship between time dependence of the energy density and bulk singularity is also di…
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 ha…
We investigate several hydrodynamization times for an ensemble of different far-from-equilibrium solutions of the strongly coupled $\mathcal{N}=4$ Supersymmetric Yang-Mills plasma undergoing Bjorken flow. For the ensemble of initial data analyzed in the present work, we find that, with typical tolerances between $3\%$ to $5\%$, the average hydrodynamization time associated with the late time convergence of the pressure anisotropy to the corresponding Borel resummed hydrodynamic attractor is approximately equal to the average hydrodynamization time associated with the Navier-Stokes result, whil…
In the AdS/CFT description of four-dimensional QCD matter undergoing Bjorken expansion, does the holographic energy-momentum tensor contain a Casimir-type contribution that should not be attributed to thermal matter? When the bulk isometry ansatz that yielded such a Casimir term for (1+1)-dimensional boundary matter is generalised to a four-dimensional boundary, we show that a Casimir term does not arise, owing to singularities in the five-dimensional bulk solution. The geometric reasons are traced to a difference between the isometries of AdS_3 and AdS_{d+1} for d>=3.
We develop a set of kinetic equations for hydrodynamic fluctuations which are equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations can be coupled to existing second order hydrodynamic codes to incorporate the physics of these fluctuations. We first show that the kinetic response precisely reproduces the renormalization of the shear viscosity and the fractional power ($\propto ω^{3/2}$) which characterizes equilibrium correlators of energy and momentum for a static fluid. Then we use the hydro-kinetic equations to analyze thermal fluctuations for a Bjorken expansion, ev…
Using the Janik-Peschanski dual to a Bjorken flow, a Langevin equation is derived for a heavy quark in an expanding N = 4 supersymmetric Yang-Mills plasma. Such a plasma is characterized by a proper-time dependence of the temperature and corresponds to a system out of equilibrium. The analysis first focuses on a quark at rest in the plasma comoving frame. The case of a quark moving across a longitudinally expanding plasma is then considered. The two-point functions for the random noise acting on such heavy quark probes are computed.
We analyse the global structure of time-dependent geometries dual to expanding plasmas, considering two examples: the boost invariant Bjorken flow, and the conformal soliton flow. While the geometry dual to the Bjorken flow is constructed in a perturbation expansion at late proper time, the conformal soliton flow has an exact dual (which corresponds to a Poincare patch of Schwarzschild-AdS). In particular, we discuss the position and area of event and apparent horizons in the two geometries. The conformal soliton geometry offers a sharp distinction between event and apparent horizon; whereas t…
Recent studies have shown that fluctuations of various types play important roles in the evolution of the fireball created in relativistic heavy ion collisions and bear many phenomenological consequences for experimental observables. The bulk dynamics of the fireball is well described by relativistic hydrodynamic expansion and the fluctuations on top of such expanding background can be studied within the linearized hydrodynamic framework. In this work we present complete and analytic sound wave solutions on top of both Bjorken flow and Hubble flow backgrounds. We also briefly discuss the appli…
We discuss the derivation of dissipative Bjorken hydrodynamics from a Schwarzschild black hole in asymptotically AdS spacetime of arbitrary dimension in the limit of large longitudinal proper time $τ$. Using an appropriate slicing near the boundary, we calculate the Schwarzschild metric to next-to-next-to-leading order in the large $τ$ expansion as well as the dual stress-energy tensor on the boundary via holographic renormalization. At next-to-next-to-leading order, it is necessary to perturb the Schwarzschild metric in order to maintain boost invariance. The perturbation has a power law time…
We study the time evolution of entanglement entropy in expanding universes with various matters. To describe expanding universes holographically, we take into account a braneworld moving in an asymptotic AdS space involving a uniform $p$-brane gas. In the braneworld model, an observer living in the braneworld detects the bulk motion of the braneworld as an expanding universe. We show that the entanglement entropy of expanding universes increases by the volume law in the early time and by the area law in the late time. We further consider the cosmological horizon, which is the border of the vis…
Cosmological phase transitions can proceed via the nucleation of bubbles that subsequently expand and collide. The resulting gravitational wave spectrum depends crucially on the properties of these bubbles. We extend our previous holographic work on planar bubbles to circular bubbles in a strongly-coupled, non-Abelian, four-dimensional gauge theory. This extension brings about two new physical properties. First, the existence of a critical bubble, which we determine. Second, the bubble profile at late times exhibits a richer self-similar structure, which we verify. These results require a new …
In expanding universes, the entanglement entropy must be time-dependent because the background geometry changes with time. For understanding time evolution of quantum correlations, we take into account two distinct holographic models, the dS boundary model and the braneworld model. In this work, we focus on two-dimensional expanding universes for analytic calculation and comparison. Although two holographic models realize expanding universes in totally different ways, we show that they result in the qualitatively same time-dependence for eternal inflation. We further investigate the time-depen…
Due to the absence of a transverse expansion with respect to the beam direction, the Bjorken flow is unable to describe certain observables in heavy ion collisions. This caveat has motivated the introduction of analytical relativistic hydrodynamics (RH) solutions with transverse expansion, in particular, the 3+1 self-similar (SSF) and Gubser flows. Inspired by recent generalizations of the Bjorken flow to the relativistic magnetohydrodynamics (RMHD), we present a procedure for a generalization of RH solutions to RMHD. Our method is mainly based on symmetry arguments. Using this method, we find…
We investigate the impact of hydrodynamic fluctuations on correlation functions in a scale invariant fluid with a conserved $U(1)$ charge. The kinetic equations for the two-point functions of pressure, momentum and heat energy densities are derived within the framework of stochastic hydrodynamics. The leading non-analytic contributions to the energy-momentum tensor as well as the $U(1)$ current are determined from the solutions to these kinetic equations. In the case of a static homogeneous background we show that the long time tails obtained from hydro-kinetic equations reproduce the one-loop…
The D3/D7 system holographically describes an N=2 gauge theory which spontaneously breaks a chiral symmetry by the formation of a quark condensate in the presence of a magnetic field. At finite temperature it displays a first order phase transition. We study out of equilibrium dynamics associated with this transition by placing probe D7 branes in a geometry describing a boost-invariant expanding or contracting plasma. We use an adiabatic approximation to track the evolution of the quark condensate in a heated system and reproduce the phase structure expected from equilibrium dynamics. We then …
We show that in the standard derivation of the holographic dark energy some conceptual issues are present. In particular, the formula used in the literature to avoid black holes is not suitable in expanding universes. A more suitable expression for a holographic motivated dark energy must contain the energy density of the remaining matter content of the universe. However, we show that under some reasonable hypothesis, we can obtain a new physically motivated expression for the holographic dark energy. By considering an appropriate time-dependence of the saturation-level parameter, a de Sitter …
The dynamics of an expanding hadron fluid at temperatures below the chiral transition is studied in the framework of AdS/CFT correspondence. We establish a correspondence between the asymptotic AdS geometry in the 4+1-dimensional bulk with the analog spacetime geometry on its 3+1 dimensional boundary with the background fluid undergoing a spherical Bjorken type expansion. The analog metric tensor on the boundary depends locally on the soft pion dispersion relation and the four-velocity of the fluid. The AdS/CFT correspondence provides a relation between the pion velocity and the critical tempe…
We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with a constant shear viscosity relaxation time. We analytically determine the hydrodynamic attractor of this fluid and discuss its properties. We show for the first time that the slow-roll expansion, a commonly used approach to characterize the attractor, diverges. This is shown to hold also in a conformal plasma. The gradient expansion is found to converge in an example where causality and stability are violated.
To understand the time-dependent quantum correlation in expanding universes, we study the time-dependent entanglement entropy in the braneworld model. If we take into account a generalized string cloud geometry caused by uniformly distributed open strings, cosmologies on the braneworld result in the standard Friedmann-Lemaître-Robertson-Walker cosmologies with various matter contents. On the dual field theory side, open strings are reinterpreted as a fundamental matter, while the black hole mass corresponds to the excitation energy of massless gauge bosons. In this work, we show how the string…
For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a multi-parameter trans-series encoding the non-perturbative dissipative contributions quantified by the Knudsen $Kn$ and inverse Reynolds $Re^{-1}$ numbers. At any given order in the asymptotic expansion of each mode, the transport coefficients get effectively renormalized by summing over all non-perturbative sectors appearing in the trans-series. This gives an eff…
Recently, a lot of effort has been put into describing the thermalization of the quark-gluon plasma using the gauge/gravity duality. In this context we here present a full numerical solution of the early far-from-equilibrium formation of the plasma, which is expanding radially in the transverse plane and is boost invariant along the collision axis. This can model the early stage of a head-on relativistic heavy ion collision. The resulting momentum distribution quickly reaches local equilibrium, after which they can be evolved using ordinary hydrodynamics. We comment on general implications for…
Gravitational holography is argued to render the cosmological constant stable against divergent quantum corrections. This provides a technically natural solution to the cosmological constant problem. Evidence for quantum stability of the cosmological constant is illustrated in a number of examples including, bulk descriptions in terms of delocalized degrees of freedom, boundary screen descriptions on stretched horizons, and non-supersymmetric conformal field theories as dual descriptions of anti-de Sitter space. In an expanding universe, holographic quantum contributions to the stress-energy t…
We propose a new scenario characterizing the transition of the quark-gluon plasma (QGP) produced in heavy-ion collisions from a highly non-equilibrium state at early times toward a fluid described by hydrodynamics at late times. We develop an analogy to the evolution of a quantum mechanical system that is governed by the instantaneous ground states. In the simplest case, these slow modes are "pre-hydrodynamic" in the sense that they are initially distinct from, but evolve continuously into, hydrodynamic modes. For a class of collision integrals, the pre-hydrodynamic mode represents the angular…
We introduce a new foliation of AdS$_5$ black holes such that the conformal boundary takes the form of a $4$-dimensional FLRW spacetime with scale factor $a(t)$. The foliation employs Eddington-Finkelstein-like coordinates and is applicable to a large class of AdS black holes, supported by matter fields or not, considerably extending previous efforts in the literature. We argue that the holographic dual picture of a CFT plasma on a FLRW background provides an interesting prototype to study the nonequilibrium dynamics of expanding plasmas and use holographic renormalization to extract the renor…
In this paper we study the cosmological evolution of the holographic dark energy in a cyclic universe, generalizing the model of holographic dark energy proposed by Li. The holographic dark energy with $c<1$ can realize a quintom behavior; namely, it evolves from a quintessence-like component to a phantom-like one. The holographic phantom energy density grows rapidly and dominates the late-time expanding phase, helping realize a cyclic universe scenario in which the high energy regime is modified by the effects of quantum gravity, causing a turnaround (and a bounce) of the universe. The dynami…
We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the condensate operator. Its accuracy for 3+1-dimensional superconductors is better than 15%. The analysis reveals a simple, and quantitative, explanation for the onset of the superconducting instability, as well as universal features of holographic superconductivity in the large D limit. In particular, this allows to easily compute the effects of backreaction on the cr…
The kinematics and dynamic interpretation of the cosmological expansion is reviewed in a widely accessible manner with emphasis on the acceleration aspect. Virtually all the approaches that can in principle account for the accelerated expansion of the Universe are reviewed, including dark energy as an item in the energy budget of the Universe; modified Einstein equations; and, on a fundamentally new level, the use of the holographic principle.
The formation of frozen classical perturbations from vacuum quantum fluctuations during inflation is described as a unitary quantum process with apparent "decoherence" caused by the expanding spacetime. It is argued that the maximum observable information content per comoving volume in classical modes is subject to the covariant entropy bound at the time those modes decohere, leading to a new quantitative bound on the information contained in frozen field modes in phase space. This bound implies holographic correlations of large-scale cosmological perturbations that may be observable.
We consider two ultrarelativistic shock waves propagating and colliding in five-dimensional Anti-de-Sitter spacetime. By transforming to Rosen coordinates, we are able to find the form of the metric shortly after the collision. Using holographic renormalization, we calculate the energy-momentum tensor on the boundary of AdS space for early times after the collision. Via the gauge-gravity duality, this gives some insights on bulk dynamics of systems created by high energy scattering in strongly coupled gauge theories. We find that Bjorken boost-invariance is explicitely violated at early times …
This article provides an in-depth look at hadron high energy scattering by using gravity dual descriptions of strongly coupled gauge theories. Just like deeply inelastic scattering (DIS) and deeply virtual Compton scattering (DVCS) serve as clean experimental probes into non-perturbative internal structure of hadrons, elastic scattering amplitude of a hadron and a (virtual) "photon" in gravity dual can be exploited as a theoretical probe. Since the scattering amplitude at sufficiently high energy (small Bjorken x) is dominated by parton contributions (= Pomeron contributions) even in strong co…
We use holographic duality to analyze the drag force on, and consequent energy loss of, a heavy quark moving through a strongly coupled conformal fluid with non-vanishing gradients in its velocity and temperature. We derive the general expression for the drag force to first order in the fluid gradients. Using this general expression, we show that a quark that is instantaneously at rest, relative to the fluid, in a fluid whose velocity is changing with time feels a nonzero force. And, we show that for a quark that is moving ultra-relativistically, the first order gradient "corrections" become l…
We analyze the validity of the generalized covariant entropy bound near the apparent horizon of isotropic expanding cosmological models. We encounter violations of the bound for cosmic times smaller than a threshold. By introducing an infrared cutoff we are able to mantain the bound for a radiation dominated universe. We study different physical mechanisms to restore the bound, as a non-additivity of the entropy at a fundamental level and/or a cosmological uncertainty relation.
