The cascading gauge theory of Klebanov et.al realizes a soluble example of gauge/string correspondence in a non-conformal setting. Such a gauge theory has a strong coupling scale Lambda, below which it confines with a chiral symmetry breaking. A holographic description of a strongly coupled cascading gauge theory plasma is represented by a black brane solution of type IIB supergravity on a conifold with fluxes. A characteristic parameter controlling the high temperature expansion of such plasma is 1/ln(T/Lambda). In this paper we study the speed of sound and the bulk viscosity of the cascading gauge theory plasma to order 1/ln(T/Lambda)^4. We find that the bulk viscosity satisfies the bound conjectured in arXiv:0708.3459. We comment on difficulties of computing the transport coefficients to all orders in T/Lambda. Previously, it was shown that a cascading gauge theory plasma undergoes a first-order deconfinement transition with unbroken chiral symmetry at T_c=0.6141111(3) Lambda. We show here that a deconfined chirally symmetric phase becomes perturbatively unstable at T_u=0.8749(0) T_c. Near the unstable point the specific heat diverges as c_V ~ |1-T_u/T|^(-1/2).
N=1 supersymmetric SU(K+P)xSU(K) cascading gauge theory of Klebanov et.al [1,2] undergoes a first-order finite temperature confinement/deconfinement phase transition at T_c=0.6141111(3) Lambda, where Lambda is the strong coupling scale of the theory. The deconfined phase of the theory, with the unbroken chiral symmetry, extends down to T_u=0.8749(0) T_c, where it becomes perturbatively unstable due to the condensation of the hydrodynamic (sound) modes. We show that at T_cSB =0.882503(0) T_c > T_u the deconfined phase of the cascading plasma is perturbatively unstable towards development of the…
Cascading gauge theories of Klebanov et.al. provide a model within a framework of gauge theory/string theory duality for a four dimensional non-conformal gauge theory with a spontaneously generated mass scale. Using the dual supergravity description we study sound wave propagation in strongly coupled cascading gauge theory plasma. We analytically compute the speed of sound and the bulk viscosity of cascading gauge theory plasma at a temperature much larger than the strong coupling scale of the theory. The sound wave dispersion relation is obtained from the hydrodynamic pole in the stress-energ…
We discuss consistent truncations of type IIB supergravity on resolved warped deformed conifolds with fluxes. These actions represent the gravitational duals to the baryonic branch deformation of the Klebanov-Strassler cascading gauge theory. As an application, we demonstrate that the baryonic branch is lifted in cascading gauge theory plasma.
We compute finite coupling correction to a nonlinear second order hydrodynamic coefficient in the boost invariant expansion of the N=4 supersymmetric Yang-Mills plasma. The result is universal for a large class of strongly coupled four dimensional conformal gauge theories.
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 compute the drag force experienced by a heavy quark that moves through plasma in a gauge theory whose dual description involves arbitrary metric and dilaton fields. As a concrete application, we consider the cascading gauge theory at temperatures high above the deconfining scale, where we obtain a drag force with a non-trivial velocity dependence. We compare our results with the jet-quenching parameter for the same theory, and find qualitative agreement between the two approaches. Conversely, we calculate the jet-quenching parameter for N=4 super-Yang-Mills with an R-charge density (or equi…
We continue our investigations on the relation between hydrodynamic and higher quasinormal modes in the AdS black hole background started in arXiv:0710.4458 [hep-th]. As is well known, the quasinormal modes can be interpreted as the poles of the retarded Green functions of the dual N=4 gauge theory at finite temperature. The response to a generic perturbation is determined by the residues of the poles. We compute these residues numerically for energy-momentum and R-charge correlators. We find that the diffusion modes behave in a similar way: at small wavelengths the residues go over into a for…
Recently Eling and Oz [1] proposed a simple formula for the bulk viscosity of holographic plasma. They argued that the formula is valid in the high temperature (near-conformal) regime, but is expected to break down at low temperatures. We point out that the formula is in perfect agreement with the previous computations of the bulk viscosity of the cascading plasma [2,3], as well as with the previous computations of the bulk viscosity of N=2^* plasma [4,5]. In the latter case it correctly reproduces the critical behaviour of the bulk viscosity in the vicinity of the critical point with the vani…
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.
Quasinormal modes of asymptotically AdS black holes can be interpreted as poles of retarded correlators in the dual gauge theory. To determine the response of the system to small external perturbations it is not enough to know the location of the poles: one also needs to know the residues. We compute them for R-charge currents and find that they are complex except for the hydrodynamic mode, whose residue is purely imaginary. For different quasinormal modes the residue grows with momentum q, whereas for the hydrodynamic mode it behaves as a damped oscillation with distinct zeroes at finite q. S…
The Klebanov-Strassler black hole is a holographic dual to ${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory plasma with spontaneously broken chiral symmetry. The chiral symmetry breaking sector of the cascading gauge theory contains two dimension-3 operators and a single dimension-7 operator. The black hole solution constructed in arXiv:1809.08484 represents the end point of the instability triggered by the condensation of one of the dimension-3 operators. We study here all three branches of the quasinormal modes of the chiral symmetry breaking sector -- there are no ad…
We analytically calculate the low-lying gravitational quasinormal modes of a topological AdS black hole of arbitrary dimension. We show that they are in agreement with corresponding results from the hydrodynamics of the gauge theory plasma on the boundary, as required by the AdS/CFT correspondence. For some of these modes, we obtain a lifetime which is comparable to or longer than the longest lifetime of perturbations of spherical black holes. Thus, these modes are expected to play an important role in the late time behavior of the gauge theory plasma.
We compute the radius of convergence of the linearized relativistic hydrodynamic expansion around a non-trivially rotating strongly coupled N=4 Super-Yang-Mills plasma. Our results show that the validity of hydrodynamics is sustained and can even get enhanced in a highly vortical quark-gluon plasma, such as the one produced in heavy-ion collisions. The hydrodynamic dispersion relations are computed using a rotating background that is an analytic solution of the ideal hydrodynamic equations of motion with non-vanishing angular momentum and large vorticity gradients, giving rise to a particular …
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 talk I will describe various features of time dependent dynamics of strongly coupled plasma from the perspective of the AdS/CFT correspondence. I will take as an example boost invariant plasma flow and concentrate on the properties of hydrodynamic expansion, thermalization versus hydrodynamization and some features of nonequilibrium behaviour.
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 study causal hydrodynamics (Israel-Stewart theory) of gauge theory plasmas from the AdS/CFT duality. Causal hydrodynamics requires new transport coefficients (relaxation times) and we compute them for a number of supersymmetric gauge theories including the N=4 SYM. However, the relaxation times obtained from the "shear mode" do not agree with the ones from the "sound mode," which implies that the Israel-Stewart theory is not a sufficient framework to describe the gauge theory plasmas.
The contribution presents a summary of the Gauge/Gravity approach to the study of hydrodynamic flow of the quark-gluon plasma formed in heavy-ion collisions. Considering the ideal case of a supersymmetric Yang-Mills theory for which the AdS/CFT correspondence gives a precise form of the Gauge/Gravity duality, the properties of the strongly coupled expanding plasma are put in one-to-one correspondence with the metric of a 5-dimensional black hole moving away in the 5th dimension and its deformations consistent with the relevant Einstein equations. Several recently studied aspects of this framew…
By making use of a covariant formulation of the chiral kinetic theory in the relaxation-time approximation, we derive the first-order dissipative hydrodynamics equations for a charged chiral plasma with background electromagnetic fields. We identify the global equilibrium state for a rotating chiral plasma confined to a cylindrical region with realistic boundary conditions. Then, by using linearized hydrodynamic equations, supplemented by the Maxwell equations, we study hydrodynamic modes of magnetized rotating chiral plasma in the regimes of high temperature and high density. We find that, in…
There is mounting evidence suggesting that relativistic hydrodynamics becomes relevant for the physics of quark-gluon plasma as the result of nonhydrodynamic modes decaying to an attractor apparent even when the system is far from local equilibrium. Here we determine this attractor for Bjorken flow in N=4 supersymmetric Yang-Mills theory using Borel summation of the gradient expansion of the expectation value of the energy momentum tensor. By comparing the result to numerical simulations of the flow based on the AdS/CFT correspondence we show that it provides an accurate and unambiguous approx…
The stress-energy tensor of a quark moving through a strongly coupled N=4 supersymmetric Yang-Mills plasma is evaluated using gauge/string duality. The accuracy with which the resulting wake, in position space, is reproduced by hydrodynamics is examined. Remarkable agreement is found between hydrodynamics and the complete result down to distances less than 2/T away from the quark. In performing the gravitational analysis, we use a relatively simple formulation of the bulk to boundary problem in which the linearized Einstein field equations are fully decoupled. Our analysis easily generalizes t…
Relativistic hydrodynamics simulations of quark-gluon plasma play a pivotal role in our understanding of heavy ion collisions at RHIC and LHC. They are based on a phenomenological description due to Mueller, Israel, Stewart (MIS) and others, which incorporates viscous effects and ensures a well-posed initial value problem. Focusing on the case of conformal plasma we propose a generalization which includes, in addition, the dynamics of the least damped far-from-equilibrium degree of freedom found in strongly coupled plasmas through the AdS/CFT correspondence. We formulate new evolution equation…
A novel description of kinetic theory dynamics is proposed in terms of resummed moments that embed information of both hydrodynamic and non-hydrodynamic modes. The resulting expansion can be used to extend hydrodynamics to higher orders in a consistent and numerically efficient way; at lowest order it reduces to an Israel-Stewart-like theory. This formalism is especially suited to investigate the general problem of particles interacting with fields. We tested the accuracy of this approach against the exact solution of the coupled Boltzmann-Vlasov-Maxwell equations for a plasma in an electromag…
We utilize the fluid-gravity duality to investigate the large order behavior of hydrodynamic gradient expansion of the dynamics of a gauge theory plasma system. This corresponds to the inclusion of dissipative terms and transport coefficients of very high order. Using the dual gravity description, we calculate numerically the form of the stress tensor for a boost-invariant flow in a hydrodynamic expansion up to terms with 240 derivatives. We observe a factorial growth of gradient contributions at large orders, which indicates a zero radius of convergence of the hydrodynamic series. Furthermore…
We study the behavior of quasinormal modes in a top-down holographic dual corresponding to a strongly coupled $\mathcal{N} = 4$ super Yang-Mills plasma charged under a $U(1)$ subgroup of the global $SU(4)$ R-symmetry. In particular, we analyze the spectra of quasinormal modes in the external scalar and vector diffusion channels near the critical point and obtain the behavior of the characteristic equilibration times of the plasma as the system evolves towards the critical point of its phase diagram. Except close to the critical point, we observe that by increasing the chemical potential one ge…
By making use of the chiral kinetic theory in the relaxation-time approximation, we derive an Israel-Stewart type formulation of the hydrodynamic equations for a chiral relativistic plasma made of neutral particles (e.g., neutrinos). The effects of chiral asymmetry are captured by including an additional continuity equation for the axial charge, as well as the leading-order quantum corrections due to the spin of particles. In a formulation of the chiral kinetic theory used, we introduce a symmetric form of the energy-momentum tensor that is suitable for the description of a weakly nonuniform c…
In this paper we obtain holographic formulas for the transport coefficients $κ$ and $τ_π$ present in the second-order derivative expansion of relativistic hydrodynamics in curved spacetime associated with a non-conformal strongly coupled plasma described holographically by an Einstein+Scalar action in the bulk. We compute these coefficients as functions of the temperature in a bottom-up non-conformal model that is tuned to reproduce lattice QCD thermodynamics at zero baryon chemical potential. We directly compute, besides the speed of sound, 6 other transport coefficients that appear at second…
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 report the continuum limits of the speed of sound, c_s, and the specific heat at constant volume, c_v, in quenched QCD at temperatures of 2Tc and 3Tc. At these temperatures, c_s is within 2-sigma of the ideal gas value, whereas c_v differs significantly from the ideal gas. However, both are compatible with results expected in a theory with conformal symmetry. We investigate effective measures of conformal symmetry in the high temperature phase of QCD.
Using holographic duality, we present results for both head-on and off-center collisions of Gaussian shock waves in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory. The shock waves superficially resemble Lorentz contracted colliding protons. The collisions results in the formation of a plasma whose evolution is well described by viscous hydrodynamics. The size of the produced droplet is $R \sim 1/T_{\rm eff}$ where $T_{\rm eff}$ is the effective temperature, which is the characteristic microscopic scale in strongly coupled plasma. These results demonstrate the applicability …
We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravit…
We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant $g$. The spin relaxation rate $Γ_s$ in spin hydrodynamics is shown to be $Γ_s\sim g^4\log(1/g)T (T/M)^2$ in the heavy-quark limit $T/M\ll 1$, which is smaller than the relaxation rate of other non-hydrodynamic modes by additional powers of $T/M$. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, …
Numerical simulations of expanding plasma based on the AdS/CFT correspondence as well as kinetic theory and hydrodynamic models strongly suggest that some observables exhibit universal behaviour even when the system is not close to local equilibrium. This leading behaviour is expected to be corrected by transient, exponentially decaying contributions which carry information about the initial state. Focusing on late times, when the system is already in the hydrodynamic regime, we analyse numerical solutions describing expanding plasma of strongly coupled N=4 supersymmetric Yang-Mills theory and…
The system of neutrino-antineutrino $(ν\barν)$ - plasma is considered taking into account their weak Fermi interaction. New fluid instabilities driven by strong neutrino flux in a plasma are found. The nonlinear stationary as well as nonstationary waves in the neutrino gas are discussed. It is shown that a bunch of neutrinos, drifting with a constant velocity across a homogeneous plasma, can also induce emission of lower energy neutrinos due to scattering, i.e. the decay of a heavy neutrino $ν_{H}$ into a heavy and a light neutrino $ν_L$ ($ν_H\toν_Hν_L$) in a plasma. Furthermore we find that t…
Using a holographic method, we further investigate the relaxation towards the hydrodynamic regime of a boost-invariant non-Abelian plasma taken out-of-equilibrium. In the dual description, the system is driven out-of-equilibrium by boundary sourcing, a deformation of the boundary metric, as proposed by Chesler and Yaffe. The effects of several deformation profiles on the bulk geometry are investigated by the analysis of the corresponding solutions of the Einstein equations. The time of restoration of the hydrodynamic regime is investigated: setting the effective temperature of the system at th…
Microseconds after the Big Bang quarks and gluons formed a strongly-coupled non-conformal liquid driven out-of-equilibrium by the expansion of the Universe. We use holography to determine the non-equilibrium behavior of this liquid in a Friedmann-Lemaitre-Robertson-Walker Universe and develop an expansion for the corresponding entropy production in terms of the derivatives of the cosmological scale factor. We show that the resulting series has zero radius of convergence and we discuss its resurgent properties. Finally, we compute the resummed entropy production rate in de Sitter Universe at la…
Hydrodynamics is nowadays understood as an effective field theory that describes the dynamics of the long-wavelength and slow-time fluctuations of an underlying microscopic theory. In this work we extend the relativistic hydrodynamics to third order in the gradient expansion for neutral fluids in a general curved spacetime of $d$ dimensions. We find 58 new transport coefficients, 19 due to third-order scalar corrections and 39 due to tensorial corrections. In the particular case of a conformal fluid, the number of new transport coefficients is reduced to 19, all of them due to third-order tens…
The near zone energy-momentum tensor of a supersonic heavy quark jet moving through a strongly-coupled $\mathcal{N}=4$ SYM plasma is analyzed in terms of first-order Navier-Stokes hydrodynamics. It is shown that the hydrodynamical description of the near quark region worsens with increasing quark velocities. For realistic quark velocities, $v=0.99$, the non-hydrodynamical region is located at a narrow band surrounding the quark with a width of approximately $3/πT$ in the direction parallel to the quark's motion and with a length of roughly $10/πT$ in the perpendicular direction. Our results ca…
We report on the approach towards the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at tau=0. The results are obtained through numerical solution of Einstein's equations for the dual geometries, as described in detail in the companion article arXiv:1203.0755. Despite the very rich far-from-equilibrium evolution, we find surprising regularities in the form of clear correlations between initial entropy and total produced entropy, as well as between initial entropy and the temperature at thermalization, unde…
