We study effective relaxation time of viscous hydrodynamics of strongly coupled non-conformal gauge theory plasma using gauge theory/string theory correspondence. We compute leading corrections to the conformal plasma relaxation time from the relevant deformations due to dim-2 and dim-3 operators. We discuss in details the relaxation time tau_eff of N=2^* plasma. For a certain choice of masses this theory undergoes a phase transition with divergent specific heat c_V ~ |1-T_c/T|^(-1/2). Although the bulk viscosity remains finite all the way to the critical temperature, we find that tau_eff diverges near the critical point as tau_eff ~ |1-T_c/T|^(-1/2).
Following recent formulation of second order relativistic viscous hydrodynamics for conformal fluids, we compute finite coupling corrections to the relaxation time of N=4 supersymmetric Yang-Mills plasma. The result is expected to be universal for any strongly coupled conformal gauge theory plasma in four dimensions.
In this paper, we study suppression of light quark in strongly coupled non-conformal plasmas using the AdS/CFT correspondence. The well-known falling string profile in the bulk is considered as light quark moving through the plasma. The maximum distance which string with energy E can travel before falling through the horizon is interpreted as thermalization distance of light quark in the hot-strongly coupled plasma. Our numerical results show that the thermalization distance of light quark increases by increasing deviation from conformal invariance. The relation between this distance and the e…
We determine analytically the dependence of the approach to thermal equilibrium of strongly coupled plasmas on the breaking of scale invariance. The theories we consider are the holographic duals to Einstein gravity coupled to a scalar with an exponential potential. The coefficient in the exponent, $X$, is the parameter that controls the deviation from the conformally invariant case. For these models we obtain analytic solutions for the plasma expansion in the late-time limit, under the assumption of boost-invariance, and we determine the scaling behaviour of the energy density, pressure, and …
We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously determines the equilibrium equation of the state, and the shear viscosity of the gauge theory plasma. While the absence of the leading pole singularities in the gravitational curvature invariants at th…
Using gauge theory/gravity duality we study sound wave propagation in strongly coupled non-conformal gauge theory plasma. We compute the speed of sound and the bulk viscosity of N=2^* supersymmetric SU(N_c) Yang-Mills plasma at a temperature much larger than the mass scale of the theory in the limit of large N_c and large 't Hooft coupling. The speed of sound is computed both from the equation of state and the hydrodynamic pole in the stress-energy tensor two-point correlation function. Both computations lead to the same result. Bulk viscosity is determined by computing the attenuation constan…
We analysis physical observables of heavy quarks in gravity models describing strongly coupled non-conformal plasmas with anisotropy via the gauge/gravity duality. The focus lies on the binding energy of static quark-antiquark $(q\bar q$-)pairs, the maximum distance (screening distance) of a bound $q\bar q$-pair and the drag force on uniformly moving quarks in the hot plasma. In order to discover universal behavior in the observables, the computations are worked out in a two parameter deformation of pure gravity in $AdS_5$ spacetime with a black brane which is assumed to be dual to a respectiv…
We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously determines the equilibrium equation of the state, and the shear viscosity of the gauge theory plasma. While the absence of the leading pole singularities in the gravitational curvature invariants at th…
Gauge/string correspondence provides an efficient method to investigate gauge theories. In this talk we discuss the results of the paper (to appear) by P. Benincasa, A. Buchel and A. O. Starinets, where the propagation of sound waves is studied in a strongly coupled non-conformal gauge theory plasma. In particular, a prediction for the speed of sound as well as for the bulk viscosity is made for the N=2* gauge theory in the high temperature limit. As expected, the results achieved show a deviation from the speed of sound and the bulk viscosity for a conformal theory. It is pointed out that suc…
We use top-down gauge theory/string theory correspondence to compute relaxation rates in strongly coupled nonconformal gauge theory plasma. We compare models with difference mechanisms of breaking the scale invariance: "hard breaking" (by relevant operators) and "soft breaking" (by marginal operators). We find that the thermalization time of the transverse traceless fluctuations of the stress-energy tensor is rather insensitive to the mechanisms of breaking the scale invariance over a large range of the scale-breaking parameter $δ=\frac 13-c_s^2$. We comment on the relevance of the results to …
In this study, the gauge/string duality is used to investigate the dynamics of a moving heavy quark in a strongly coupled, non-conformal plasma. The drag force in this non-conformal model is smaller than that of $\mathcal{N} = 4$ supersymmetric Yang-Mills (SYM) plasma and decreases as the level of non-conformality is increased. At intermediate temperatures, the world-sheet temperature, which is derived numerically by calculating the world-sheet horizon, deviates from its conformal value, but at high temperatures, it tends to its conformal value.
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 fluctuations around equilibrium in a class of strongly interacting non-conformal plasmas using holographic techniques. In particular we calculate the quasi-normal mode spectrum of black hole backgrounds that approach to Chamblin-Reall plasmas in the IR. In a specific limit, related to the exact linear-dilaton background in string theory, we observe that the plasma approaches criticality and we obtain the quasi-normal spectrum analytically. We regulate the critical limit by gluing the IR geometry that corresponds to the non-conformal plasma to a part of AdS space-time in the UV. Near c…
We consider possible conformal field theory (CFT) descriptions of the various inertial ranges that exist in $2d$ duality invariant Magnetohydrodynamics. Such models arise as effective theories of dyonic plasmas in 3 dimensions in which all fields are independent of the third coordinate. We find new constraints on the allowed CFT's compared to those that may describe turbulence in $2d$ plasmas of electric charges only. The predictions from CFT concerning equipartition of energy amongst the electric and magnetic fields are discussed, and quantities exhibiting universal scaling are derived.
Gauge/string duality is a potentially important framework for addressing the properties of the strongly coupled quark gluon plasma produced at RHIC. However, constructing an actual string theory dual to QCD has so far proven elusive. In this paper, we take a partial step towards exploring the QCD plasma by investigating the thermodynamics of a non-conformal system, namely the N=2^* theory, which is obtained as a mass deformation of the conformal N=4 gauge theory. We find that at temperatures of order the mass scale, the thermodynamics of the mass deformed plasma is surprisingly close to that o…
A novel technique is used to compute the bulk viscosity of high temperature holographic gauge theory plasmas with softly broken conformal symmetry. Working in a black hole background which corresponds to a non-trivial solution to the Navier-Stokes equation, and using a Ward identity for the trace of the stress-energy tensor, it is possible to obtain an analytic expression for the bulk viscosity. This can be used to verify the high temperature limit of a conjectured bound on the bulk viscosity for these theories. The bound is saturated when the conformal symmetry-breaking operator becomes margi…
We study the process of relaxation back to thermal equilibrium in $(1+1)$-dimensional conformal field theory at finite temperature. When the size of the system is much larger than the inverse temperature, perturbations decay exponentially with time. On the other hand, when the inverse temperature is large, the relaxation is oscillatory with characteristic period set by the size of the system. We then analyse the intermediate regime in two specific models, namely free fermions, and a strongly coupled large $\tt k$ conformal field theory which is dual to string theory on $(2+1)$-dimensional anti…
We present evidence for the universality of the shear viscosity of conformal gauge theory plasmas beyond infinite coupling. We comment of subtleties of computing the shear viscosity in effective models of gauge/gravity correspondence rather than in string theory.
Motivated by recent studies of deep inelastic scattering (DIS) off the $\mathcal{N}=4$ super-Yang-Mills (SYM) plasma, holographically dual to $AdS_5\times S^5$ black hole, we in this note use the spacelike flavor current to probe the internal structure of one holographic quark-gluon plasma, which is described by the Sakai-Sugimoto model at high temperature phase (i.e., the chiral symmetric phase). The plasma structure function is extracted from the retarded flavor current-current correlator. Our main aim here is to explore the effect of non-conformality on these physical quantities. As usual, …
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, …
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.
We compute the dynamical relaxation times for chiral transport phenomena in strongly coupled regime using the AdS/CFT correspondence. These relaxation times can be a useful proxy for the dynamical time scale for achieving equilibrium spin-polarization of quasi-particles in the presence of magnetic field and fluid vorticity. We identify the Kubo relations for these relaxation times and clarify some previous issues regarding time-dependence of the Chiral Vortical Effect. We study the consequences of imposing time-reversal invariance on parity-odd thermal noise fluctuations that are related to ch…
The drag of a heavy quark and the jet quenching parameter are studied in the strongly coupled N=2* plasma using the AdS/CFT correspondence. Both increase in units of the spatial string tension as the theory departs from conformal invariance. The description of heavy quark dynamics using a Langevin equation is also considered. It is found that the difference between the velocity dependent factors of the transverse and longitudinal momentum broadening of the quark admit an interpretation in terms of relativistic effects, so the distribution is spherical in the quark rest frame. When conformal in…
We study the equilibrium and near-equilibrium properties of a holographic five-dimensional model consisting of Einstein gravity coupled to a scalar field with a non-trivial potential. The dual four-dimensional gauge theory is not conformal and, at zero temperature, exhibits a renormalisation group flow between two different fixed points. We quantify the deviations from conformality both in terms of thermodynamic observables and in terms of the bulk viscosity of the theory. The ratio of bulk over shear viscosity violates Buchel's bound. We study relaxation of small-amplitude, homogeneous pertur…
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 analyze the large frequency behavior of the spectral densities that govern the generalized Langevin diffusion process for a heavy quark in the context of the gauge/gravity duality. The bare Langevin correlators obtained from the trailing string solution have a singular short-distance behavior. We argue that the proper dressed spectral functions are obtained by subtracting the zero-temperature correlators. The dressed spectral functions have a sufficiently fast fall-off at large frequency so that the Langevin process is well defined and the dispersion relations are satisfied. We identify the…
We continue the study initiated in [arXiv:1708.02252] of the fluctuations of a strongly-coupled non-conformal plasma described holographically by Einstein gravity coupled to a dilaton with an exponential potential. The plasma approaches a critical point of a continuous phase transition in a specific limit, where the metric becomes a linear-dilaton background. This results to an analytic description of the quasi-normal mode spectrum, that can be extended perturbatively in the deviation away from the critical point. In the previous paper we showed that at criticality the quasinormal frequencies …
We numerically simulate gravitational shock wave collisions in a holographic model dual to a non-conformal four-dimensional gauge theory. We find two novel effects associated to the non-zero bulk viscosity of the resulting plasma. First, the hydrodynamization time increases. Second, if the bulk viscosity is large enough then the plasma becomes well described by hydrodynamics before the energy density and the average pressure begin to obey the equilibrium equation of state. We discuss implications for the quark-gluon plasma created in heavy ion collision experiments.
Recently Liu, Rajagopal and Wiedemann (LRW) [hep-ph/0605178] proposed a first principle, nonperturbative quantum field theoretic definition of ``jet quenching parameter'' \hat{q} used in models of medium-induced radiative parton energy loss in nucleus-nucleus collisions at RHIC. Relating \hat{q} to a short-distance behavior of a certain light-like Wilson loop, they used gauge theory-string theory correspondence to evaluate \hat{q} for the strongly coupled N=4 SU(N_c) gauge theory plasma. We generalize analysis of LRW to strongly coupled non-conformal gauge theory plasma. We find that a jet que…
We study the screening length L_s of a heavy quark-antiquark pair in strongly coupled gauge theory plasmas flowing at velocity v. Using the AdS/CFT correspondence we investigate, analytically, the screening length in the ultra-relativistic limit. We develop a procedure that allows us to find the scaling exponent for a large class of backgrounds. We find that for conformal theories the screening length is (boosted energy density)^{-1/d}. As examples of conformal backgrounds we study R-charged black holes and Schwarzschild-anti-deSitter black holes in (d+1)-dimensions. For non-conformal theories…
Experiments at the Relativistic Heavy Ion Collider (RHIC) have measured the net polarization of $Λ$ and $\barΛ$ hyperons and attributed it to a coupling between their spin and the vorticity of the fluid created in heavy ion collisions. Equipartition of energy is generally assumed, but the dynamical mechanism which polarizes them has yet to be determined. We consider two such mechanisms: vorticity fluctuations and helicity flip in scatterings between strange quarks and light quarks and gluons. With reasonable parameters both mechanisms lead to equilibration times orders of magnitude too large t…
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…
In the present work, we have studied the collective behaviour of a chiral plasma with first and second order dissipative corrections allowed by conformal symmetry. We have derived dispersion relations for ideal, first order and second order MHD for the chiral plasma. We have also used our results to explain the observed pulsar kicks.
This is the first of two lectures on a new powerful technique employed by Brown, Preston, and Singleton (BPS) to calculate transport quantities in a plasma. This exposition will be self-contained and intended for those who are not specialists in quantum field theory, where the technique of dimensional continuation exploited by BPS first arose. The method is highlighted by the interesting analogy between the Coulomb logarithm of Lyman Spitzer on the one hand, and the Lamb shift as calculated by Hans Bethe on the other. BPS employed the method in a novel way that provides the leading and sublead…
We discuss thermodynamic properties of open confining strings introduced via static sources in the vacuum of Yang-Mills theory. We derive new sum rules for the chromoelectric and chromomagnetic condensates and use them to show that the presence of the confining string lowers the gluonic pressure in the bulk of the system. The pressure deficit of the gluon plasma is related to the potential energy in the system of heavy quarks and anti-quarks in the plasma.
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 nonlinear transport features of inhomogeneous chiral plasma in the presence of electromagnetic fields, in rotating coordinates are studied within the relaxation time approach. The chiral distribution functions up to second order in the electric field in rotating coordinates and the derivatives of chemical potentials are established by solving the Boltzmann transport equation. First, the vector and axial current densities in the weakly ionized chiral plasma for vanishing magnetic field are calculated. They involve the rotational analogues of the Hall effect as well as several new terms aris…
We consider a simple extension to the previously found gravity solution corresponding to a boost invariant Bjorken plasma, by allowing components that are asymmetric under parity flipping of the spacetime rapidity. Besides the question whether this may have a realization in collisions of different species of projectiles, such as lead-gold collision, our new time dependent gravity background can serve as a test ground for the recently proposed second order conformal viscous hydrodynamics. We find that non-trivial parity-asymmetric effects start to appear at second order in late time expansion, …
We extend our previous analysis of holographic heavy ion collisions in non-conformal theories. We provide a detailed description of our numerical code. We study collisions at different energies in gauge theories with different degrees of non-conformality. We compare four relaxation times: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value), the isotropization time (when the longitudinal and transverse pressures approach each other) and the condensate relaxation time (when the expectation value of a…
