In this paper, the Einstein AdS black brane solution in the presence of a string cloud in the context of d-dimensional massive gravity is introduced. The ratio of shear viscosity to entropy density for this solution violates the KSS bound by applying the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of string cloud in any arbitrary dimensions.
We propose a lower bound on bulk viscosity of strongly coupled gauge theory plasmas. Using explicit example of the N=2^* gauge theory plasma we show that the bulk viscosity remains finite at a critical point with a divergent specific heat. We present an estimate for the bulk viscosity of QGP plasma at RHIC.
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…
Motivated by gauge theory/string theory correspondence, a lower bound on the bulk viscosity of strongly coupled gauge theory plasma was proposed in arXiv:0708.3459. We consider strongly coupled N=4 supersymmetric Yang-Mills plasma compactified on a two-manifold of constant curvature beta. We show that the effective (1+1)-dimensional hydrodynamic description of the system is governed by the bulk viscosity violating the bound of arXiv:0708.3459, once beta<0.
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 use gauge theory/string theory correspondence to study the bulk viscosity of strongly coupled, mass deformed SU(N_c) N=4 supersymmetric Yang-Mills plasma, also known as N=2^* gauge theory. For a wide range of masses we confirm the bulk viscosity bound proposed in arXiv:0708.3459. For a certain choice of masses, the theory undergoes a phase transition with divergent specific heat c_V ~ |1-T_c/T|^(-1/2). We show that, although bulk viscosity rapidly grows as T -> T_c, it remains finite in the vicinity of the critical point.
Black hole membrane paradigm states that a certain viscous membrane seems to be sitting on a stretched horizon of a black hole from the viewpoint of a distant observer. We show that the shear viscosity of the fictitious membrane can be reproduced by a highly excited string covering the stretched horizon except for a numerical coefficient.
The Einstein AdS black brane with a cloud of strings background in context of massive gravity is introduced. There is a momentum dissipation on the boundary because of graviton mass on the bulk. The ratio of shear viscosity to entropy density is calculated for this solution. This value violates the KSS bound if we apply the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of the cloud of strings.
We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in arXiv:0708.34…
In four dimensions, we consider a generalized scalar-tensor theory where the coupling functions only depend on the kinetic term of the scalar field. For this model, we obtain a set of hairy Anti-de-Sitter black hole solutions, allowing us to calculate the computational complexity, according to the Complexity equals Action conjecture. To perform this, the system contains a particle moving on the boundary, corresponding to the insertion of a fundamental string in the bulk. The effect string is given by the Nambu-Goto term, analyzing the time development of this system. Together with the above, w…
We show that the cosmic bulk viscosity estimated in our previous works is sufficient to bridge the $H_0$ value inferred from observations of the early universe with the value inferred from the local (late) universe.
Hydro-kinetic theory of thermal fluctuations is applied to a non-conformal relativistic fluid. Solving the hydro-kinetic equations for an isotropically expanding background we find that hydrodynamic fluctuations give ultraviolet divergent contributions to the energy-momentum tensor. After shifting the temperature to account for the energy of non-equilibrium modes, the remaining divergences are renormalized into local parameters, e.g. pressure and bulk viscosity. We also confirm that the renormalization of the pressure and bulk viscosity is universal by computing them for a Bjorken expansion. T…
In this work we compute the entropy density, speed of sound, and the resulting impact on the bulk viscosity to shear viscosity ratio of an ideal Quark Gluon Plasma when the effects of a generalized uncertainty principle are taken into consideration. When the parameter of the generalized uncertainty principle tends to zero, i.e., $α\rightarrow 0$, we obtain the value of the speed of sound for the ideal gas of massless particles, i.e., $c^{2}_{s}\rightarrow 1/3$, and we recover the expected result that the bulk viscosity $ζ\rightarrow 0$ when $α\rightarrow 0$. In addition, in the high temperatur…
We compute the bulk viscosity in holographic models dual to theories with Lifshitz scaling and/or hyperscaling violation, using a generalization of the bulk viscosity formula derived in arXiv:1103.1657 from the null focusing equation. We find that only a class of models with massive vector fields are truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other holographic models with scalars and/or massless vector fields we find a universal formula in terms of the dynamical exponent and the hyperscaling violation exponent.
We provide a discussion of the bulk viscosity of two-flavor quark plasma, described by the Nambu--Jona-Lasinio model, within the framework of Kubo-Zubarev formalism. This discussion, which is complementary to our earlier study, contains a new, detailed derivation of the bulk viscosity in the case of multiple conserved charges. We also provide some numerical details of the computation of the bulk viscosity close to the Mott transition line, where the dissipation is dominated by decays of mesons into quarks and their inverse processes. We close with a summary of our current understanding of this…
In a recent Letter [Phys. Rev. Lett. 114 091301 (2105)] the cause of the acceleration of the present Universe has been identified with the shear viscosity of an imperfect relativistic fluid even in the absence of any bulk viscous contribution. The gist of this comment is that the shear viscosity, if anything, can only lead to an accelerated expansion over sufficiently small scales well inside the Hubble radius.
We present a simple (microscopic) model in which bulk viscosity plays a role in explaining the present acceleration of the universe. The effect of bulk viscosity on the Friedmann equations is to turn the pressure into an "effective" pressure containing the bulk viscosity. For a sufficiently large bulk viscosity, the effective pressure becomes negative and could mimic a dark energy equation of state. Our microscopic model includes self-interacting spin-zero particles (for which the bulk viscosity is known) that are added to the usual energy content of the universe. We study both background equa…
The null horizon focusing equation is equivalent via the fluid/gravity correspondence to the entropy balance law of the fluid. Using this equation we derive a simple novel formula for the bulk viscosity of the fluid. The formula is expressed in terms of the dependence of scalar fields at the horizon on thermodynamic variables such as the entropy and charge densities. We apply the formula to three classes of gauge theory plasmas: non-conformal branes, perturbations of the N=4 supersymmetric Yang-Mills theory and holographic models of QCD, and discuss its range of applicability.
Based on the previous paper arXiv:1207.5309, we investigate the possibility to find out the bulk viscosity of dual fluid at the finite cutoff surface via gravity/fluid correspondence in Einstein-Maxwell gravity. We find that if we adopt new conditions to fix the undetermined parameters contained in the stress tensor and charged current of the dual fluid, two new terms appear in the stress tensor of the dual fluid. One new term is related to the bulk viscosity term, while the other can be related to the perturbation of energy density. In addition, since the parameters contained in the charged c…
Einstein equations projected on to a black hole horizon gives rise to Navier-Stokes equations. Horizon-fluids typically possess unusual features like negative bulk viscosity and it is not clear whether a statistical mechanical description exists for such fluids. In this work, we provide an explicit derivation of the Bulk viscosity of the horizon-fluid based on the theory of fluctuations a la Kubo. The main advantage of our approach is that our analysis remains for the most part independent of the details of the underlying microscopic theory and hence the conclusions reached here are model inde…
Bulk viscosity is an important transport coefficient that exists in the hydrodynamical limit only when the underlying theory is non-conformal. One example being thermal QCD with large number of colors. We study bulk viscosity in such a theory at low energies and at weak and strong 't Hooft couplings when the temperature is above the deconfinement temperature. The weak coupling analysis is based on Boltzmann equation from kinetic theory whereas the strong coupling analysis uses non-conformal holographic techniques from string and M-theories. Using these, many properties associated with bulk vis…
The ratio of bulk to shear viscosity is expected to exhibit a different behaviour in weakly and in strongly coupled systems. This can be expressed by its dependence on the squared sound velocity. In the high temperature QCD plasma at small running coupling, the viscosity ratio is uniquely determined by a quadratic dependence on the conformality measure, whereas in certain strongly coupled and nearly conformal theories this dependence is linear. Employing an effective kinetic theory of quasiparticle excitations with medium-modified dispersion relation, we analyze the ratio of bulk to shear visc…
We solve second order relativistic hydrodynamics equations for a boost-invariant 1+1-dimensional expanding fluid with an equation of state taken from lattice calculations of the thermodynamics of strongly coupled quark-gluon plasma. We investigate the dependence of the energy density as a function of proper time on the values of the shear viscosity, the bulk viscosity, and second order coefficients, confirming that large changes in the values of the latter have negligible effects. Varying the shear viscosity between zero and a few times s/(4 pi), with s the entropy density, has significant eff…
In this paper the temperature dependence of the $SU(3)$--gluodynamics bulk viscosity is studied within lattice simulations. To carry out this study we measure the correlation function of the trace of the energy-momentum tensor for a set of temperatures within the range $T/T_c \in (0.9, 1.5)$. To extract the bulk viscosity from the correlation function we apply the Backus-Gilbert method and the Tikhonov regularization method. We show that the ratio $ζ/s$ is small in the region $T/T_c \geqslant 1.1-1.2$ and in the vicinity of the transition $T/T_c \leqslant 1.1-1.2$ it quickly rises. Our results…
In this paper, we investigate the viscous modified Chaplygin gas cosmological model. Solutions for different values of the viscosity parameter are obtained using both analytical and numerical methods. We have calculated the deceleration and defined {\em newly} statefinder $\{r, s \}$ pair in D dimensions. It is shown that when $D=4$, the usual statefinder parameters are recovered. Furthermore, we apply the statefinder diagnostic to the MCG model with and without viscosity in $D$ dimensions and explore these parameters graphically.
In this work, we show the dependence of bulk viscosity on Polyakov loop in 3+1 dimensional topologically massive model (TMM). This model contains equally massive non-Abelian gauge fields without spontaneous symmetry breaking. In earlier works, the bulk viscosity was found from the trace anomaly in massless $ϕ^4$ model and Yang-Mills (YM) theory and its dependence on the quantum corrections was established. In TMM, the trace anomaly is absent due to the presence of kinetic term of a two-form field $B$ in the action. This model also provides the dependence of bulk viscosity on the mass of the ga…
We examine the behavior of the spectral function for the trace of the stress tensor in QCD in the two regimes where it is possible to make analytical progress; weak coupling, and close to a second order QCD phase transition. We determine the behavior of the bulk viscosity in each regime. We discuss the problem of analytic continuation of the (lattice) Euclidean correlation function to determine the spectral function. In each case the spectral function has a narrow peak at small frequency; its shape would be challenging to extract accurately from lattice data with error bars.
The microscopic formulas for the shear viscosity $η$, the bulk viscosity $ζ$, and the corresponding relaxation times $τ_π$ and $τ_Π$ of causal dissipative relativistic fluid-dynamics are obtained at finite temperature and chemical potential by using the projection operator method. The non-triviality of the finite chemical potential calculation is attributed to the arbitrariness of the operator definition for the bulk viscous pressure.We show that, when the operator definition for the bulk viscous pressure $Π$ is appropriately chosen, the leading-order result of the ratio, $ζ$ over $τ_Π$, coinc…
Recent studies of the hot QCD matter indicate that the bulk viscosity ($ζ$) of quark-gluon plasma (QGP) rises sharply near the critical point of the QCD phase transition. In this work, we show that such a sharp rise of the bulk viscosity will lead to an effective negative pressure near the critical temperature, $T_{c}$ which in turn drives the Universe to inflate. This inflation has a natural graceful exist when the viscous effect evanesce. We estimate that, depending upon the peak value of $ζ$, universe expands by a factor of $10$ to $80$ times in a very short span ($Δt\sim 10^{-8}$ seconds).…
We investigate dynamic properties of a plasma whose constituents are confining gluons resulting from the Gribov quantization. In a static formulation, this system reproduces qualitatively the pure-glue equation of state and thereby encodes crucial features of the phase transition. The dynamic description proposed in this work allows us to study non-equilibrium transport phenomena with the inclusion of confinement effects. In particular, we determine the non-equilibrium behaviour of the interaction measure (trace anomaly) and find the form of the bulk viscosity coefficient. The latter may be us…
A calculation of the bulk viscosity for the massive Gross-Neveu model at zero fermion chemical potential is presented in the large-$N$ limit. This model resembles QCD in many important aspects: it is asymptotically free, has a dynamically generated mass gap, and for zero bare fermion mass it is scale invariant at the classical level (broken through the trace anomaly at the quantum level). For our purposes, the introduction of a bare fermion mass is necessary to break the integrability of the model, and thus to be able to study momentum transport. The main motivation is, by decreasing the bare …
