Strongly interacting matter undergoes a crossover phase transition at high temperatures T ∼ 10 12 K and zero net-baryon density. A fundamental question in the theory of strong interactions, Quantum Chromodynamics (QCD), is whether a hot and dense system of quarks and gluons displays critical phenomena when doped with more quarks than antiquarks, where net-baryon number fluctuations diverge. Recent lattice QCD work indicates that such a critical point can only occur in the baryon dense regime of the theory, which defies a description from first principles calculations. Here we use the holographic gauge/gravity correspondence to map the fluctuations of baryon charge in the dense quark-gluon liquid onto a numerically tractable gravitational problem involving the charge fluctuations of holographic black holes. This approach quantitatively reproduces ab initio results for the lowest order moments of the baryon fluctuations and makes predictions for the higher order baryon susceptibilities and also for the location of the critical point, which is found to be within the reach of heavy ion collision experiments.

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-order in the derivative expansion. We also give an estimate for the temperature dependence of 11 other transport coefficients taking into account the simplest contribution from non-conformal effects that appear near the QCD crossover phase transition. Using these results, we construct an Israel-Stewart-like theory in flat spacetime containing 13 of these 17 transport coefficients that should be suitable for phenomenological applications in the context of numerical hydrodynamic simulations of the strongly-coupled, non-conformal quark-gluon plasma. Using several different approximations, we give parametrizations for the temperature dependence of all the second-order transport coefficients that appear in this theory in a format that can be easily implemented in existing numerical hydrodynamic codes.

Lattice data for the QCD equation of state and the baryon susceptibility near the crossover phase transition (at zero baryon density) are used to determine the input parameters of a 5-dimensional Einstein-Maxwell-Dilaton holographic model that provides a consistent holographic framework to study both equilibrium and out-of-equilibrium properties of a hot and baryon rich strongly coupled quark-gluon plasma (QGP). We compare our holographic equation of state computed at nonzero baryon chemical potential, µ B , with recent lattice calculations and find quantitative agreement for the pressure and the speed of sound for µ B ≤ 400 MeV. This holographic model is used to obtain holographic predictions for the temperature and µ B dependence of the drag force and the Langevin diffusion coefficients associated with heavy quark jet propagation as well as the jet quenching parameter q and the shooting string energy loss of light quarks in the baryon dense plasma. We find that the energy loss of heavy and light quarks generally displays a nontrivial, fast-varying behavior as a function of the temperature near the crossover. Moreover, energy loss is also found to generally increase due to nonzero baryon density effects even though this strongly coupled liquid cannot be described in terms of well defined quasiparticle excitations. Furthermore, to get a glimpse of how thermalization occurs in a hot and baryon dense QGP, we study how the lowest quasinormal mode of an external massless scalar disturbance in the bulk is affected by a nonzero baryon charge. We find that the equilibration time associated with the lowest quasinormal mode decreases in a dense medium.

Five dimensional black hole solutions that describe the QCD crossover transition seen in (2 + 1)-flavor lattice QCD calculations at zero and nonzero baryon densities are used to obtain predictions for the baryon susceptibility, baryon conductivity, baryon diffusion constant, and thermal conductivity of the strongly coupled quark-gluon plasma in the range of temperatures 130 MeV ≤ T ≤ 300 MeV and baryon chemical potentials 0 ≤ µB ≤ 400 MeV. Diffusive transport is predicted to be suppressed in this region of the QCD phase diagram, which is consistent with the existence of a critical end point at larger baryon densities. We also calculate the fourth-order baryon susceptibility at zero baryon chemical potential and find quantitative agreement with recent lattice results. The baryon transport coefficients computed in this paper can be readily implemented in state-of-the-art hydrodynamic codes used to investigate the dense QGP currently produced at RHIC's low energy beam scan.Keywords: Quark-gluon plasma, gauge/gravity duality, baryon density, transport coefficients.1. Introduction. After more than a decade of intense experimental [1-5] and theoretical investigation, it is now widely believed that the strongly interacting quark-gluon plasma (QGP) formed in high energy ultrarelativistic heavy ion collisions at RHIC and LHC behaves as a nearly perfect relativistic fluid [6]. This surprising feature of the QGP may be best illustrated by the very small value of its shear viscosity to entropy density ratio, η/s ∼ 0.2, which has been extracted from comparisons between viscous relativistic hydrodynamic modeling and experimental data (for a recent review, see [7]). Neither ordinary hadronic transport [8] nor weak coupling calculations [9] have been able to explain such a small value for this ratio in QCD, though alternative explanations have been proposed [10][11][12][13] that rely on the appearance of a different set of degrees of freedom at the crossover transition.

We employ an Einstein-Maxwell-Dilaton (EMD) holographic model, which is known to be in good agreement with lattice results for the QCD equation of state with (2 + 1) flavors and physical quark masses, to investigate the temperature and baryon chemical potential dependence of the susceptibilities, conductivities, and diffusion coefficients associated with baryon, electric, and strangeness conserved charges. We also determine how the bulk and shear viscosities of the plasma vary in the plane of temperature and baryon chemical potential. The diffusion of conserved charges and the hydrodynamic viscosities in a baryon rich quark-gluon plasma are found to be suppressed with respect to the zero net baryon case. The transition temperatures associated with equilibrium and non-equilibrium quantities are determined as a function of the baryon chemical potential for the first time. Because of the crossover nature of the QCD phase transition even at moderately large values of the chemical potential, we find that the transition temperatures associated with different quantities are spread in the interval between 130 − 200 MeV and they all decrease with increasing baryon chemical potential.

We present a holographic perspective on momentum transport in strongly coupled, anisotropic non-Abelian plasmas in the presence of strong magnetic fields. We compute the anisotropic heavy quark drag forces and Langevin diffusion coefficients and also the anisotropic shear viscosities for two different holographic models, namely, a top-down deformation of strongly coupled N = 4Super-Yang-Mills (SYM) theory triggered by an external Abelian magnetic field, and a bottomup Einstein-Maxwell-dilaton (EMD) model which is able to provide a quantitative description of lattice QCD thermodynamics with (2 + 1)-flavors at both zero and nonzero magnetic fields. We find that, in general, energy loss and momentum diffusion through strongly coupled anisotropic plasmas are enhanced by a magnetic field being larger in transverse directions than in the direction parallel to the magnetic field. Moreover, the anisotropic shear viscosity coefficient is smaller in the direction of the magnetic field than in the plane perpendicular to the field, which indicates that strongly coupled anisotropic plasmas become closer to the perfect fluid limit along the magnetic field. We also present, in the context of the EMD model, holographic predictions for the entropy density and the crossover critical temperature in a wider region of the (T, B) phase diagram thathas not yet been covered by lattice simulations. Our results for the transport coefficients in the phenomenologically realistic magnetic EMD model could be readily used as inputs in numerical codes for magnetohydrodynamics.

Lattice data for the QCD equation of state and the magnetic susceptibility computed near the crossover transition at zero magnetic field are used to determine the input parameters of a five dimensional Einstein-Maxwell-Dilaton holographic model. Once the model parameters are fixed at zero magnetic field, one can use this holographic construction to study the effects of a magnetic field on the equilibrium and transport properties of the quark-gluon plasma. In this paper we use this model to study the dependence of the crossover temperature with an external magnetic field. Our results for the pressure of the plasma and the crossover temperature are in quantitative agreement with current lattice data for values of the magnetic field 0 ≤ eB 0.3 GeV 2 , which is the relevant range for ultrarelativistic heavy ion collision applications.

We review two methods used to approach the condensation of defects phenomenon. Analyzing in details their structure, we show that in the limit where the defects proliferate until occupy the whole space these two methods are dual equivalent prescriptions to obtain an effective theory for the phase where the defects (like monopoles or vortices) are completely condensed, starting from the fundamental theory defined in the normal phase where the defects are diluted.Comment: 7 pages, major modifications. Version accepted for publication in Physics Letters