1. Opening remarks 2. A heavy ion phenomenology primer 3. Results from lattice QCD at nonzero temperature 4. Introducing the gauge/string duality 5. A duality toolbox 6. Bulk properties of strongly coupled plasma 7. From hydrodynamics for far-from-equilibrium dynamics 8. Probing strongly coupled plasma 9. Quarkonium mesons in strongly coupled plasma 10. Concluding remarks and outlook Appendixes References Index.

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Gauge/String Duality, Hot QCD and Heavy Ion Collisions

Over the last decade, both experimental and theoretical advances have brought the need for strong coupling techniques in the analysis of deconfined QCD matter and heavy ion collisions to the forefront. As a consequence, a fruitful interplay has developed between analyses of strongly-coupled non-abelian plasmas via the gauge/string duality (also referred to as the AdS/CFT correspondence) and the phenomenology of heavy ion collisions. We review some of the main insights gained from this interplay to date. To establish a common language, we start with an introduction to heavy ion phenomenology and finite-temperature QCD, and a corresponding introduction to important concepts and techniques in the gauge/string duality. These introductory sections are written for nonspecialists, with the goal of bringing readers ranging from beginning graduate students to experienced practitioners of either QCD or gauge/string duality to the point that they understand enough about both fields that they can then appreciate their interplay in all appropriate contexts. We then review the current state-of-the art in the application of the duality to the description of the dynamics of strongly coupled plasmas, with emphases that include: its thermodynamic, hydrodynamic and transport properties; the way it both modifies the dynamics of, and is perturbed by, high-energy or heavy quarks passing through it; and the physics of quarkonium mesons within it. We seek throughout to stress the lessons that can be extracted from these computations for heavy ion physics as well as to discuss future directions and open problems for the field.

We derive a static potential for a heavy quark- antiquark pair propagating in Minkowski time at finite temperature, by defining a suitable gauge-invariant Green's function and computing it to first non-trivial order in Hard Thermal Loop resummed perturbation theory. The resulting Debye- screened potential could be used in models that attempt to describe the "melting" of heavy quarkonium at high temperatures. We show, in particular, that the potential develops an imaginary part, implying that thermal e effects ects generate a finite width for the quarkonium peak in the dilepton production rate. For quarkonium with a very heavy constituent mass M, the width can be ignored for T <= g(2)M/12 pi, where g2 is the strong gauge coupling; for a physical case like bottomonium, it could become important at temperatures as low as 250 MeV. Finally, we point out that the physics related to the finite width originates from the Landau-damping of low-frequency gauge fields, and could be studied non-perturbatively by making use of the classical approximation.

https://iopscience.iop.org/article/10.1088/1126-6708/2007/03/054/pdf

Real-time static potential in hot QCD

The holographic dual of a finite-temperature gauge theory with a small number of flavours typically contains D-brane probes in a black hole background. We have recently shown that these systems undergo a first order phase transition characterised by a `melting' of the mesons. Here we extend our analysis of the thermodynamics of these systems by computing their free energy, entropy and energy densities, as well as the speed of sound. We also compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations.

Thermodynamics of the brane

We consider aspects of dynamical baryons in a holographic dual of QCD that is formulated on the basis of a D4/D8-brane configuration. We construct a soliton solution carrying a unit baryon number and show that it is obtained as an instanton solution of four-dimensional Yang-Mills theory with fixed size. The Chern-Simons term on the flavor D8-branes plays a crucial role of protecting the instanton from collapsing to zero size. By quantizing the collective coordinates of the soliton, we derive the baryon spectra. Negative-parity baryons as well as baryons with higher spins and isospins can be obtained in a simple manner.

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Baryons from instantons in holographic QCD

We make use of the AdS/CFT correspondence to determine the energy of an external quark-antiquark pair that moves through strongly-coupled thermal = 4 super-Yang-Mills plasma, both in the rest frame of the plasma and in the rest frame of the pair. It is found that the pair feels no drag force, has an energy that reproduces the expected 1/L (or γ/L) behavior at small quark-antiquark separations, and becomes unbound beyond a certain screening length whose velocity-dependence we determine. We discuss the relation between the high-velocity limit of our results and the lightlike Wilson loop proposed recently as a definition of the jet-quenching parameter.

https://iopscience.iop.org/article/10.1088/1126-6708/2006/09/068/pdf

The energy of a moving quark-antiquark pair in an Script N = 4 SYM plasma

We make use of the AdS/CFT correspondence to determine the energy of an external quark-antiquark pair that moves through strongly-coupled thermal N=4 super-Yang-Mills plasma, both in the rest frame of the plasma and in the rest frame of the pair. It is found that the pair feels no drag force, has an energy that reproduces the expected 1/L (or gamma/L) behavior at small quark-antiquark separations, and becomes unbound beyond a certain screening length whose velocity-dependence we determine. We discuss the relation between the high-velocity limit of our results and the lightlike Wilson loop proposed recently as a definition of the jet-quenching parameter.

The Energy of a Moving Quark-Antiquark Pair in an N=4 SYM Plasma

We explore various aspects of the motion of heavy quarks in strongly-coupled gauge theories, employing the AdS/CFT correspondence. Building on earlier work by Mikhailov, we study the dispersion relation and energy loss of an accelerating finite-mass quark in = 4 super-Yang-Mills, both in vacuum and in the presence of a thermal plasma. In the former case, we notice that the application of an external force modifies the dispersion relation. In the latter case, we find in particular that when a static heavy quark is accelerated by an external force, its rate of energy loss is initially insensitive to the plasma, and there is a delay before this rate approaches the value derived previously from the analysis of stationary or late-time configurations. Following up on work by Herzog et al., we also consider the evolution of a quark and antiquark as they separate from one another after formation, learning how the AdS/CFT setup distinguishes between the singlet and adjoint configurations, and locating the transition to the stage where the deceleration of each particle is properly accounted for by a constant friction coefficient. Additionally, we examine the way in which the energy of a quark-antiquark pair moving jointly through the plasma scales with the quark mass. We find that the velocity-dependence of the screening length is drastically modified in the ultra-relativistic region, and is comparable with that of the transition distance mentioned above.

https://iopscience.iop.org/article/10.1088/1126-6708/2008/06/005/pdf

Acceleration, energy loss and screening in strongly-coupled gauge theories

We calculate the drag force experienced by an infinitely massive quark propagating at constant velocity through an anisotropic, strongly coupled $ \mathcal{N} = 4 $
 plasma by means of its gravity dual. We find that the gluon cloud trailing behind the quark is generally misaligned with the quark velocity, and that the latter is also misaligned with the force. The drag coefficient μ can be larger or smaller than the corresponding isotropic value depending on the velocity and the direction of motion. In the ultra-relativistic limit we find that generically μ ∝ p. We discuss the conditions under which this behaviour may extend to more general situations.

Drag force in a strongly coupled anisotropic plasma

The jet quenching parameter of an anisotropic plasma depends on the relative orientation between the anisotropic direction, the direction of motion of the parton, and the direction along which the momentum broadening is measured. We calculate the jet quenching parameter of an anisotropic, strongly coupled N = 4 plasma by means of its gravity dual. We present the results for arbitrary orientations and arbitrary values of the anisotropy. The anisotropic value can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. We compare our results to analogous calculations for the real-world quark-gluon plasma and nd agreement in some cases and disagreement in others.

Mariano Chernicoff

Papers

The energy of a moving quark-antiquark pair in an Script N = 4 SYM plasma

The Energy of a Moving Quark-Antiquark Pair in an N=4 SYM Plasma

Acceleration, energy loss and screening in strongly-coupled gauge theories

Drag force in a strongly coupled anisotropic plasma

Jet quenching in a strongly coupled anisotropic plasma