Heavy ion collision experiments recreating the quark-gluon plasma that filled the microseconds-old universe have established that it is a nearly perfect liquid that flows with such minimal dissipation that it cannot be seen as made of particles. String theory provides a powerful toolbox for studying matter with such properties. This book provides a comprehensive introduction to gauge/string duality and its applications to the study of the thermal and transport properties of quark-gluon plasma, the dynamics of how it forms, the hydrodynamics of how it flows, and its response to probes including jets and quarkonium mesons. Calculations are discussed in the context of data from RHIC and LHC and results from finite temperature lattice QCD. The book is an ideal reference for students and researchers in string theory, quantum field theory, quantum many-body physics, heavy ion physics and lattice QCD.

Models of medium-induced radiative parton energy loss account for the strong suppression of high-pT hadron spectra in √ sNN = 200 GeV Au-Au collisions at RHIC in terms of a single "jet quenching parameter"q. The available suite of jet quenching measurements makeq one of the experimentally best constrained properties of the hot fluid produced in RHIC collisions. We observe thatq can be given a model-independent, nonperturbative, quantum field theoretic definition in terms of the short-distance behavior of a particular light-like Wilson loop. We then use the AdS/CFT correspondence to obtain a strong-coupling calculation ofq in hot N = 4 supersymmetric QCD, findingqSYM = 26.69 √ αSYMNc T 3 in the limit in which both Nc and 4παSYMNc are large. We thus learn that at strong couplingq is not proportional to the entropy density s, or to some "number density of scatterers" since, unlike the number of degrees of freedom,q does not grow like N Ultrarelativistic nucleus-nucleus collisions are studied at RHIC and at the LHC to determine the properties of QCD matter at extreme energy density and temperature [1,2]. If we could do the gedanken experiment of deep inelastic scattering on the hot fluid produced in a heavy ion collision, we could learn a lot. Even though the short lifetime of the transient dense state precludes the use of such external probes, a conceptually similar method is available at RHIC and LHC energies. This method is based upon internally generated probes: energetic partons produced in rare high transverse momentum elementary interactions in the initial stage of the collision, which then interact strongly with the hot, dense fluid produced in the collision as they plough through it [3]. The characterization of the resulting mediuminduced modification of high-p T parton fragmentation ("jet quenching") and its connection to properties of the hot, dense matter that is the object of study have become one of the most active areas of research stimulated by RHIC data [3]. Models which supplement the standard perturbative QCD formalism for high-p T hadron production with medium-induced parton energy loss successfully account for the strong (up to a factor ∼ 5) suppression of hadronic spectra in √ s N N = 200 GeV Au-Au collisions at RHIC, its dependence on centrality and orientation with respect to the reaction plane, and the corresponding reduction of back-to-back hadron correlations [4,5]. These models typically involve one medium-sensitive "jet quenching parameter" denotedq. This parameter is usually defined only perturbatively, and is often thought of as proportional to 1/(λ 2 D λ MFP ), with λ D the Debye screening length and λ MFP some perturbatively defined transport mean-free path [6]. In the present paper, we address the question of howq can be defined and calculated from first principles in nonperturbative quantum field theory, without assuming the existence of quasiparticles with a well-defined mean-free path.There are many indications from data at RHIC and from calculations of lattice-discretized QCD th...

Analyses of two-particle correlations have provided the chief means for determining spatio-temporal characteristics of relativistic heavy ion collisions. We discuss the theoretical formalism behind these studies and the experimental methods used in carrying them out. Recent results from RHIC are put into context in a systematic review of correlation measurements performed over the past two decades. The current understanding of these results is discussed in terms of model comparisons and overall trends.

We calculate the probability ͑''quenching weight''͒ that a hard parton radiates an additional energy fraction ⌬E due to scattering in spatially extended QCD matter. This study is based on an exact treatment of a finite in-medium path length; it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation ͓Baier-Dokshitzer-Mueller-Peigné-Schiff-Zakharov ͑BDMPSZ͒ formalism͔ and in the single hard scattering approximation ͓Nϭ1 opacity approximation͔. By comparison, we establish a simple relation between the transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus collisions. Remarkably, the kinematic constraint resulting from finite in-medium path lengths reduces significantly the p Ќ dependence of the nuclear modification factor, thus leading to consistency with the data measured at the BNL Relativistic Heavy Ion Collider.

We study the relation between the Baier-DokshitzerMueller-Peigné-Schiff (BDMPS) and Zakharov formalisms for medium-induced gluon radiation off hard quarks, and the radiation off very few scattering centers. Based on the nonabelian Furry approximation for the motion of hard partons in a spatially extended colour field, we derive a compact diagrammatic and explicitly colour trivial expression for the N -th order term of the k ⊥ -differential gluon radiation cross section in an expansion in the opacity of the medium. Resumming this quantity to all orders in opacity, we obtain Zakharov's path-integral expression (supplemented with a regularization prescription). This provides a new proof of the equivalence of the BDMPS and Zakharov formalisms which extends previous arguments to the k ⊥ -differential cross section. We give explicit analytical results up to third order in opacity for both the gluon radiation cross section of free incoming and of in-medium produced quarks. The N -th order term in the opacity expansion of the radiation cross section is found to be a convolution of the radiation associated to Nfold rescattering and a readjustment of the probabilities that rescattering occurs with less than N scattering centers. Both informations can be disentangled by factorizing out of the radiation cross section a term which depends only on the mean free path of the projectile. This allows to infer analytical expressions for the totally coherent and totally incoherent limits of the radiation cross section to arbitrary orders in opacity.

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, highenergy 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.

In this report we give a detailed account on Hanbury Brown/Twiss (HBT) particle interferometric methods for relativistic heavy-ion collisions. These exploit identical two-particle correlations to gain access to the space-time geometry and dynamics of the final freeze-out stage. The connection between the measured correlations in momentum space and the phase-space structure of the particle emitter is established, both with and without final state interactions. Suitable Gaussian parametrizations for the two-particle correlation function are derived and the physical interpretation of their parameters is explained. After reviewing various model studies, we show how a combined analysis of single-and two-particle spectra allows to reconstruct the final state of relativistic heavy-ion collisions.

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