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.

We express the heavy quark diffusion coefficient as the temporal variation of a Wilson line along the Schwinger-Keldysh contour. This generalizes the classical formula for diffusion as a force-force correlator to a non-Abelian theory. We use this formula to compute the diffusion coefficient in strongly coupled N 4 Yang-Mills theory by studying the fluctuations of a string in AdS 5 S 5 . The string solution spans the full Kruskal plane and gives access to contour correlations. The diffusion coefficient is D 2= p T and is therefore parametrically smaller than momentum diffusion, =e p 1=4T. The quark mass must be much greater than T p in order to treat the quark as a heavy quasiparticle. The result is discussed in the context of the Relativistic Heavy Ion Collider (RHIC) experiments.

Quenching is a recently discovered phenomenon in which QCD jets created in heavy ion collisions deposit a large fraction or even all their energy and momentum into the produced matter . At RHIC and higher energies, where that matter is a strongly coupled Quark-Gluon Plasma (sQGP) with very small viscosity, we suggest that this energy/momentum propagate as a collective excitation or "conical flow". Similar hydrodynamical phenomena are well known, e.g. the so called sonic booms from supersonic planes. We solve the linearized relativistic hydrodynamic equations to detail the flow picture. We argue that for RHIC collisions the direction of this flow should make a cone at a specific large angle with the jet, of about 70 o , and thus lead to peaks in particle correlations at the angle ∆φ = π ± 1.2 rad relative to the large-pt trigger. This angle happens to match perfectly the position of the maximum in the angular distribution of secondaries associated with the trigger recently seen by the STAR and PHENIX collaborations. We also discuss briefly possible alternative explanations and suggest some further tests to clarify the mechanism.

We compute the momentum broadening of a heavy fundamental charge propagating through a N = 4 Yang Mills plasma at large t' Hooft coupling. We do this by expressing the medium modification of the probe's density matrix in terms of a Wilson loop averaged over the plasma. We then use the AdS/CFT correspondence to evaluate this loop, by identifying the dual semiclassical string solution. The calculation introduces the type "1" and type "2" fields of the thermal field theory and associates the corresponding sources with the two boundaries of the AdS space containing a black hole. The transverse fluctuations of the endpoints of the string determine κ T = √ γλT 3 π -the mean squared momentum transfer per unit time. (γ is the Lorentz gamma factor of the quark.) The result reproduces previous results for the diffusion coefficient of a heavy quark. We compare our results with previous AdS/CFT calculations ofq.