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.