Time-dependent AdS/CFT correspondence and the Quark-Gluon plasma
Résumé
Experiments on high-energy heavy-ion collisions reveal the formation and some intriguing properties of the
Quark-Gluon Plasma (QGP), a new phase of matter predicted by Quantum Chromodynamics (QCD), the quantum field theory of strong interactions. The phenomenological success of relativistic hydrodynamic simulations
with remarkably weak shear viscosity, modeling QGP as an almost perfect fluid, are in favor of the occurrence
of a strongly-coupled QGP expanding and cooling during the reaction. A derivation of these features in QCD at
strong coupling is still lacking and represents a very intricate theoretical challenge. As a quite unique modern tool
to relate these dynamical features to a microscopic gauge field theory at strong coupling, time-dependent realizations of the AdS/CFT correspondence provide a fruitful way to study these properties in a realistic kinematic
configuration. Relating a 4-dimensional Yang-Mills gauge theory with four supersymmetries (which is a conformal
field theory, CFT4) with gravity in Anti-de Sitter space in five dimensions (AdS5), the AdS/CFT correspondence
provides a useful “laboratory” to study yet unknown strong coupling properties of QCD. Besides the interest of
revealing new aspects of the AdS/CFT correspondence in a dynamical set-up, the application to plasma formation
leads to non trivial theoretical properties, as we will discuss in the lectures. The highlights of the present lectures
are:
1. Emergence of an (almost) perfect hydrodynamic fluid at late proper-times after the collision.
2. Duality between an expanding 4-dimensional plasma and a black hole moving radially in the bulk.
3. Intimate link between conformal hydrodynamics and Einstein’s equations in the asymptotically AdS5 space.
4. Possibility of studying the far-from-equilibrium stage of a gauge field theory at early collisional proper-times.
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