Motivated by problems arising from the Quark-Gluon Plasma (QGP) formation in heavy-ion experiments at very high energy, one makes use of the AdS/CFT correspondence as a tool for understanding thermal gauge field theories at strong coupling in the relativistic kinematics of heavy-ion reactions. The AdS/CFT correspondence is said “holographic” since it establishes a “Gauge/Gravity duality” between a (supersymmetric) gauge theory in the 4-dimensional physical space and gravity in a (Anti-de-Sitter ) background in one more dimension. We will show that the “gravity dual” of an expanding and cooling plasma appears as a Black Hole moving away in the fifth dimension. It leads to the prediction of a nearly “perfect” hydrodynamic fluid at large time in striking agreement with the QGP. Very recently, the AdS/CFT correspondence has been extended to the early-time, out-of-equilibrium, pre-hydrodynamic stage of the plasma formation, with quite intriguing results related by duality to the dynamical formation of a Black Hole.

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After a (pedestrian) introduction to the AdS/CFT correspondence and to the physical motivations from heavy-ion experiments, we will discuss the late-time expansion of the plasma and the construction of its holographic dual. In the second part we will come to the recent results on the far-from-equilibrium early-time expansion and its relation to the puzzling QGP thermalisation problem. We conclude by a discussion on the future prospects of this Gauge/Gravity duality approach.

IPhT