We discuss the non-perturbative regime of QCD, which is supposed to be relevant for the description of the transient phase as quark--gluon plasma formed during heavy-ion collisions at very high energies. Since there is not yet an available field-theoretical scheme for non perturbative QCD in those conditions, we study the dynamics of strongly interacting gauge-theory matter (modelling quark--gluon plasma) using the AdS/CFT duality between gauge field theory at strong coupling and a gravitational background in Anti-de Sitter space. The relevant gauge theory is a-priori equipped with N=4 supersymmetries, but qualitative results may give lessons on this issue. As an explicit example, we show that perfect fluid hydrodynamics emerges at large times as the unique nonsingular asymptotic solution of the nonlinear Einstein equations in the bulk. The gravity dual can be interpreted as a black hole moving off in the fifth dimension.

PACS numbers: 11.25.Tq, 12.38.Mh