We study finite temperature properties of four dimensional QCD-like gauge theories in the gauge theory/gravity duality picture. The gravity dual contains two deformed 5d AdS metrics, with and without a black hole, and a dilaton. We study the thermodynamics of the 4d boundary theory and constrain the two metrics so that they correspond to a high and a low temperature phase separated by a first order phase transition. The equation of state has the standard form for the pressure of a strongly coupled fluid modified by a vacuum energy, a bag constant. We determine the parameters of the deformation by using QCD results for T c and the hadron spectrum. With these parameters, we show that the phase transition in the 4d boundary theory and the 5d bulk Hawking-Page transition agree. We probe the dynamics of the two phases by computing the quark-antiquark free energy in them and confirm that the transition corresponds to confinement-deconfinement transition.

We study the application of AdS/CFT duality to longitudinal boost invariant Bjorken expansion of QCD matter produced in ultrarelativistic heavy ion collisions. As the exact (1 + 4)-dimensional bulk solutions for the (1 + 3)-dimensional boundary theory are not known, we investigate in detail the (1 + 1)-dimensional boundary theory, where the bulk is AdS 3 gravity. We find an exact bulk solution, show that this solution describes part of the spinless Bañados-Teitelboim-Zanelli (BTZ) black hole with the angular dimension unwrapped, and use the thermodynamics of the BTZ hole to recover the time-dependent temperature and entropy density on the boundary. After separating from the holographic energy-momentum tensor a vacuum contribution, given by the extremal black hole limit in the bulk, we find that the boundary fluid is an ideal gas in local thermal equilibrium. Including angular momentum in the bulk gives a boundary flow that is boost invariant but has a nonzero longitudinal velocity with respect to the Bjorken expansion.

We discuss an exact time dependent O(3) symmetric solution with a horizon of the 5d AdS classical gravity equations searching for a 4d boundary theory which would correspond to expanding gauge theory matter. The boundary energy-momentum tensor and entropy density are computed. The boundary metric is the flat Friedmann one and any time dependence on the boundary is incompatible with Minkowski metric. At large times when curvature effects are negligible, perfect fluid behavior arises in a natural way.