The asymptotically-logarithmically-AdS black-hole solutions of 5D dilaton gravity with a monotonic dilaton potential are analyzed in detail. Such theories are holographically very close to pure Yang-Mills theory in four dimensions. The existence and uniqueness of black-hole solutions is shown. It is also shown that a Hawking-Page transition exists at finite temperature if and only if the potential corresponds to a confining theory. The physics of the transition matches in detail with that of deconfinement of the Yang-Mills theory. The high-temperature phase asymptotes to a free gluon gas at high temperature matching the expected behavior from asymptotic freedom. The thermal gluon condensate is calculated and shown to be crucial for the existence of a non-trivial deconfining transition. The condensate of the topological charge is shown to vanish in the deconfined phase.

The thermodynamics of 5D dilaton gravity duals to confining gauge theories is analyzed. We show that they exhibit a first order Hawking-Page type phase transition. In the explicit background of improved holographic QCD of [U. Gursoy and E. Kiritsis, J. High Energy Phys. 02 (2008) 03210.1088/1126-6708/2008/02/032] [U. Gursoy, E. Kiritsis, and F. Nitti, J. High Energy Phys. 02 (2008) 01910.1088/1126-6708/2008/02/019], we find T_{c}=235 MeV. The temperature dependence of various thermodynamic quantities such as the pressure, entropy, and speed of sound is calculated. The results are in agreement with the corresponding lattice data.

The semi-phenomenological improved holographic model for QCD is confronted with data of the pure glue, large-N c gauge theory. After fitting two phenomenological parameters in the potential, the model can reproduce in detail all thermodynamic functions at finite temperature. It also reproduces in detail all known spin-0 and spin-2 glueball observables at zero temperature and predicts the rest of the 0 ++ and 2 ++ towers. A similar two parameter fit in the CP-odd sector postdicts the correct second 0 +− glueball mass, and predicts the rest of the 0 +− tower. Appendix 30A. Numerical technique 30 A.1 An alternative technique 34References 36