Thermodynamics of AdS${}_5$ black holes: holographic QCD and St\"uckelberg model

We explore the thermodynamics of AdS${}_5$ black holes in two models: i) an improved holographic QCD model with a simple dilaton potential, and ii) the St"uckelberg model in 5D. In the former case, by applying techniques of singular perturbation theory, we obtain a resummation of the naive expansion at high temperatures, providing a good fit to the lattice data for the trace anomaly. In the latter, we find a solution of the equations of motion by considering an expansion in the conformal dimension of the current associated to the gauge field.