Singular Perturbation Theory for the Thermodynamic Properties of Holographic QCD

We explore the thermodynamics of a black-hole solution in improved holographic QCD with a simple dilaton potential having two parameters. By applying techniques of singular perturbation theory, we get uniform approximations for the metric and the dilaton field in the two regimes of big and small black-holes. These techniques lead to a resummation of the naive expansion at high temperatures, providing a good fit to lattice data for the trace anomaly at high temperature. It is provided as well an estimate of the value of the gluon condensate at zero temperature which turns out to be in quite good agreement with the accepted values in the literature from phenomenological studies of QCD.