Singular perturbation theory for the thermodynamic properties of holographic QCD

TL;DR

This paper applies singular perturbation theory to improve the understanding of thermodynamics in holographic QCD, providing uniform approximations for black-hole solutions and matching lattice data.

Contribution

It introduces a novel application of singular perturbation techniques to holographic QCD, yielding more accurate thermodynamic predictions across temperature regimes.

Findings

Resummation of high-temperature expansions improves theoretical accuracy.

Quadratic temperature dependence emerges naturally in free energy.

Gluon condensate estimate aligns well with phenomenological values.

Abstract

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 an important theoretical improvement with respect to previous results in the literature. By using this technique, it is shown how a quadratic dependence at low enough temperatures can naturally appear in the free energy. A comparison with lattice data of gluodynamics is performed. 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.