Pure gauge QCD and holography

Holographic models for the pure gauge QCD vacuum are explored. The holographic renormalization of these models is considered as required by a phenomenological approach that takes the $\beta$-functions of the models as the only input. This approach is done taking the dilaton as the coordinate orthogonal to the border. This choice greatly simplifies the analysis and gives a geometrical interpretation for the fixed points of the renormalization group flow. Examples are constructed that present asymptotic freedom, confinement of static quarks, either with vanishing or non-vanishing gluon condensate $G_{2}$. The latter models require an extension of the dilaton-gravity models already considered in the literature. This extension is also determined by the only input, i.e. the $\beta$-function. In addition the restrictions imposed by the trace anomaly equation are studied. In doing so a holographic derivation of this equation is presented.