Holographic models and the QCD trace anomaly

Abstract

Five-dimensional dilaton models are considered as possible holographic duals of the pure gauge QCD vacuum. In the framework of these models, the QCD trace anomaly equation is considered. Each quantity appearing in that equation is computed by holographic means. Two exact solutions for different dilaton potentials corresponding to perturbative and nonperturbative β-functions are studied. It is shown that in the perturbative case, where the β-function is the QCD one at leading order, the resulting space is not asymptotically anti-de Sitter. In the nonperturbative case, the model considered presents confinement of static quarks and leads to a nonvanishing gluon condensate, although it does not correspond to an asymptotically free theory. Calculating the Nambu-Goto action, corresponding to a small circular Wilson loop, leads to an expression for the gluon condensate. The validity of the trace anomaly equation is considered for both models. It holds for the perturbative model and it does not hold for the nonperturbative one.