On the Evaluation of Gluon Condensate Effects in the Holographic Approach to QCD

In holographic QCD the effects of gluonic condensate can be encoded in a suitable deformation of the 5D metric. We develop two different methods for the evaluation of first order perturbative corrections to masses and decay constants of vector resonances in 5D Hard-Wall models of QCD due to small deformations of the metric. They are extracted either from a novel compact form for the first order correction to the vector two-point function, or from perturbation theory for vector bound-state eigenfunctions: the equivalence of the two methods is shown. Our procedures are then applied to flat and to AdS 5D Hard-Wall models; we complement results of existing literature evaluating the corrections to vector decay constant and to two-pion-one-vector couplings: this is particularly relevant to satisfy the sum rules. We concentrate our attention on the effects for the Gasser-Leutwyler coefficients; we show that, as in the Chiral Quark model, the addition of the gluonic condensate improves the consistency, the understanding and the agreement with phenomenology of the holographic model.