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In holographic QCD the effects of gluonic condensate can be encoded in asuitable deformation of the 5D metric. We develop two different methods for theevaluation of first order perturbative corrections to masses and decayconstants of vector resonances in 5D Hard-Wall models of QCD due to smalldeformations of the metric. They are extracted either from a novel compact formfor the first order correction to the vector two-point function, or fromperturbation theory for vector bound-state eigenfunctions: the equivalence ofthe two methods is shown. Our procedures are then applied to flat and to AdS 5DHard-Wall models; we complement results of existing literature evaluating thecorrections to vector decay constant and to two-pion-one-vector couplings: thisis particularly relevant to satisfy the sum rules. We concentrate our attentionon the effects for the Gasser-Leutwyler coefficients; we show that, as in theChiral Quark model, the addition of the gluonic condensate improves theconsistency, the understanding and the agreement with phenomenology of theholographic model.

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