We construct some AdS/QCD models by the systematic procedure of GKN. These models reflect three rather different asymptotics the gauge theory beta functions approach at the infrared region, $betapropto-lambda^2, -lambda^3$ and $betapropto-lambda$, wh
ere $lambda$ is the t Hooft coupling constant. We then calculate the heavy quark potentials in these models by holographic methods and find that they can more consistently fit the lattice data relative to the usual models which do not include the renormalization group improving effects. But only use the lattice QCD heavy quark potentials as constrains, we cannot distinguish which kind of infrared asymptotics is the better one.
We extend BCCNRs flavored KW and KS geometries into the negative coupling constant region and try giving physical explanations from the dual gauge theory side. We show that, in the extended region, except the coupling constant being negative, all oth
er fields of the super-gravity theory having good properties which can be described by the dual gauge theory.