Deconfinement Transition of AdS/QCD at ${\cal O}(\alpha'^3)$

We study the confinement/deconfinement phase transition of holographic AdS/QCD models by using Ricci flat $AdS_5$ black holes up to ${\cal O}(\alpha'^3)$, which corresponds to the $\lambda$ expansion correction in the dual field theory to $\lambda^{-3/2}$, where $\lambda$ is the 't Hooft coupling constant. We consider two cases: one is the hard-wall AdS/QCD model where a small radius region of the $AdS_5$ is removed; the other is the case where one of spatial coordinates for the $AdS_5$ space is compactified, resulting in Witten's QCD model in 2+1 dimensions. We find that in the hard-wall AdS/QCD model, the deconfinement temperature decreases when the $\lambda$ expansion corrections are taken into account, while in Witten's QCD model, the deconfinement transition always happens when the ratio of inverse temperature $\beta$ to the period $\beta_s$ of the compactified coordinate decreases to one, $\beta/\beta_s=1$, the same as the case without the ${\cal O}(\alpha'^3)$ correction.