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

Abstract

We study the confinement/deconfinement phase transition of holographic AdS/QCD models by using Ricci flat $Ad{S}_5$ black holes up to $\mathcal{O}({\alpha }^{\prime 3})$, 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 $Ad{S}_5$ is removed; the other is the case where one of spatial coordinates for the $Ad{S}_5$ 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 $\mathcal{O}({\alpha }^{\prime 3})$ correction.

Comments: Latex, 14 pages; v2: the version to appear in PRD