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

Abstract

We study the confinement/deconfinement phase transition of holographic AdS/QCD models by using Ricci flat $AdS_5$ black holes up to ${\cal O}(α'^3)$, which corresponds to the $λ$ expansion correction in the dual field theory to $λ^{-3/2}$, where $λ$ 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 $λ$ expansion corrections are taken into account, while in Witten's QCD model, the deconfinement transition always happens when the ratio of inverse temperature $β$ to the period $β_s$ of the compactified coordinate decreases to one, $β/β_s=1$, the same as the case without the ${\cal O}(α'^3)$ correction.

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