Confinement/deconfinement at low temperatures and rotation in the exact soft wall model

Abstract: We study the effects of rotation on the confinement/deconfinement phase transition of strongly interacting matter, at low temperatures, in the soft wall AdS/QCD model at finite density. To achieve it, we apply the Hawking-Page approach to the exact Andreev's solution of a charged rotating black hole in five-dimensional AdS space. We observe that there is a most critical angular velocity ($\omega_0$) of hadronic matter that depends on the baryon density, representing a strong constraint on the rotation in hadronic matter. We obtain the curve $\omega_0(\mu)$, which shows that the critical rotational velocity allowed for hadronic matter decreases as the chemical potential ($\mu$) increases. When $\mu$ approaches the most critical quark chemical potential, identified as the density of a phase transition at zero temperature for a non-rotating plasma, the rotational velocity allowed for the hadrons tends to zero. If $\omega \geq \omega_0 $, there is no phase transition and the QCD matter remains in the deconfined plasma phase. The QCD phase diagram is also obtained for the exact solution, and the critical temperatures are compared with the ones obtained from the Reissner-Nordstr\"om approximation.