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

TL;DR

This work analyzes how rotation and finite density influence the confinement/deconfinement transition in the soft-wall AdS/QCD framework by employing Andreev's exact rotating AdS5 black hole solution and the Hawking-Page transition. It derives a density-dependent critical angular velocity $\omega_0(μ)$, showing that allowed rotation decreases with chemical potential and vanishes at a zero-temperature transition, thereby constraining rotating hadronic matter. The study reveals that IR bulk contributions reduce deconfinement temperatures relative to the RN approximation, yielding richer phase diagrams and lower critical temperatures. These holographic results offer insights for noncentral heavy-ion collisions, where vorticity and density are substantial, and highlight the importance of far-from-boundary physics in strong-coupling QCD phase structure.

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 critical angular velocity ($ω_0$) of hadronic matter that depends on the baryon density, representing a strong constraint on the rotation in hadronic matter. We obtain the curve $ω_0(μ)$, which shows that the critical rotational velocity allowed for hadronic matter decreases as the chemical potential ($μ$) increases. When $μ$ 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 $ω\geq ω_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-Nordström approximation. The results are interpreted as a consequence of contributions from regions relatively distant from the AdS boundary, which cause a non-negligible reduction in the deconfinement temperatures.

Figures (9)

• Figure 1: Action density of regularized rotating BH at finite density versus horizon position from the exact Andreev's solution of soft wall model, at a fixed plasma rotational velocity ($\omega l = 0.5$), and different quark chemical potentials.
• Figure 2: (A) Action density of regularized rotating BH as a function of $\bar{z}_h$ and $\omega l$, at a fixed quark chemical potential $\bar{\mu} = 0.6$, with the intersection with the plane $\Delta \bar{\mathcal{E}} = 0$. (B) Critical horizon versus plasma rotational velocity at the same fixed $\bar{\mu}$.
• Figure 3: Critical temperature of deconfinement as a function of the plasma rotational velocity, at different values of quark chemical potential, in the exact Andree's model..
• Figure 4: (Left) The same, in the RN approximation. (Right) Comparison between the exact and RN critical temperatures as a function of $\omega l$ at a fixed rotational velocity ($\omega l = 0.6)$.
• Figure 5: Most critical angular velocity of hadronic matter versus quark chemical potential, assuming $l=1$, in the exact Andreev's model and in the RN approximation. The angular velocity is approaching the speed of light limit at small chemical potential.