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

TL;DR

This paper investigates how rotation influences the confinement/deconfinement phase transition in strongly interacting matter at low temperatures using the soft wall AdS/QCD model, revealing a critical angular velocity dependent on density.

Contribution

It introduces an exact charged rotating black hole solution in AdS space to study rotation effects on QCD phase transitions, providing new insights into the phase diagram under rotation.

Findings

Critical angular velocity decreases with increasing chemical potential.

No phase transition occurs if rotation exceeds the critical angular velocity.

Deconfinement temperatures are reduced due to contributions from regions away from the AdS boundary.

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 ($\omega_0$) 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. 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.