Hot QCD phase diagram from holographic Einstein–Maxwell–Dilaton models

In this review, we provide an up-to-date account of quantitative bottom-up holographic descriptions of the strongly coupled quark–gluon plasma (QGP) produced in relativistic heavy-ion collisions, based on the class of gauge-gravity Einstein–Maxwell–Dilaton (EMD) effective models. The holographic approach is employed to tentatively map the QCD phase diagram at finite temperature onto a dual theory of charged, asymptotically Anti-de Sitter (AdS) black holes living in five dimensions. With a quantitative focus on the hot QCD phase diagram, the nonconformal holographic EMD models reviewed here are adjusted to describe first-principles lattice results for the finite-temperature QCD equation of state, with $2+1$ flavors and physical quark masses, at zero chemical potential and vanishing electromagnetic fields. We review the evolution of such effective models and the corresponding improvements produced in quantitative holographic descriptions of the deconfined hot QGP phase of QCD. The predictive power of holographic EMD models is tested by quantitatively comparing their predictions for the hot QCD equation of state at nonzero baryon density and the corresponding state-of-the-art lattice QCD results. Hydrodynamic transport coefficients such as the shear and bulk viscosities predicted by these EMD constructions are also compared to the corresponding profiles favored by the latest phenomenological multistage models simultaneously describing different types of heavy-ion data. We briefly report preliminary results from a Bayesian analysis using EMD models, which provide systematic evidence that lattice QCD results at finite temperature and zero baryon density strongly constrains the free parameters of such bottom-up holographic constructions. Remarkably, the set of parameters constrained by lattice results at vanishing chemical potential turns out to produce EMD models in quantitative agreement with lattice QCD results also at finite baryon density. We also review results for equilibrium and transport properties from magnetic EMD models, which effectively describe the hot and magnetized QGP at finite temperatures and magnetic fields with zero chemical potentials. Finally, we provide a critical assessment of the main limitations and drawbacks of the holographic models reviewed in the present work, and point out some perspectives we believe are of fundamental importance for future developments.