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The holographic Einstein-Maxwell-dilaton model is employed to map state-of-the-art lattice QCD thermodynamics data from the temperature ($T$) axis towards the baryon-chemical potential ($\mu_B$) axis aimed at gaining a warm equation of state (EoS) of deconfined QCD matter which can be supplemented with a cool and confined part suitable for subsequent compact (neutron) star (merger) investigations. The model exhibits a critical end point (CEP) at $T_\mathrm{CEP} = \mathcal{O}(100)$ MeV and $\mu_{B \, \mathrm{CEP}} = 500 \ldots 700$ MeV with emerging first-order phase transition (FOPT) curve which extends to large values of $\mu_B$ without approaching the $\mu_B$ axis. We consider the impact and peculiarities of the related phase structure on the EoS for the employed dilaton potential and dynamical coupling parameterizations. These seem to prevent to design an overall trustable EoS without recourse to hybrid constructions.

We parameterize the core of compact spherical star configurations by a mass ($m_x$) and a radius ($r_x$) and study the resulting admissible areas in the total-mass vs. total-radius plane. The employed fiducial equation-of-state models of the corona at radii $r \ge r_x$ and pressures $p \le p_x = p(r = r_x)$ are that (i) of constant sound velocity and (ii) a proxy of DY$\Delta$ DD-ME2 provided by Buchdahl's exactly solvable ansatz. The core ($r < r_x$) may contain any type of material, e.g. Standard-Model matter with unspecified equation of state or/and an unspecified Dark-Matter admixture. Employing a toy model for the cool equation of state with first-order phase transition we discuss also the mass-radius relation of compact stars with an admixture of Dark Matter in a Mirror-World scenario.

The shrinking of the bottomonium spectral function towards narrow quasi-particle states in a cooling strong-interaction medium at finite baryon density is followed within a holographic bottom-up model. The 5-dimensional Einstein-dilaton-Maxwell background is adjusted to lattice-QCD results of sound velocity and susceptibilities. The zero-temperature bottomonium spectral function is adjusted to experimental $\Upsilon$ ground-state mass and first radial excitations. At baryo-chemical potential $\mu_B = 0$, these two pillars let emerge the narrow quasi-particle state of the $\Upsilon$ ground state at a temperature of about 150 MeV. Excited states are consecutively formed at lower temperatures by about 10 (20) MeV for the $2S$ ($3S$) vector states. The baryon density, i.e. $\mu_B > 0$, pulls that formation pattern to lower temperatures. At $\mu_B =$ 200 MeV, we find a shift by about 15 MeV.

A holographic model of probe vector mesons (quarkonia) is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The vector meson action is modified to account for various quark masses. We focus on the $\Phi$, $J/\psi$ and $\Upsilon$ meson melting in agreement with hadron phenomenology in heavy-ion collisions at LHC, that is the formation of hadrons at the observed freeze-out temperature of 155 MeV., Comment: Contribution to the 40th Max Born Symposium

Asymptotic AdS Riemann space-times in five dimensions with a black brane (horizon) sourced by a fully back-reacted scalar field (dilaton) offer -- via the holographic dictionary -- various options for the thermodynamics of the flat four-dimensional boundary theory, uncovering Hawking-Page, first-order and second-order phase transitions up to a cross-over or featureless behavior. The relation of these phase structures to the dilaton potential is clarified and illustrating examples are presented. Having in mind applications to QCD we study probe vector mesons with the goal to figure out conditions for forming Regge type series of radial excitations and address the issue of meson melting.

Within a holographic framework, we consider vector mesons riding on a gravity-dilaton background. The latter one is determined directly from a Schr\"odinger equivalent potential which delivers a proper $\rho$ meson Regge trajectory. The mapping on the dilaton potential yields a thermodynamic phase structure with a first-order transition., Comment: Contribution to FAIRness 2017 - FAIR next generation scientists - 5th Edition Workshop (May 28, 2017 to June 3, 2017 in Sitges, Spain)

Within an extended soft wall model, we study the temperature dependence of the lowest vector meson states. Scales are adjusted by using as input the $\rho$ meson mass in vacuum and the velocity of sound from lattice QCD which displays a minimum at $T_{\rm c}$. The melting of the $\rho$ meson occurs at temperatures $\mathcal{O}(T_{\rm c})$., Comment: Contribution to Workshop on Discovery Physics at the LHC (Kruger 2016), December 5-9 2016, South Africa

The soft wall model is extended to accommodate at the same time (i) approximately linear $\rho$ meson Regge trajectories at zero temperature $T$, (ii) various options for the thermodynamics with reference to QCD (cross over or second-order transition or first-order transition at $T_c$), and (iii) the appearance of vector meson states at $T \leq T_c$. While the vector meson masses display some modest model dependence very near to $T_c$, they stay below $T_c$ to good accuracy independent of the temperature, that is nearly as at $T=0$, thus being very consistent with the thermo-statistical models widely employed in analyses of the hadron yields in relativistic heavy-ion collisions in a region where baryon densitiy effects can be neglected and the vacuum hadron masses are used.

The soft-wall model, emerging as bottom-up holographic scenario anchored in the AdS/CFT correspondence, displays the disappearance of normalisable modes referring to vector mesons at a temperature $T_{\dis}$ depending on the chemical potential $\mu$, $T_{\dis}(\mu)$. We explore options for making $T_{\dis}(\mu)$ consistent with the freeze-out curve $T_{\rm f.o.}(\mu)$ from relativistic heavy-ion collisions and the cross-over curve $T_{\rm c}(\mu)$ from QCD at small values of $\mu$., Comment: Conference proceeding to Critical Point and Onset of Deconfinement 2016, Wroc{\l}aw, Poland

Descent extensions of the soft-wall model are used to accommodate two variants of Regge trajectories of vector meson excitations. At non-zero temperatures, various options for either sequential or instantaneous disappearance of vector mesons as normalisable modes are found, thus emulating deconfinement at a certain temperature in the order of the (pseudo-) critical temperature of QCD. The crucial role of the blackness function, which steers the thermodynamic properties of the considered system, is highlighted., Comment: 11 pages