Towards a warm holographic equation of state by an Einstein-Maxwell-dilaton model

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.