Phase transition of hot dense QCD Matter from a refined holographic EMD model

Abstract: In this study, we begin by delineating the Einstein-Maxwell-Dilaton (EMD) model within the holographic QCD framework and deriving the equation of state through holographic renormalization. Subsequently, we utilize the Wald method to determine the first law of thermodynamics for a five-dimensional black hole, thereby confirming the alignment of our EMD model with the thermodynamics of the grand canonical ensemble in the boundary field theory. By employing the $n-2$ form in the Wald method, we proceed to calculate the shear viscosity in Gauss-Bonnet gravity. The results we obtain demonstrate consistency with those from first-order metric perturbation. Furthermore, we construct a refined EMD model that attains quantitative agreement with the lattice QCD equation of state and baryon number susceptibility data at finite density. Using this enhanced model, we delve into the investigation of signals related to the QCD phase transition critical endpoint. At present, no non-monotonic changes in $\kappa\sigma^2$ have been observed within the 7$\sim$200 GeV collision energy range at STAR. However, our theoretical analysis suggests that if the chemical freeze-out line does not intersect the first-order phase transition line, a peak-like structure in $\kappa\sigma^2$ is anticipated within the 3$\sim$5 GeV range.