Systematic Bayesian investigation of the (2+1)-flavor QCD phase transition in a holographic model

In this study, we construct a bayesian holographic QCD model by integrating the Einstein-Maxwell-Dilaton (EMD) framework with lattice quantum chromodynamics (QCD) data at zero chemical potential, specifically entropy, the square of the speed of sound, and baryon number susceptibilities, while systematically incorporating error estimates from the lattice QCD (LQCD) results. Leveraging a bayesian inference framework, we first achieve a precise calibration of the model parameters, then perform a comprehensive investigation into the thermodynamic properties of $(2+1)$-flavor QCD at both zero and finite chemical potentials, and finally provide a prediction for the location of the critical end point (CEP) in the QCD phase diagram. Our results indicate that, under the maximum a posteriori (MAP) estimation, the CEP is located at $(T,\mu {)}_{\mathrm{M}\mathrm{A}\mathrm{P}}=(0.119,0.615)\mathrm{G}\mathrm{e}\mathrm{V}$. Furthermore, we provide the predicted regions for the CEP at $68\mathrm{\%}$ and $95\mathrm{\%}$ confidence levels (CL), yielding $(T,\mu {)}_{68\mathrm{\%}\mathrm{C}\mathrm{L}}=(0.1176\text{–}0.1204,0.59\text{–}0.63)\mathrm{G}\mathrm{e}\mathrm{V}$ and $(T,\mu {)}_{95\mathrm{\%}\mathrm{C}\mathrm{L}}=(0.1172\text{–}0.1206,0.58\text{–}0.63)\mathrm{G}\mathrm{e}\mathrm{V}$, respectively. A thorough comparison with predictions from other theoretical models validates the robustness and predictive power of our approach. This work not only establishes a novel analytical framework for holographic modeling but also provides valuable theoretical insights into the phase transitions of strongly interacting matter under extreme conditions.