Phase structure of 2+1-flavor QCD from an Einstein-dilaton-flavor holographic model

Abstract

We construct a holographic QCD model based on the Einstein--dilaton--flavor framework with 2+1 flavors and investigate its phase structure using machine-learning techniques. At zero chemical potential, the model reproduces the equation of state and chiral transition in quantitative agreement with lattice QCD results. By varying the light and strange quark masses, we map out the quark-mass dependence of the transition order and obtain the corresponding phase diagram, which is consistent with phase structures extracted from lattice simulations and other nonperturbative approaches. In particular, the predicted first-order region is found to be small, in line with the most recent lattice QCD analyses. We also examine the critical behavior along the second-order boundaries and the tricritical region, finding that the critical exponents exhibit mean-field scaling characteristic of classical holographic constructions. Integrating machine learning with holographic QCD significantly enhances the efficiency of parameter optimization, providing a robust and practical strategy for improving the predictive power of holographic modeling of QCD thermodynamics.