Unified Functional‐Holographic Theory of the QCD Critical End Point

ABSTRACT We develop a thermodynamically consistent nonperturbative framework for equilibrium criticality in QCD matter by unifying Dyson–Schwinger quark propagation, functional renormalization‐group (FRG) evolution of the effective action, and Polyakov–Nambu–Jona–Lasinio (PNJL) thermodynamics for the coupled chiral and deconfinement order parameters. A holographic Maxwell–Chern–Simons sector supplies the topological response, and its topological susceptibility is fed into the FRG flow of the determinantal ('t Hooft) interaction to encode the evolution of the axial anomaly across the phase diagram. At , the construction is anchored to continuum‐extrapolated lattice thermodynamics and conserved‐charge susceptibilities through a lattice‐calibrated Polyakov sector, while exact thermodynamic identities are enforced by evaluating all derivatives at the stationary solution of the grand potential at each RG scale. Solving the coupled DSE, FRG, and holographic system yields, within this framework and at the present level of approximation, an equilibrium critical end point (CEP) at to and together with an internally quantified sensitivity to regulator, Polyakov‐sector, and holographic‐normalization variations. The critical region is organized by a nonperturbative mapping to universal 3D Ising scaling variables with anomalous‐dimension effects absorbed into nonuniversal metric factors, leading to equilibrium predictions for the hierarchy, nonmonotonicity, and sign structure of higher‐order net‐baryon cumulant ratios along the smooth freeze‐out trajectories, as well as equilibrium softening of the speed of sound. Comparisons to RHIC beam energy scan fluctuation measurements are presented as qualitative consistency checks on correlated equilibrium trends and sign patterns, because finite size and lifetime, critical slowing down, baryon number conservation, acceptance and efficiency corrections, the net‐proton to net‐baryon conversion, and baryon‐transport dynamics can round or reshape cumulants in the experimental system. The results, therefore, provide a unified equilibrium baseline and a set of controlled inputs for finite‐size scaling and dynamical embeddings of heavy‐ion data.