Unified Functional-Holographic Theory of the QCD Critical End Point

TL;DR

This paper presents a comprehensive nonperturbative framework combining DSE, FRG, and holography to study the QCD critical end point, predicting its location and universal critical behavior consistent with lattice and experimental data.

Contribution

It develops a unified thermodynamic approach integrating multiple methods to accurately locate the QCD critical end point and analyze its universal critical properties.

Findings

Critical end point at T ≈ 130-135 MeV and μ_B ≈ 600 MeV predicted.

Universal 3D Ising scaling variables organize the critical region.

Qualitative consistency with RHIC BES fluctuation measurements.

Abstract

We develop a thermodynamically consistent nonperturbative framework for equilibrium QCD criticality, unifying DSE quark propagation, FRG flow, and PNJL thermodynamics for coupled chiral/deconfinement order parameters. A holographic Maxwell-Chern-Simons sector supplies topological response; its topological susceptibility enters the FRG flow of the determinantal ('t Hooft) interaction, encoding axial-anomaly evolution across the phase diagram. At $\mu_B=0$ we anchor to continuum-extrapolated lattice thermodynamics and conserved-charge susceptibilities through a lattice-calibrated Polyakov sector, enforcing exact thermodynamic identities by evaluating derivatives at the stationary grand-potential solution at each RG scale. Solving the coupled DSE-FRG-holographic system yields, at the present approximation level, an equilibrium critical end point at $T_{\mathrm{CEP}}\simeq130\text{--}135,\mathrm{MeV}$ and $\mu_{B,\mathrm{CEP}}\simeq600,\mathrm{MeV}$, with quantified sensitivity to regulator, Polyakov-sector, and holographic-normalization choices. The critical region is organized by a nonperturbative map onto universal 3D Ising scaling variables, with anomalous-dimension effects absorbed into nonuniversal metric factors, yielding predictions for the hierarchy, nonmonotonicity, and sign structure of higher-order net-baryon cumulant ratios along smooth freeze-out trajectories and speed-of-sound softening. Comparisons to RHIC BES fluctuation measurements are qualitative consistency checks on correlated equilibrium trends and sign patterns, because finite size/lifetime, critical slowing down, baryon-number conservation, acceptance/efficiency corrections, net-proton-to-net-baryon conversion, and baryon transport can round or reshape experimental cumulants. The results provide a unified equilibrium baseline and controlled inputs for finite-size scaling and dynamical embeddings of heavy-ion data.