Unified Functional-Holographic Theory of the QCD Critical End Point

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 $T_{\mathrm{CEP}}\simeq 130\text{–}135,\mathrm{MeV}$ and ${\mu }_{B,\mathrm{CEP}}\simeq 600,\mathrm{MeV}$, 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.

67 pages, 17 figures

References in corpus (31)

• Exact evolution equation for the effective potential
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The equation of state in (2+1)-flavor QCD
• The Phase Structure of the Polyakov--Quark-Meson Model
• Exploring improved holographic theories for QCD: Part II
• Mimicking the QCD equation of state with a dual black hole
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Chiral symmetry breaking as open string tachyon condensation
• Susceptibilities and speed of sound from PNJL model
• Phase structure of three and four flavor QCD
• Phase diagram and critical endpoint for strongly-interacting quarks
• Dynamic universality class of the QCD critical point
• The renormalization group and quark number fluctuations in the Polyakov loop extended quark-meson model at finite baryon density
• Propagators and phase structure of Nf=2 and Nf=2+1 QCD
• Chiral phase structure and critical end point in QCD
• Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
• Observation of the critical end point in the phase diagram for hot and dense nuclear matter
• Locating the critical endpoint of QCD: mesonic backcoupling effects
• Second order cumulants of conserved charge fluctuations revisited I. Vanishing chemical potentials
• Curvature of the chiral pseudo-critical line in QCD
• Finite-size scaling as a tool in the search for the QCD critical point in heavy ion data
• Chemical potential and the gap equation
• Status of Lattice Studies of the QCD Phase Diagram
• Rapidity dependence of proton cumulants and correlation functions
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• Topological susceptibility in finite temperature QCD with physical $(u/d,s,c)$ domain-wall quarks
• Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition
• Collision Energy Dependence of Particle Ratios and Freeze-out Parameters in Ultra Relativistic Nucleus Nucleus Collisions
• Effects of strangeness on the chiral pseudocritical line
• Vector interaction bounds in NJL-like models from LQCD estimated curvature of the chiral crossover line
• Numerical universal solutions in $a$-gauge in open string field theory