Emergent Gravitational Dynamics and SU(3) Yang-Mills from PEPS Tensor Networks: Glueball Spectrum, Running G_N(μ), and Entanglement Thermodynamics

This preprint presents a unified theoretical framework in which both quantum chromodynamics (QCD) and gravitational dynamics emerge from a single Projected Entangled Pair State (PEPS) tensor network describing the QCD vacuum. The SU(3) gauge vacuum on a two-dimensional lattice is combined with a Multiscale Entanglement Renormalization Ansatz (MERA) modular Hamiltonian, generating an effective potential U(Λ)U(Λ) for a collective collapse field Λ(x)Λ(x). Quantized energy levels of this potential reproduce the pure glueball spectrum of QCD, while the entanglement structure yields emergent gravitational dynamics. Key Results (Version 20) Glueball Spectrum & QCD Observables Four pure glueball channels (0++0++, 0−+0−+, 2++2++, 1+−1+−) reproduced at 5–11% accuracy using a single free parameter J=0.54J=0.54 fitted to modern quenched lattice m(0++)=1.71(5)m(0++)=1.71(5) GeV. One-loop beta function coefficient b0=11Nc/(48π2)b0=11Nc/(48π2) derived from MERA entropy flow without Feynman diagrams. String tension σ=0.194σ=0.194 GeV² obtained from area-law entanglement entropy, consistent with lattice QCD. Full baryon octet/decuplet spectrum with RMS accuracy 6.7%, satisfying Gell-Mann–Okubo relation to 0.4%. Emergent Gravity & RG Flow Newton's constant derived as GN(μ)=1/[4 cent μ2 Svac(μ)]GN(μ)=1/[4centμ2Svac(μ)] with Svac(μ)=b0ln⁡(μ/ΛQCD)Svac(μ)=b0ln(μ/ΛQCD). The historical 10381038 hierarchy between GN(ΛQCD)GN(ΛQCD) and GN(MPl)GN(MPl) is resolved as genuine RG running: cent≈0.095cent≈0.095 yields exact agreement with observed GNGN at the Planck scale. Massive emergent graviton mgrav≈85mgrav≈85 MeV with Yukawa range λY≈2.3λY≈2.3 fm, fully compatible with Eöt-Wash, GW170817, and all fifth-force constraints. Speed of light derived as the Lieb-Robinson velocity of the PEPS network, converging to c=1c=1 in the continuum limit. Strict 2D → 3+1D Mapping In the confining phase, dominant degrees of freedom are transverse flux-tube modes (D−2=2D−2=2 bosons). PEPS on the transverse plane provides an exact lattice regularization of the Nambu-Goto worldsheet CFT. Independent reproduction of Lüscher term (−π/12R−π/12R), Casimir scaling, and flux-tube width w(R)w(R) confirms the mapping. Verification Suite & Transparency 11 independent tests organized in three groups: Group I (internal consistency): dimensionless combination D(χ)=O(1)D(χ)=O(1), χ(MPl)∼111χ(MPl)∼111, RG closure via ZrenZren, running αsPEPSαsPEPS. Group II (lattice validation): Casimir scaling, deconfinement temperature Tc=277Tc=277 MeV, topological susceptibility χtop1/4=177χtop1/4=177 MeV. Group III (beyond-QCD phenomenology): mgrav=85mgrav=85 MeV, chiral constants fπ/σ=0.21fπ/σ=0.21, baryon spectrum RMS=6.7%, dark energy wa=+0.006wa=+0.006. Parameter audit: 1 free parameter (JJ) → 11 quantitative predictions; all other parameters derived, assumed, or fixed by external input. Reproducibility: Full Python pipeline with fixed seeds, modular structure, and notebooks for regenerating all tables and figures. Model Limitations (Transparently Stated) Anharmonicity of U(Λ)U(Λ) is ~0.3%: the glueball spectrum is essentially harmonic; lattice mass ratios arise from quantum-number-to-level assignments. The 2D PEPS → 3+1D map applies strictly to the confining IR regime (R≳0.7R≳0.7 fm); UV completion requires 3D PEPS or holographic lifting. Chiral constants and baryon masses are computed in pure Yang-Mills (Nf=0Nf=0); dynamical quarks (Nf>0Nf>0) require fermionic PEPS (fPEPS) and are deferred to future work. The 10381038 hierarchy is resolved as RG running of GN(μ)GN(μ), but the absolute value of centcent is fitted; a first-principles derivation remains open. Experimental Roadmap Prediction Experiment Sensitivity Timeline Falsification Criterion wa=+0.006wa=+0.006 Euclid, LSST, DESI σ(wa)∼0.03σ(wa)∼0.03 2025–2032 wa<−0.05wa<−0.05 mgrav=85mgrav=85 MeV MAGIS-100, OTIMA λY>0.1λY>0.1 fm 2028–2030 mgrav>10mgrav>10 MeV excluded Lieb-Robinson cc LISA, ET (GW dispersion) vg/c - 1 < 10⁻¹⁸ η/sη/s in QGP ALICE, sPHENIX ∼0.05∼0.05 Current η/s<1/(4π)η/s<1/(4π) This work establishes PEPS tensor networks as a viable bridge between non-perturbative QCD and emergent gravity, offering testable predictions for collider physics, precision gravity experiments, and cosmological surveys.