Emergent Gravitational Dynamics and SU (3) Yang-Mills from PEPS Tensor Networks: Glueball Spectrum, Running GN (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 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 wa0. 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.