Emergent Gravity and QCD from PEPS Tensor Networks: Glueball Spectrum, Beta Function, 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 PEPS ansatz for 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) for a collective collapse field Λ(x). Quantized levels of this approximately anharmonic potential reproduce the pure glueball spectrum of QCD—including scalar 0⁺⁺, pseudoscalar 0⁻⁺, tensor 2⁺⁺, and exotic 1⁺⁻ channels—with a single free parameter J controlling the bond dimension. Key results (v16): Glueball spectrum: Four low-lying pure glueball masses reproduced at 5–11% accuracy using J = 0.54 fitted to modern quenched lattice m(0⁺⁺) = 1.71(5) GeV. Beta function: One-loop coefficient b₀ = 11N_c/(48π²) derived from MERA entropy flow without Feynman diagrams. String tension: σ = 0.194 GeV² obtained from area-law entanglement entropy, consistent with lattice QCD. Newton's constant: Transparent derivation G_N(χ, a) = a²/(4·c_ent·lnχ) with explicit scale parameters; qualitative reproduction of gravitational dynamics within the QCD framework. Massive graviton: Emergent graviton mass m_grav ≈ 40 MeV from finite-χ Yukawa corrections; nuclear and astrophysical constraints shown to be negligible. Speed of light: Derived as the Lieb-Robinson velocity of the PEPS entanglement network, converging to c = 1 in the continuum limit. RG interpretation: Bond dimension reinterpreted as χ(μ) = exp(S_vac(μ)), connecting to asymptotic safety and Van Raamsdonk's entanglement program. Strict 2D→3+1D map (v15): Resolution of dimensionality mismatch via flux tube transverse modes; PEPS on the transverse plane shown to be a lattice regularization of the Nambu-Goto worldsheet CFT, reproducing the Lüscher term, Casimir scaling, and flux tube width. Numerical verification suite (v14): Seven independent tests organized into Group I (internal PEPS self-consistency) and Group II (external validation against lattice QCD): dimensionless combination D(χ) = O(1), bond dimension at Planck scale χ(M_Pl) ~ 111, RG closure through Z_ren, running coupling α_sPEPS, Casimir scaling of string tensions, deconfinement temperature T_c = 277 MeV, and topological susceptibility χ_top1/4 = 177 MeV. Parameter transparency: One free parameter (J = 0.54) produces eight quantitative predictions; full audit of derived vs. fitted parameters provided. The framework includes a reproducibility package with Python scripts for all numerical tests, figure generation, and preprint compilation. Keywords PEPS tensor networks, emergent gravity, QCD vacuum, glueball spectrum, beta function, string tension, Lieb-Robinson bound, speed of light, MERA, entanglement thermodynamics, collapse field, SU(3) gauge theory, fifth force, graviton mass, holographic principle, asymptotic safety, Van Raamsdonk, running G_N, numerical verification, Casimir scaling, deconfinement temperature, topological susceptibility, Witten-Veneziano, Svetitsky-Yaffe mapping, flux tube transverse modes, worldsheet CFT, Lüscher term, Nambu-Goto effective string, 2D-to-3+1D map, reproducibility