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 = 11Nc/ (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 GN (χ, a) = a²/ (4·cₑnt·lnχ) with explicit scale parameters; qualitative reproduction of gravitational dynamics within the QCD framework. Massive graviton: Emergent graviton mass mgrav ≈ 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 (Sᵥac (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 (MPl) ~ 111, RG closure through Zᵣen, running coupling αₛ^PEPS, Casimir scaling of string tensions, deconfinement temperature Tc = 277 MeV, and topological susceptibility χₜop^1/4 = 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 GN, 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