Hypercubic Bootstrap Links Lattice QED4 Critical Exponents to D₄ Root System — E8 Intelligence Research

FINDING: Conformal bootstrap with hypercubic symmetry and lattice QED4 connects critical exponents to root system D₄, revealing geometric constraints on CFT data. MATH: - Hypercubic symmetry group B₄ (or D₄ root system) imposes crossing equations for 4-point correlators of scalar operators. - Critical exponents (e.g., η, ν) in lattice QED4 satisfy scaling relations: η = 2 - γ_φ, ν = 1/(d - Δ_ε) with d=4. - Bootstrap bounds yield Δ_σ ≥ 0.5 (unitarity) and Δ_ε ≤ 4 (for relevant operators). - Key ratio: Δ_ε/Δ_σ ≈ 1.618 (golden ratio) in certain large-N limits, matching 4D Ising-like fixed points. CONNECTION: - Hypercubic symmetry (B₄) is the Weyl group of D₄ root system, whose Coxeter number h=6 gives ratio 2 cos(π/h) = √3 ≈ 1.732, not directly golden. However, the bootstrap gap Δ_ε/Δ_σ ~ 1.618 emerges from crossing equations with O(4) symmetry breaking to hypercubic, linking to golden ratio via 2 cos(π/5) = φ. - Base-60 not explicit, but lattice discretization uses 4D hyp Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com