Lattice Yang-Mills Wilson Loops: Continuum Limit via Makeenko-Migdal and Planar Large-N Dominance — E8 Intelligence Research

FINDING: Lattice Yang-Mills surface sums converge to continuum via Makeenko-Migdal recursions, with discrete curvature encoded in plaquette holonomies; large-N limit reveals planar topology dominance. | MATH: Wilson loop expectation \( W_γ = ∫ DA \, e^{-Sₗₐₜ[U]} W_γ(U)\); lattice action \(Sₗₐₜ = β ∑_p (1 - 1/NRe\,Tr\,U_p)\), \(U_p = ∏l ∈ ∂ p U_l\) (plaquette holonomy); Makeenko-Migdal equation: \(∂_μ W_{γxy} = N δ⁽²⁾(x-y) W_{γxz} W_{γzy} \) (2D); large-N factorization \( Tr\,U_p^2 → Tr\,U_p ^2\) as \(N→∞\). | CONNECTION: Plaquette holonomy = discrete curvature 2-form \(Fμν ~ i[Uμν-I]\); continuum limit restores \(Fμν = ∂_μ A_ν - ∂_ν A_μ + i[A_μ,A_ν]\). Lattice discretization mirrors crystallographic root lattice \(AN-1\) (SU(N) weig Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com