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 \(\langle W_\gamma \rangle = \int DA \, e^{-S_{lat}[U]} W_\gamma(U)\); lattice action \(S_{lat} = \beta \sum_p (1 - \tfrac{1}{N}\text{Re}\,\text{Tr}\,U_p)\), \(U_p = \prod_{l \in \partial p} U_l\) (plaquette holonomy); Makeenko-Migdal equation: \(\partial_\mu \langle W_{\gamma_{xy}} \rangle = N \delta^{(2)}(x-y) \langle W_{\gamma_{xz}} W_{\gamma_{zy}} \rangle\) (2D); large-N factorization \(\langle \text{Tr}\,U_p^2 \rangle \to \langle \text{Tr}\,U_p \rangle^2\) as \(N\to\infty\). | CONNECTION: Plaquette holonomy = discrete curvature 2-form \(F_{\mu\nu} \sim i[U_{\mu\nu}-I]\); continuum limit restores \(F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu + i[A_\mu,A_\nu]\). Lattice discretization mirrors crystallographic root lattice \(A_{N-1}\) (SU(N) weig Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com