Block-Spin RG Yields Improved Wilson Action for SU(N) Lattice Gauge Theory — E8 Intelligence Research

FINDING: Block-spin RG transformation for SU(N) lattice gauge theory yields improved Wilson action near non-trivial fixed point, with explicit Wilson loop expectation values on renormalized trajectory. | MATH: Fixed-point action satisfies \( S^*[U] = \min_{V} \{ S^*[V] + T[V,U] \} \) where \( T \) is block-spin transformation kernel; Wilson loop expectation values \( \langle W(C) \rangle \) computed to one-loop order; coupling constant \( g^2 \) flows under RG with beta function \( \beta(g^2) = -\beta_0 g^4 - \beta_1 g^6 + \dots \), \( \beta_0 = \frac{11N}{3(4\pi)^2} \) for SU(N). | CONNECTION: Hypercubic lattice structure (4D) relates to root system \( B_4 \) (crystallographic symmetry); fixed-point action exhibits scale invariance with anomalous dimensions; no direct golden ratio or base-60 link, but lattice spacing \( a \) defines UV cutoff, and RG flow approaches conformal fixed point — reminiscent of self-similarity at criticality. | DEPTH: 7 — Rigorous perturbative construction o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com