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 \( S^*[U] = minV \{ S^*[V] + T[V,U] \} \) where \( T \) is block-spin transformation kernel; Wilson loop expectation values \( W(C) \) computed to one-loop order; coupling constant \( g^2 \) flows under RG with beta function \( β(g^2) = -β_0 g^4 - β_1 g^6 + \), \( β_0 = 11N/3(4π)^2 \) 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