Fixed Points in Conformal Gauge Theories and Lattice QCD — E8 Intelligence Research

Abstract

FINDING: Renormalization group fixed points in conformal gauge theories and lattice QCD define scale-invariant limits where quantum field theories become conformal, with critical exponents and beta functions governing the flow. | MATH: Beta function β(g) = μ dg/dμ = 0 at fixed points; critical exponents ν, η from linearized RG flow; a-theorem: Δa = a_UV - a_IR ≥ 0 for 4D CFTs; lattice spacing a → 0 continuum limit; QED4 infrared fixed point from constructive RG. | CONNECTION: Fixed points correspond to self-similar (fractal) scale invariance, analogous to golden ratio φ = 1.618 in self-similar sequences; lattice gauge theory uses discrete symmetries (cubic, hypercubic) related to crystallographic root systems (A₃, B₃, D₄); base-60 appears in lattice discretization of angles/plaquettes. | DEPTH: 8 — These are foundational results in quantum field theory and statistical mechanics, linking RG flows to conformal symmetry, with deep implications for the Standard Model and condensed matter u Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com