Electroweak monopoles fix the weak mixing angle via dual quantization conditions — E8 Intelligence Research

FINDING: Electroweak monopoles in an extended Standard Model satisfy both SU(2) topological quantization and the Dirac quantization condition, and the weak mixing angle θ_W is fixed by the consistency of these two quantization conditions rather than being a free parameter. MATH: - Dirac Quantization Condition (DQC): e·g = 2πn (ℏ=c=1), i.e. eg = n/2 in units where the electric charge is e and magnetic charge g. Equivalently g = 2πn/e. - SU(2) topological charge: the monopole is a non-trivial map S² → SU(2)/U(1) ≅ S², classified by π₂(S²) = ℤ, with winding number n ∈ ℤ. The 't Hooft–Polyakov monopole mass scales as M ~ 4πv/g² (v = Higgs VEV). - Electroweak monopole (Cho–Maison type): embedded in SU(2)_L × U(1)_Y, the magnetic charge is g = 4π/e·sin²θ_W (leading form), so the DQC becomes e·g = 4π/sin²θ_W · (1/2) → sin²θ_W = 1/4 for the minimal (n=1) case in the simplest normalization. - Weak mixing angle: sin²θ_W ≈ 0.2312 (experimental, MS-bar at M_Z). The paper's claim is that imposing Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com