Paper XXXVIII: Magnetic Monopoles and Dyons in the Hopf Framework
Description
Title: Paper XXXVIII: Magnetic Monopoles and Dyons in the Hopf Framework
Author: Alexander Novickis (alex.novickis@gmail.com)
Magnetic monopoles have been sought since Dirac's 1931 charge-quantization argument, and Grand Unified Theories predict superheavy (~10^16 GeV) monopoles whose cosmological overproduction motivated inflation. We show that in the Hopf soliton framework monopoles are forbidden as finite-energy Faddeev–Niemi solitons: on the target S², electric charge is the Hopf invariant (π₃(S²)=ℤ), while the monopole-like π₂(S²) textures are Derrick-unstable and unwind in 3+1 dimensions. GUT monopoles never form (the breaking is the S³→S² Hopf fibration, π₂(S³)=0), so the cosmological monopole problem dissolves and the Witten effect is moot (θ_QCD=0); charge quantization instead follows from π₃(S²)=ℤ. The Standard Model's own electroweak (Cho–Maison) monopole is, however, a separate gauge-stabilized object — outside the ungauged no-go — which the framework contains and, via its Higgs-as-modulus field-dependent coupling (the Berger–Skyrme multiplier η²=4(λ²−1)/λ), renders finite: using the finite-energy BPS mass formula we predict M_EW ≈ 7 TeV, a MoEDAL-accessible target, whose relic is a negligible extra dark component (Ω/Ω_DM ~ 10⁻⁶–10⁻³, neutral monopolium). We predict null results for GUT-scale and light-soliton monopole searches; a ~7 TeV electroweak monopole is expected, whereas a light-soliton or GUT-scale monopole would falsify the framework.
Keywords: monopoles, dyons, electroweak monopole, Cho-Maison, topology, Hopf soliton, Faddeev-Niemi, charge quantization, dark matter, falsifiable prediction
Series: Paper XXXVIII in the Hopf Soliton Programme