Dark Matter as Topological Electromagnetic Structures

Title: Dark Matter as Topological Electromagnetic Structures Author: Alexander Novickis ([email protected]) We propose that dark matter consists of stable, electrically neutral (H = 0) topological configurations of the electromagnetic field within the Faddeev-Niemi nonlinear sigma model. Candidates are classified by knot theory (trefoil, figure-eight, Whitehead link) and conformal SO(4,2) representations. A ropelength-based mass spectrum, with VK saturation calibration (structure correction f = 1.20), yields m_trefoil = 2.12 (+0.44/−0.28) MeV. The framework predicts null nuclear recoil results while requiring monoenergetic MeV gamma-ray lines from annihilation. Key original results include: H = 0 classification: dark matter particles are knotted, electrically neutral EM solitons classified by knot type (trefoil, figure-eight, Whitehead link) and topological invariants (§4–5) Hopf charge conservation theorem: exact topological protection ensures absolute stability of knotted configurations (§6) Vanishing transverse magnetic dipole moment: C_N symmetry (N ≥ 3) enforces zero transverse dipole; first nonvanishing multipole is octupole — this explains null direct detection results (§6) Ropelength mass spectrum: E ∝ L³⁴ (ropelength) with VK saturation calibration (f = 1.20) gives m_trefoil = 2.12 (+0.44/−0.28) MeV with mass ratios between species determined by ropelength ratios alone (§9) Cold dark matter proof: free-streaming length λ_fs < 10⁻² Mpc for MeV-scale masses, satisfying Lyman-α and structure formation constraints (§13) Monoenergetic gamma-ray signature: DM + DM → 2γ at E_γ = m_DM c² — distinctive spectral line testable by COSI mission (expected 2027) (§10) BBN compatibility: ΔN_eff ≈ 0.042 per species if fully thermalized before BBN; consistent with Planck bounds (§13) Null nuclear recoil prediction: no QCD coupling means no WIMP-like signal in xenon or germanium detectors; existing null results are a feature, not a problem (§10) Unified topological classification: leptons (H = ±1), baryons (multi-sector), dark matter (H = 0, knotted) — all from the same Faddeev-Niemi field (§14) The numerical construction of H = 0 knotted solitons in the full Faddeev-Niemi model remains the principal open problem. The COSI gamma-ray telescope provides the most promising near-term test of the framework's distinctive MeV-line prediction. Keywords: dark matter, topological soliton, knot theory, Hopf charge, electromagnetic structure, Faddeev-Niemi model, cold dark matter, conformal field theory, ropelength, neutral soliton, MeV dark matter, gamma-ray lines