Electroweak Symmetry Breaking and the Higgs from Spectral Worldvolume Geometry (IGPS X)

This manuscript presents Paper X of the Information-Geometric Physics System (IGPS) series, extending the framework to the electroweak sector. It explores an approach where the Standard Model Higgs doublet is modeled as a BPS domain wall within a five-dimensional SU(2)_L × U(1)_Y gauge theory. By analyzing the spectral geometry and conformal field theory (CFT) of the Higgs kink worldvolume, this paper attempts to derive fundamental electroweak observables structurally, without introducing additional free parameters. Key Concepts and Results: The Weinberg Angle (sin²θ_W): Building on Callan-Harvey anomaly inflow and topological charge quantization, the framework yields a tree-level value of sin²θ_W = 1/4. This mathematically preserves the gauge boson mass ratio m_Z/m_W = 2/√3 and the exact custodial symmetry parameter ρ = 1. The Electroweak Worldvolume: Utilizing the Goddard-Kent-Olive (GKO) coset construction, we propose an identification of the combined lepton-Higgs worldvolume with the 3-state Potts minimal model M(5,6) carrying a central charge c = 4/5. The Higgs Quartic Coupling (λ_H): Formulated through structural VOA data, specifically combining the primary conformal weight with the UV crossover scale derived from the Schwinger-Dyson equation. This geometric approach yields λ_H = 31/240 ≈ 0.12917, showing a close numerical agreement (-0.17% deviation) with the current experimental value. This result subsequently provides a conditional estimate for the Higgs vacuum expectation value of v ≈ 246.4 GeV. The Observer Necessity Principle: Discussed in the Appendix, this section aims to formalize the mapping of 4D physical couplings from 2D CFT boundary data. By applying the Cauchy functional equation and standard thermodynamic identities, we outline a structural rationale for selecting the specific derivation route presented in this study. Overall, this paper aims to provide a topological and algebraic perspective on the Standard Model's dimensionless electroweak couplings, suggesting that these foundational parameters might be understood as structural invariants of an underlying spectral geometry.