Flavor Geometry in SU(36)

Key Points

• To develop a geometric framework for flavor physics based on the SU(36) gauge structure.
• Proposed a coordinate-based description for fermion flavor degrees of freedom on a unified internal manifold with a flavor metric G.
• Analyzed the emergence of fermion mass and CP violation from the geometry of G and its connection Γ.
• Studied implications for the standard model flavor sector as an effective low-energy structure.
• Demonstrated that the observed mixing matrix corresponds to projections of higher-dimensional unitary transformations.
• Predicted enhancements in CP violation due to non-trivial holonomy in flavor space.
• Identified a characteristic flavor scale ΛF that suppresses these effects beyond current accelerator energies.