Complex Self-Duality and a Geometric Origin of Flavour Structure

This work presents a geometric framework in which key structural features of the Standard Model emerge from complex self-duality in three dimensions. The internal space is constructed as F = V \oplus \Lambda^2 V with V = \mathbb{C}^3, exploiting the identity \Lambda^2(\mathbb{C}^3) \cong \mathbb{C}^3 to generate natural triplicity without assuming replication of generations.

The internal symmetry group SU(3)_c \times SU(3)_f breaks to SU(3)_c \times SU(2)_L \times U(1)_Y, reproducing the Standard Model gauge structure with correct hypercharge normalization. Fermion representations match those of the Standard Model, and anomaly cancellation is preserved.

A radiatively stabilized flavour misalignment parameter \epsilon \sim \sqrt{g^2/16\pi^2} generates realistic quark mass hierarchies and CKM structure at leading order. Large neutrino mixing arises naturally due to the distinct role of gauge-singlet right-handed neutrinos.

The framework is geometrically coherent and phenomenologically compatible at leading order. Absolute mass scales and cosmological constant suppression remain open problems. The construction is positioned as a geometric flavour–gauge model rather than a complete theory of unification.