In the D1 composite Higgs model, the SO(9)/SO(8) coset is deformed by a scalar operator ΦD1 that transforms the usual Mexican hat potential into a characteristic four-toothed clover shape with exact Z4 symmetry. This deformation naturally lifts the flat directions and produces precisely four degenerate discrete minima---termed crystalline vacua--- without fine-tuning or additional ad-hoc symmetries.
We provide numerical confirmation of this structure through toy lattice relaxation simulations, which show that random initial field configurations dynamically cluster into exactly four sharp Z4 -related points. The renormalisation group flow of the deformation coupling ΦD1 exhibits a robust O(1) plateau at the TeV scale, ensuring naturalness.
Full phenomenological scans of the modified Higgs couplings κV and κf demonstrate excellent agreement with the latest 2025 LHC Run 3 constraints. The distinctive shape of the effective potential and the resulting pattern of fermion coupling deviations provide clear experimental signatures that distinguish the D1 framework from conventional continuous coset models.
