The Standard Model gauge group SU (3) × SU (2) × U (1) is derived as the automorphism group of the octonionic brane-bulk rotation algebra, specically as the subgroup of G2 = Aut (O) that preserves the split into H+ and H−sectors. SU (3) arises from the rotations of the H−= e4, e5, e6, e7 sector that x the real axis and e7 the colour rotations. SU (2) × U (1) arises from the rotations of H+ = 1, e1, e2, e3 the electroweak symmetry. The Weinberg angle sin2θW = 3/8 is the natural projection of the G2 structure constants onto the SU (2) × U (1) subalgebra. G2 is simply connected (π2 (G2) = 0), forbidding magnetic monopoles of the sump type. GUT unication beyond the SM gauge group is excluded because it would require extending the automorphism group beyond G2, which has no natural octonionic basis. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.
Bharathi Jagadeesan (Fri,) studied this question.