Fermion masses and mixings from heterotic orbifold models

We search for a possibility of getting realistic fermion mass ratios and mixing angles from renormalizable couplings on the Z_6-I heterotic orbifold with one pair of Higgs doublets. In the quark sector, we find cases with reasonable m_c/m_t, m_s/m_b, and V_{cb}, if we ignore the first family. In the lepton sector, we can fit the charged lepton mass ratios, the neutrino mass squared difference ratio, and the lepton mixing angles, considering all three families.Comment: 4 pages, 2 figures, 5 tables; talk presented at PASCOS-05, Gyeongju, May 30-Jun 4, 2005; to appear in the proceeding

Universal Bundle, Generalized Russian Formula and Non-Abelian Anomaly in Topological Yang-Mills Theory

We re-examine the geometry and algebraic structure of BRST's of Topological Yang-Mills theory based on the universal bundle formalism of Atiyah and Singer. This enables us to find a natural generalization of the {\it Russian formula and descent equations\/}, which can be used as algebraic method to find the non-Abelian anomalies counterparts in Topological Yang-Mills theory. We suggest that the presence of the non-Abelian anomaly obstructs the proper definition of Donaldson's invariants.Comment: 16 pages, harvmac TeX, ESENAT-92-07, (TeXnical and stupid errors are corrected.