Higher-dimensional supersymmetry as an origin of the three families for quarks and leptons

In a (0,1) supersymmetric (SUSY) six-dimensional gauge theory, a gauge fermion gives rise to box anomalies. These anomalies are completely canceled by assuming a vector multiplet of (1,1) SUSY. With a T2/Z3 orbifold compactification of the extra two-dimensional space, the theory provides three chiral multiplets and three equivalent fixed points. We regard them as the origin of the three families of quarks and leptons. Quasi anarchy structure in the SU(5)-5∗ sector and hence the bilarge mixing in the neutrino oscillation are explained quite naturally in this framework. We also discuss a family symmetry as a remnant of the higher-dimensional R symmetry.