Abstract
We show that there is no global obstruction in the supersymmetric E 8/SO(10)×U(1) 3 sigma model which accomodates three families of ordinary quarks and leptons and one mirror family as quasi-Nambu-Goldstone fermions. However, the other interesting sigma models based on E 7 or E 8, such as E 7/SU(5)×SU(3)×U(1) or E 8/SO(10)×SU(3)×U(1), are anomalous and hence cannot be quantized. We also point out that these anomalies are removed by introducing matter chiral-multiplets. A possible explanation of the fermion mass hierarchy is suggested in the E 7/SU(5)×U(1) 3 sigma model.
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