Family number, Wilson line phases and hidden supersymmetry
  We study the relationship between the family number of chiral fermions and the Wilson line phases, based on the orbifold family unification. We find that flavor numbers are independent of the Wilson line phases relating extra-dimensional components of gauge bosons, as far as the standard model gauge symmetry is respected. This feature originates from a hidden quantum-mechanical supersymmetry. 
Yuhei Goto, Yoshiharu Kawamura and Takashi Miura
hep-th hep-ph