Family Unification in a Six Dimensional Theory with an Orthogonal Gauge Group

We propose a simple model of family unification, which is a six dimensional $SO(20)$ gauge theory with a single fermion in the spinorial representation. After compactification to five dimensions, our model gives a five dimensional model where the Standard Model Higgs field is unified into the fifth component of the five dimensional gauge field as well as three generations of quarks and leptons are unified into a single spinor field.