Reduction of the rank of gauge groups by noncommuting Wilson lines on orbifolds

A simple set of rules for constructing four-dimensional string models with lower-rank gauge groups is presented in orbifold compactification with non-Abelian Wilson lines. Noncommuting automorphisms associated with different twisted boundary conditions are used to reduce the rank of the subgroup. The method easily gives rank-four models which possess phenomenologically interesting gauge groups and chiral fermions