Is Symmetry Breaking into Special Subgroup Special?

Abstract

The purpose of this paper is to show that the symmetry breaking into special subgroups is not special at all, contrary to the usual wisdom. To demonstrate this explicitly, we examine dynamical symmetry breaking pattern in 4D $SU(N)$ Nambu--Jona-Lasinio type models in which the fermion matter belongs to an irreducible representation of $SU(N)$. The potential analysis shows that for almost all cases at the potential minimum the $SU(N)$ group symmetry is broken to its special subgroups such as $SO(N)$ or $USp(N)$ when symmetry breaking occurs.