# Is Symmetry Breaking into Special Subgroup Special?

## TL;DR

This paper challenges the conventional view by showing that symmetry breaking into special subgroups like SO(N) or USp(N) in 4D SU(N) models is actually common, not exceptional, based on potential analysis.

## Contribution

It explicitly demonstrates that symmetry breaking into special subgroups is a typical outcome in certain dynamical models, contradicting prior assumptions.

## Key findings

- Symmetry breaking often results in special subgroups like SO(N) or USp(N).
- Potential analysis confirms the ubiquity of these symmetry breaking patterns.
- Most cases at the potential minimum exhibit breaking to these subgroups.

## 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.