It is recently shown that in 4D $SU(N)$ Nambu--Jona-Lasinio (NJL) type models, the $SU(N)$ symmetry breaking into its special subgroups is not special but much more common than that into the regular subgroups, where the fermions belong to complex representations of $SU(N)$. We perform the same analysis for $SO(N)$ NJL model for various $N$ with fermions belonging to an irreducible spinor representation of $SO(N)$. We find that the symmetry breaking into special or regular subgroups has some correlation with the type of fermion representations; i.e., complex, real, pseudo-real representations.

中文翻译：

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SO(N) Nambu–Jona-Lasinio 模型中特殊或规则子群的动态分解

最近的研究表明，在 4D $SU(N)$ Nambu--Jona-Lasinio (NJL) 型模型中，突破到其特殊子群的 $SU(N)$ 对称性并不特殊，但比进入正则的更常见。子群，其中费米子属于 $SU(N)$ 的复杂表示。我们对各种 $N$ 的 $SO(N)$ NJL 模型执行相同的分析，费米子属于 $SO(N)$ 的不可约自旋量表示。我们发现分解成特殊或规则子群的对称性与费米子表示的类型有一定的相关性；即，复杂的、真实的、伪真实的表示。