Dynamical Breaking to Special or Regular Subgroups in $SO(N)$ Nambu--Jona-Lasinio Model

TL;DR

This paper investigates symmetry breaking patterns in 4D $SO(N)$ NJL models with fermions in spinor representations, revealing correlations between subgroup types and fermion representation types, extending previous $SU(N)$ results.

Contribution

It extends the analysis of symmetry breaking patterns to $SO(N)$ NJL models with spinor fermions, highlighting the influence of fermion representation types on subgroup breaking.

Findings

Symmetry breaking into special or regular subgroups depends on fermion representation type.

Patterns observed are consistent with previous $SU(N)$ NJL model results.

The analysis provides insights into the role of fermion representations in symmetry breaking.

Abstract

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.