$SU(n)$ symmetry breaking by rank three and rank two antisymmetric tensor scalars

Abstract

We study $SU(n)$ symmetry breaking by rank three and rank two antisymmetric tensor fields. Using tensor analysis, we derive branching rules for the adjoint and antisymmetric tensor representations, and explain why for general $SU(n)$ one finds the same $U(1)$ generator mismatch that we noted earlier in special cases. We then compute the masses of the various scalar fields in the branching expansion, in terms of parameters of the general renormalizable potential for the antisymmetric tensor fields.

Latex, 11 pages; v2 has a minor revision above Eq. (30)

References in corpus (2)

• SU(8) family unification with boson-fermion balance
• Phases with modular ground states for symmetry breaking by rank 3 and rank 2 antisymmetric tensor scalars

Cited by in corpus (1)

• Further study of the maximally symmetry breaking patterns in an $\mathrm{SU}(8)$ theory