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

TL;DR

This paper analyzes how $SU(n)$ symmetry is broken by rank three and two antisymmetric tensor scalars, deriving branching rules and scalar mass spectra within a general renormalizable potential framework.

Contribution

It provides a detailed tensor analysis of $SU(n)$ symmetry breaking, including branching rules and mass calculations for antisymmetric tensor scalars.

Findings

Derived branching rules for adjoint and antisymmetric tensor representations.

Identified the $U(1)$ generator mismatch in general $SU(n)$ cases.

Computed scalar mass spectra in terms of potential parameters.

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.