= SU(3) gauge theory with an adjoint Higgs field
{c}
A traceless Hermitian $3\times3$ <adjoint scalar field> transforms by $\Phi\mapsto U\Phi U^\dagger$. A diagonal vacuum with eigenvalues $(\lambda_1,\lambda_2,\lambda_3)$, summing to zero, leaves its <centralizer> unbroken. The <adjoint scalar gauge-boson mass matrix> assigns <mass> $g|\lambda_i-\lambda_j|$ to the vector fields linking the $i$th and $j$th eigenspaces. Coincident eigenvalues preserve non-Abelian rotations of their eigenspace; distinct eigenvalues preserve only a <maximal torus>.
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