Real scalar triplet ($\Phi =({\Phi }_1,{\Phi }_2,{\Phi }_3{)}^T$)

A real scalar triplet groups three real scalar components into a vector under SO(3). Equivalently it is the three-dimensional Adjoint representation of SU(2), whose center acts trivially. Its rotationally invariant quadratic and quartic potentials depend on $\Phi \cdot \Phi$. A nonzero vacuum direction leaves rotations around that direction unbroken.