= Global triplet scalar symmetry breaking
{title2=$O(3)\to O(2)$}
= O(3) triplet symmetry breaking
{c}
{synonym}
For a <real scalar triplet> with $V=\frac12m^2\Phi^2+\frac\lambda4(\Phi^2)^2$, $\lambda>0$ and $m^2<0$, the vacuum sphere has radius $v^2=-m^2/\lambda$. At $\Phi_0=ve_3$, the Hessian is $\operatorname{diag}(0,0,2\lambda v^2)$. Global $O(3)\to O(2)$ breaking therefore gives two physical massless <Goldstone bosons> and one radial scalar with squared <mass> $2\lambda v^2$. The angular modes cannot be gauged away in a theory with only global rotations.
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