 Complete breaking by an SU2 scalar doublet

A nonzero complex fundamental doublet has trivial stabilizer in the gauged $SU(2)$. Its three angular directions are gauge directions, absorbed by the Higgs mechanism. For vacuum ${\varphi }_0=(0,v/\sqrt{2}{)}^T$, the three gauge bosons have equal mass $gv/2$; one radial scalar remains. There is no unbroken photon-like gauge generator in this theory.