 Fundamental-doublet breaking of SU(2)

A single complex scalar field in the two-dimensional fundamental representation with potential $\lambda ({\varphi }^{†}\varphi -v^2/2{)}^2$, $\lambda ,v>0$, has a three-sphere vacuum manifold. The stabilizer in $SU(2)$ of a chosen nonzero vector is trivial, so all three gauge bosons acquire the common mass $gv/2$. In unitary gauge, $\varphi =(0,v+h{)}^T/\sqrt{2}$ leaves one physical radial scalar of squared mass $2\lambda v^2$. Its couplings are $g^{2}vh{A}^2/4+g^2{h}^2{A}^2/8-\lambda v{h}^3-\lambda h^4/4$. The three angular fields become longitudinal vector polarizations through the Higgs mechanism.