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When every $m_i$ and $\zeta$ vanishes, the Coulomb branch again has ${\varphi }_i={\tilde{\varphi }}_i=0$ and arbitrary $x$. A Higgs branch also occurs at $x=0$: it is the zero-level quotient ofby U(1), and has complex dimension $2N-2$ for $N>1$. The two branches meet at the origin. For $N=1$, the F- and D-flat equations force both charged fields to vanish, so the Higgs branch collapses to that intersection point.

Let $m_i=0$ and first take $\zeta >0$. The mass terms and D-flatness require $x=0$ and ${\sum }_i|{\varphi }_i{|}^2-{\sum }_i|{\tilde{\varphi }}_i{|}^2=\zeta$, while F-flatness adds ${\sum }_i{\tilde{\varphi }}_i{\varphi }_i=0$. Dividing by the U(1) gauge action gives the Higgs branchwith complex dimension $2N-2$. For $\zeta <0$, the same result follows after exchanging $\varphi$ and $\tilde{\varphi }$.