= Neutral flat direction with oppositely charged chiral fields
{title2=$W=\lambda X\Phi_+\Phi_-,\quad\phi_+=\phi_-=0,\quad X\text{ arbitrary}$}
For canonical <chiral superfields>, nonzero $\lambda$, a gauged $U(1)$ with charges $(0,+1,-1)$, and no <Fayet–Iliopoulos term>, <F-flatness> requires the charged product to vanish and <D-flatness> requires equal charged magnitudes. Together they force both charged scalar values to zero, leaving the neutral scalar arbitrary. The <vacuum moduli space of a supersymmetric gauge theory> has zero energy, unbroken gauge symmetry and unbroken <supersymmetry>. At $\lambda=0$, equal nonzero charged magnitudes instead permit a gauge-Higgsed supersymmetric branch. A neutral modulus alone does not imply internal gauge breaking.
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