= Supersymmetric vacuum manifold of a bilinear hybrid superpotential
{title2=$S=0,\quad uv=\zeta$}
For nonzero $g$ and $\zeta$, these field values give $W=0$ and all <Kähler covariant derivatives of a superpotential> zero, hence zero <supergravity auxiliary fields> and zero vacuum energy. With only the supplied chiral fields, the product condition gives a complex vacuum manifold rather than one isolated point. A specified gauged opposite-charge symmetry can add a <D-flatness> condition and a gauge quotient, but no such gauge sector should be invented from the field labels alone.
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