For $W=XYZ$,
$$
V=|YZ|^2+|XZ|^2+|XY|^2.
$$
The <F-flatness> equations require at least two of $X,Y,Z$ to vanish. The <vacuum moduli space of a supersymmetric gauge theory>[vacuum space] is therefore the union of the three coordinate axes in $\mathbb C^3$,
$$
\boxed{\{Y=Z=0\}\cup\{X=Z=0\}\cup\{X=Y=0\}},
$$
and every point on it has zero vacuum energy.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 307 / 1 / ii / Solution

The vacuum moduli space is the space of simultaneous F-flat and D-flat configurations modulo gauge transformations. Gauge-invariant chiral operators often provide holomorphic coordinates, subject to algebraic constraints.


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 Incoming links: Vacuum moduli space of a supersymmetric gauge theory