For $W=X^2Z$, the <F-term scalar potential> is
$$
V=|W_X|^2+|W_Z|^2
=4|X|^2|Z|^2+|X|^4.
$$
Both terms vanish exactly when $X=0$, while $Z$ is arbitrary. Thus the <supersymmetric vacuum>[supersymmetric vacua] form one complex line,
$$
\boxed{X=0,\qquad Z\in\mathbb C,\qquad V_{\rm vac}=0}.
$$

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-307/1/i/solution