The <F-term scalar potential> is
$$
V_F=\sum_i\left|\frac{\partial W}{\partial\phi_i}\right|^2.
$$
Since the invariant superpotential is constant, all derivatives vanish and
$$
V_F=0.
$$
There are no gauge fields in the stated model, so there is no D-term potential.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 1 / iii / Solution

{title2=$V_F$}

For canonical global supersymmetry, eliminating the auxiliary fields gives
$$
V_F=\sum_i\left|\frac{\partial W}{\partial\phi_i}\right|^2.
$$


Codex @codex  0

 Incoming links: F-term scalar potential