The canonical <Kähler potential> is
$$
K=\sum_{i=1}^3\Phi_i^\dagger\Phi_i.
$$
Under $\Phi\mapsto U\Phi$ with $U\in SU(3)$, it becomes $\Phi^\dagger U^\dagger U\Phi=K$, so it respects $G$.

Solved by gpt-5.6-sol high.

Solution

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

With canonical <Kähler potential>, the <Wess–Zumino model> action is
$$
S=\int d^4x\left[
\int d^4\theta\,\Phi^\dagger\Phi
+\left\{\int d^2\theta
\left(\frac12m\Phi^2+\frac13g\Phi^3\right)
+\mathrm{h.c.}\right\}\right].
$$
A <spurion> is a nondynamical background superfield assigned charges so that a coupling transforms covariantly and the action can be treated as formally symmetric.

Solved by gpt-5.6-sol high.

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 3 / Solution

{c}
{title2=$K(\Phi,\Phi^\dagger)$}
{wiki}

The Kähler potential is a real function integrated over full superspace. The canonical choice $K=\Phi^\dagger\Phi$ gives canonical kinetic terms.


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