= Solution
For ungauged <chiral superfields>, the two-derivative <supersymmetric action> is a real full-<superspace> integral plus a holomorphic half-<superspace> integral:
$$
\boxed{S=\int d^4x\left[\int d^2\theta\,d^2\bar\theta\,K(\Phi,\Phi^\dagger)+\left(\int d^2\theta\,W(\Phi)+\mathrm{h.c.}\right)\right].}
$$
The real <Kähler potential> $K$ determines the <Kähler metric> and kinetic terms; the <superpotential> $W$ determines <Yukawa interactions> and the <F-term scalar potential>. For canonical normalization, $K=\sum_i\Phi_i^\dagger\Phi_i$. <Berezin integration> is normalized to extract the highest component, $\int d^2\theta\,\theta^2=1$, and the conjugate measure is chosen so the canonical term is $F_i^*F_i$. The <D-term> and <F-term> highest components vary by spacetime <total derivatives>, making the action invariant under <supersymmetry>. Gauging would replace the canonical bilinear by its gauge-covariant version and add a gauge kinetic <F-term>; no gauge multiplet is needed for the chiral theory here.
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