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$$\mathcal{L} = \underbrace{K(\Phi^k,\Phi^{k\dagger})_{|\theta^2\bar{\theta}^2}}_{\text{D-term}} + \underbrace{\left( W(\Phi^k)_{|\theta^2} + W^{\dagger}(\Phi^{k\dagger})_{|\bar{\theta}^2}\right)}_{\text{F-terms}}$$

Initially this rustled my Jimmies because they had just spent the preceding section having me jump through hoops to deal with all the other component fields then decided only to use these 3, but then they address this directly: "In the Lagrangian, only the D-term ... and the F-terms enter". Unfortunately, this is as detailed as the explanation gets and I was hoping someone could please explain why this is the case and why the remaining 6 component fields don't show up?

Thanks in advance