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I'm reading a book on AdS/CFT by Ammon and Erdmenger and chapter 3 covers supersymmetry. This isn't my first look at SUSY but it's my first in depth look to really try to understand it, and when they talk about constructing a Lagrangian for $\mathcal{N}=1$ chiral superfields they write the most general form,

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

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?

I posted this in PhysicsForums and failed to get an answer unfortunately, so hopefully this sees more attention

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  • $\begingroup$ Link to PhysicsForum post? $\endgroup$
    – Qmechanic
    Jan 31, 2019 at 20:10
  • $\begingroup$ Book: inspirehep.net/record/1376202 $\endgroup$
    – Qmechanic
    Jan 31, 2019 at 20:18
  • $\begingroup$ @Qmechanic physicsforums.com/threads/… Like I said, it's the exact same post, just with no answers $\endgroup$
    – jj7510
    Jan 31, 2019 at 20:39
  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/397670/2451 $\endgroup$
    – Qmechanic
    Feb 2, 2019 at 22:40
  • $\begingroup$ @Qmechanic I saw that question but it seems to suggest that the exclusive inclusion of F and D terms is a result of writing them as integrals over the superspace, whereas the book I'm using makes it seems more like the integrals over the superspace are just a convenient way of projecting these terms out. Perhaps I'm misinterpreting one (or both) of the sources, but from what I could tell, we want the F and D terms for some deeper reason, and the integrals are just a nice way of achieving that. My question is what is that deeper reason? $\endgroup$
    – jj7510
    Feb 4, 2019 at 13:53

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This answer should help https://physics.stackexchange.com/a/403388/221660 . Also, you may check Section 95 of "Quantum Field Theory" by Srednicki or Section 4 and 5 of "Supersymmetry and Supergravity " by Wess and Baggar. I wanted to write this as a comment but I can't due to the low reputation. XD

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