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People say that

In superconformal field theories with extended susy (say 4d, $\mathcal{N}=2$) we have protected local operators annihilated by some supercharges $Q_I$. Also, upon breaking conformal symmetry there is a well defined particle spectrum which contains in particular BPS states.

I am not sure I understand the term "protected". Protected operators against what? Also, how and why these operators lead to BPS states? I know that the latter are annihilated by half or quarter the supersymmetries, but again why protected?

Is there a simple example of such an operator $\mathcal{O}$ where it is obvious that $$ Q \mathcal{O} =0? $$

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    $\begingroup$ What people? Source? $\endgroup$ – JamalS Dec 21 '17 at 15:20
  • $\begingroup$ Heard it today in a talk. But I think it is written in many papers. $\endgroup$ – Marion Dec 21 '17 at 15:21

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