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Killing spinor equations are equations that result from supersymmetric transformations. One example of those is for example is in $N=2$ Supergravity theories.

As suggested by some books and papers on the web, there is the vanishing of the gravitini supersymmetry.

So if fermions here should vanish in $N=2$ supergravity theories, what KSE's should we see in $N=2$ sugra?

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  • $\begingroup$ Which books and papers? $\endgroup$
    – Qmechanic
    Dec 27, 2015 at 19:19

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If we want to find a background preserving some supersymmetry then by assuming that fermions vanish, we have to find a combination of the bosonic fields such that the supersymmetry variation of the fermionic fields is zero. It means that all supersymmetry variations of fermions are required to vanish, not only gaugino or gravitino.

I am not very familiar with $N=2,D=4$ SUGRA, but it seems like in this case the variations are the first, third and forth line in eq (9.46) http://itf.fys.kuleuven.be/~toine/LectParis.pdf They are respectively the variations of gravitino, gaugino and hyperino.

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  • $\begingroup$ @PhilosophicalPhysics On the top of the page 8 he says "As we neglect here the hypermultiplets, we have to consider the basic supergravity multiplet and the vector multiplets", so I guess in your paper he just considers the simplified action. $\endgroup$
    – Yuri
    Dec 28, 2015 at 20:52
  • $\begingroup$ @PhilosophicalPhysics It is just a simplification, simplifications are always good :) $\endgroup$
    – Yuri
    Dec 28, 2015 at 22:04
  • $\begingroup$ I have edited the question to suit the answer you gave and removed the one that has to do with gauginos because I was not convinced that it has to do with hypermltiplets. I'm going to choose this as best answer though. Thank you $\endgroup$ Dec 29, 2015 at 17:49

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