How do we use the Killing spinors to determine the resulting supersymmetry conserved?

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How do we exactly use the Killing spinors to determine the resulting supersymmetry conserved? Is there some nice "toy" example you could provide me with to see this and convince my self? And is there some nice reference where I can see some example for this?

E.g. how do we determine the amount of SUSY preserved on a sphere, torus, or some cone over a Calabi-Yau etc?

This post imported from StackExchange Physics at 2015-03-08 11:28 (UTC), posted by SE-user Marion
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