I never understood why supergravity $\mathcal N=8$, nor why the spin of a graviton is 2.
I've been reading around but I still don't have a back-of-the-envolope understanding.
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4Hi, welcome to this site. I don't think these two questions are related. If so, could you please split them up in two separate questions? Also, the question about the graviton has been asked before, see for instance this question and this in general. – Hunter May 30 '14 at 01:51
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Actually they are related - it takes 8 supersymmetry transformations to go from the spin=+2 graviton to the spin=-2 graviton. – Mitchell Porter May 30 '14 at 05:38
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1Regarding the graviton, see my answer http://physics.stackexchange.com/q/108230/ – JamalS May 30 '14 at 05:58
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On the $\mathcal N = 8$ part: This is just the maximal supergravity. There can be no more than 32 supercharges, because more supercharges would necessarily introduce higher spins than 2 into the theory - and we don't know how to deal with spins larger than 2. Smaller supergravities exist, though, see e.g. mSuGra – Neuneck May 30 '14 at 10:14
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This post (v2) asks two questions (instead of the recommended one question). – Qmechanic Aug 10 '14 at 20:39