Many supersymmetry textbook state that the maximal supersymmetry in any dimension has 32 hermitian supercharges. (Actually for lowest number of supersymmetry N=1 the highest dimension is D=11)
I want to know why the maximal supercharge is restricted as 32.
Answer
Because you want the maximal spin particle allowed to be 2 (since there is no higher spin field theory interacting non trivially), thus in a supermultiplet starting with a particle with helicity 0, say in d=4, the maximal number of susy you can apply is 8, thus N=8 in d=4 is the maximal supersymmetry admitted, which means 32 supercharges.
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