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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