# supersymmetry in 7, 8, 9 dimension

Why above dimension (7,8,9) the number of supercharge per supersymmetry is equal? $i.e$ For 32 supercharges, supersymmetry in 7,8,9 dimension is describe by $N=2$. And for 16 supercharges, supersymmetry in 7,8,9 dimension is described by $N=1 \qquad \text{i.e.} \qquad 9d \\\\\\\\N = 2 \rightarrow 8d \\\\\\\ N=2 \rightarrow 7d$

## 1 Answer

Weyl Invariance in 8d, Majorana invariance in 9D and no reductions are possible in 7D.

So the minimum number of supercharges in 8,9D = $2^{8/2}/2$ complex components = 16 real supercharges.

And in 7D that number is $2^{6/2}$ complex components = 16 real supercharges

For further details, refer to the appendix of Polchinski vol 2