It's really just a dumb question about spinors. The book says that for N=1 SYM, in 3 or 4D we use Majorana spinors. In 6D we use Weyl spinors. And in 10D we use Majorana-Weyl spinors, so that the number of fermionic states matches D-2. My questions is, in 4D, Weyl spinors (chiral spinors) also have only 2 degrees of freedom. Why must we use Majorana spinors instead? In which dimensions do Majorana spinors exist? And which dimensions allow Majorana-Weyl spinors? What are the gamma matrices in these representations? What's the best reference for these issues? Thanks in advance.