To study $S$-duality in more detail, i tried to read, Electric-magnetic duality and the Geometric Langlands Program. In section 2.1, there is a comment about 10d SYM. Excerpt from the paper above,
Ten dimensions is the maximum possible dimension for supersymmetric Yang-Mills theory by the virtue of Nahm's theorem.
I know that Nahm's theorem as a theorem for classfication of superconformal algebra. (Nahm's paper: SUPERSYMMETRIES AND THEIR REPRESENTATIONS). I just took a glance of this paper, but I couldn't find relevant physics behind its mathematical description.
I want to know how the ten dim, SYM is the maximum possible dimension. And know some physical application like SYM in 10d for Nahm's theorem.