Chiasmus Resources

An explicit correspondence between simple super-Yang-Mills and classical superstrings in dimensions 3, 4, 6, 10 and the division algebras R, C, H, O is established. A gamma matrix identity necessary and sufficient for their existence is shown to yield trialities, objects which are equivalent to division algebras. The physical states lie in representations of the group of triples of the division algebra, exhibiting outer automorphisms exchanging the bosons and fermions. The identities are also interpreted in terms of projective lines over division algebras.