In the page for superstring theory, Wikipedia states:

Another approach to the number of superstring theories refers to the mathematical structure called composition algebra. In the findings of abstract algebra there are just seven composition algebras over the field of real numbers. In 1990 physicists R. Foot and G.C. Joshi in Australia stated that "the seven classical superstring theories are in one-to-one correspondence to the seven composition algebras".

The paper being cited does not explain this quote in the abstract and is otherwise inaccessible for me.

My understanding is as follows. The seven composition algebras over R are R, C, H, O, split-C, split-H, split-O. The five consistent superstring theories are Type I, Type IIA, Type IIB, SO(32) heterotic, E8×E8 heterotic. The citation implies that there are at least two more.

What are the other two superstring theories, and what is this correspondence?

This post imported from StackExchange MathOverflow at 2023-05-26 20:29 (UTC), posted by SE-user L. E.