Classification of String Theories via Topological Phases

Abstract

We point out that the choice of phases in Gliozzi-Scherk-Olive projections can be accounted for by a choice of fermionic symmetry-protected topological phases on the world sheet of the string. This point of view not only easily explains why there are essentially two type II theories, but also predicts that there are unoriented type 0 theories labeled by n mod 8 and that there is an essentially unique choice of the type I world sheet theory. We also discuss the relationship between this point of view and the K-theoretic classification of D-branes.