Topological superconductors on superstring worldsheets

Abstract

We point out that different choices of Gliozzi-Scherk-Olive (GSO) projections in superstring theory can be conveniently understood by the inclusion of fermionic invertible phases, or equivalently topological superconductors, on the worldsheet. This allows us to find that the unoriented Type 0 string theory with Ω2 = (-1)f admits different GSO projections parameterized by n mod 8, depending on the number of Kitaev chains on the worldsheet. The presence of n boundary Majorana fermions then leads to the classification of D-branes by KOn(X) ⊗ KO-n(X) in these theories, which we also confirm by the study of the D-brane boundary states. Finally, we show that there is no essentially new GSO projection for the Type I worldsheet theory by studying the relevant bordism group, which classifies corresponding invertible phases. In two appendixes the relevant bordism group is computed in two ways.