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 00 string theory with \Omega^2=(-1)^{f}Ω2=(−1)f admits different GSO projections parameterized by nn mod 8, depending on the number of Kitaev chains on the worldsheet. The presence of nn boundary Majorana fermions then leads to the classification of D-branes by KO^n(X)\oplus KO^{-n}(X)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 II 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.

The algebra of anomaly interplay

“…More generally, the mod 8 anomaly counts the number of left-moving Majorana-Weyl fermions minus the right-moving ones. This conclusion, which we have derived from a purely local U(1) anomaly using the interplay diagram (4.5), agrees with other examples of /8 anomalies in fermionic system with a unitary /2 symmetry [43,45,46], where a Majorana-Weyl fermion that couples to the /2 symmetry contributes the finest anomaly of 1 mod 8.…”

Boundary states for chiral symmetries in two dimensions

“…The case of √ 2 Z is telling us that the system has an unpaired Majorana zero mode, and hence the two boundary conditions are mutually incompatible. Indeed, related factors of √ 2 have appeared in the early study of non-BPS D-branes [8,9] and, more recently, in the analysis of SPT phases [10,11].…”

Stringy tachyonic instabilities of non-supersymmetric Ricci flat backgrounds

“…The resulting theories exhibit typical tachyonic instabilities as in many other non-supersymmetric string compactifications studied previously, see e.g. [7,8,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for constructions in the NSR formalism.…”