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.
| Original language | English |
|---|---|
| Article number | 010 |
| Journal | SciPost Physics |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 2020 |
Bibliographical note
Publisher Copyright:© Copyright J. Kaidi et al.
Funding
The authors thank the TASI 2019 summer school at University of Colorado, Boulder, where JK and JPM were students and YT was a lecturer, for providing an ideal environment for collaboration; this paper grew out of a lunchtime conversation there. The authors are especially grateful to Edward Witten for many useful correspondences, and for providing much of the content of Appendix D. We also thank Arun Debray, Ryohei Kobayashi, and Ryan Thorngren for their help in computing bordism groups, as well as Oren Bergman, Jake McNamara, Max Metlitski, Matthew Heydeman, and Juven Wang for useful discussions. JPM thanks the Center for Mathematical Sciences and Applications at Harvard University for hospitality while this work was being completed. YT is in part supported by WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo, and in part by JSPS KAKENHI Grant-in-Aid (Wakate-A), No.17H04837 and JSPS KAKENHI Grant-in-Aid (Kiban-S), No.16H06335. JPM is supported by the US Department of State through a Fulbright scholarship. JK and JPM thank the Mani L. Bhaumik Institute for generous support.
| Funders | Funder number |
|---|---|
| WPI Initiative | |
| U.S. Department of State | |
| Harvard Transdisciplinary Research in Energetics and Cancer Center, Harvard University | |
| Japan Society for the Promotion of Science Fund for the Promotion of Joint International Research | 16H06335, 17H04837 |
| Japan Society for the Promotion of Science Fund for the Promotion of Joint International Research | |
| Ministry of Education, Culture, Sports, Science and Technology | |
| University of Tokyo |
ASJC Scopus subject areas
- General Physics and Astronomy