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Topological superconductors on superstring worldsheets

by Justin Kaidi, Julio Parra-Martinez, Yuji Tachikawa, with a mathematical appendix by Arun Debray

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Submission summary

Authors (as registered SciPost users): Julio Parra-Martinez
Submission information
Preprint Link: scipost_202002_00003v6  (pdf)
Date accepted: 2020-07-16
Date submitted: 2020-06-24 02:00
Submitted by: Parra-Martinez, Julio
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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 $\rm 0$ string theory with $\Omega^2=(-1)^{\sf f}$ 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 $KO^n(X)\oplus KO^{-n}(X)$ 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 $\rm I$ worldsheet theory by studying the relevant bordism group, which classifies corresponding invertible phases. This paper provides the details for the results announced in the letter \cite{Kaidi:2019pzj}.

Published as SciPost Phys. 9, 010 (2020)

Author comments upon resubmission

We thank the referees for their comments, which have been included in the revised version of the manuscript.

List of changes

- We have added additional paragraphs at the end of Section 3 and Appendix C, with comments about the possibility of branes which are stable according to K-theory becoming unstable in the presence of D9-branes required by tadpole cancellation.

- We have fixed the typo in Eq. (2.4).

- We have added a new Appendix F with a computation of the relevant bordism groups using the Adams spectral sequence, where agreement is found with the results of the AHSS. This appendix is by Arun Debray, who has been added to the list of authors.

Submission & Refereeing History

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Resubmission scipost_202002_00003v6 on 24 June 2020

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