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Topological Superconductors on Superstring Worldsheets

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arxiv 1911.11780 v2 pith:UY2W5AT2 submitted 2019-11-26 hep-th cond-mat.str-el

classification hep-thcond-mat.str-el
keywords theoryworldsheetboundarydifferentinvertiblephasesprojectionssuperconductors
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $\rm 0$ 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}.

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Cited by 3 Pith papers

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    Verification of Blum-Dienes and Bergman-Gaberdiel dualities shows agreement in gauge group global forms from orientifold brane states and internal lattices, with one subtle projection exception.

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    Stable D-branes in the Dabholkar-Park background are derived from world-sheet anomalies with boundary Majorana fermions, matching the known relative KR-theory classification and explaining its 4-fold periodicity.

  3. Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT

    hep-th 2024-11 conditional novelty 4.0 of 10

    Known one- and two-loop superstring chiral measures are restated as path integrals of the Gelca-Hamilton 3D TQFT over handlebodies, with modular transformations interpreted as bulk mapping class group moves.

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