### Abstract

We show that supercocycles on super L_{∞}-algebras capture, at the rational level, the twisted cohomological charge structure of the fields of M-theory and of type IIA string theory. We show that rational 4-sphere-valued supercocycles for M-branes in M-theory descend to supercocycles in type IIA string theory with coefficients in the free loop space of the 4-sphere, to yield the Ramond–Ramond fields in the rational image of twisted K-theory, with the twist given by the B-field. In particular, we derive the M2/M5 ↔ F1/Dp/NS5 correspondence via dimensional reduction of sphere-valued super-L_{∞}-cocycles.

Original language | English (US) |
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Pages (from-to) | 91-108 |

Number of pages | 18 |

Journal | Journal of Geometry and Physics |

Volume | 114 |

DOIs | |

State | Published - Apr 1 2017 |

### Keywords

- Branes
- Homotopy Lie algebras
- Rational homotopy theory
- Supersymmetry

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

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## Cite this

Fiorenza, D., Sati, H., & Schreiber, U. (2017). Rational sphere valued supercocycles in M-theory and type IIA string theory.

*Journal of Geometry and Physics*,*114*, 91-108. https://doi.org/10.1016/j.geomphys.2016.11.024