### 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) |
---|---|

Pages (from-to) | 91-108 |

Number of pages | 18 |

Journal | Journal of Geometry and Physics |

Volume | 114 |

DOIs | |

State | Published - Apr 1 2017 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Geometry and Physics*,

*114*, 91-108. https://doi.org/10.1016/j.geomphys.2016.11.024

**Rational sphere valued supercocycles in M-theory and type IIA string theory.** / Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Rational sphere valued supercocycles in M-theory and type IIA string theory

AU - Fiorenza, Domenico

AU - Sati, Hisham

AU - Schreiber, Urs

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

KW - Branes

KW - Homotopy Lie algebras

KW - Rational homotopy theory

KW - Supersymmetry

UR - http://www.scopus.com/inward/record.url?scp=85007140105&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007140105&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2016.11.024

DO - 10.1016/j.geomphys.2016.11.024

M3 - Article

AN - SCOPUS:85007140105

VL - 114

SP - 91

EP - 108

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

ER -