### Abstract

We compute the L_{∞}-theoretic dimensional reduction of the F1/Dp-brane super L_{∞}-cocycles with coefficients in rationalized twisted K-theory from the 10d type IIA and type IIB super Lie algebras down to 9d. We show that the two resulting coefficient L_{∞}-algebras are naturally related by an L_{∞}-isomorphism which we find to act on the super p-brane cocycles by the infinitesimal version of the rules of topological T-duality and inducing an isomorphism between K^{0} and K^{1}, rationally. In particular this is a derivation of the Buscher rules for RR-fields (Hori's formula) from first principles. Moreover, we show that these L_{∞}-algebras are the homotopy quotients of the RR-charge coefficients by the "T-duality Lie 2-algebra". We find that the induced L_{∞}-extension is a gerby extension of a 9+(1+1) dimensional (i.e. "doubled") T-duality correspondence super-spacetime, which serves as a local model for T-folds. We observe that this still extends, via the D0-brane cocycle of its type IIA factor, to a 10+(1+1)-dimensional super Lie algebra. Finally we observe that this satisfies expected properties of a local model space for F-theory elliptic fibrations.

Original language | English (US) |
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Pages (from-to) | 1209-1270 |

Number of pages | 62 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 22 |

Issue number | 5 |

DOIs | |

State | Published - 2018 |

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)

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## Cite this

*Advances in Theoretical and Mathematical Physics*,

*22*(5), 1209-1270. https://doi.org/10.4310/atmp.2018.v22.n5.a3