### Abstract

We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with non-geometric fluxes, and in M-theory with non-geometric Kaluza-Klein monopoles. After a brief overview of the main historical appearences of nonassociativity in quantum mechanics, string theory and M-theory, we provide a detailed account of the classical and quantum dynamics of electric charges in the backgrounds of various distributions of magnetic charge. We apply Born reciprocity to map this system to the phase space of closed strings propagating in R-flux backgrounds of string theory, and then describe the lift to the phase space of M2-branes in R-flux backgrounds of M-theory. Applying Born reciprocity maps this M-theory configuration to the phase space of M-waves probing a non-geometric Kaluza-Klein monopole background. These four perspective systems are unified by a covariant 3-algebra structure on the M-theory phase space.

Original language | English |
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Article number | 100 |

Journal | Proceedings of Science |

Volume | 347 |

DOIs | |

Publication status | Published - 19 Sep 2019 |

Event | Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" - Corfu, Greece Duration: 31 Aug 2018 → 28 Sep 2018 |

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### Keywords

- hep-th
- math-ph
- math.MP
- math.QA
- math.SG