## Abstract

We introduce a magnetic analogue of the seven-dimensional nonassociative octonionic *R*-flux algebra that describes the phase space of M2-branes in four-dimensional locally non-geometric M-theory backgrounds. We show that these two algebras are related by a Spin(7) automorphism of the 3-algebra that provides a covariant description of the eight-dimensional M-theory phase space. We argue that this algebra also underlies the phase space of electrons probing a smeared magnetic monopole in quantum gravity by showing that upon appropriate contractions, the algebra reduces to the noncommutative algebra of a spin foam model of three-dimensional quantum gravity, or to the nonassociative algebra of electrons in a background of uniform magnetic charge. We realise this set-up in M-theory as M-waves probing a delocalised Kaluza-Klein monopole, and show that this system also has a seven-dimensional phase space. We suggest that the smeared Kaluza-Klein monopole is non-geometric because it cannot be described by a local metric. This is the magnetic analogue of the local non-geometry of the *R*-flux background and arises because the smeared Kaluza-Klein monopole is described by a U(1)-gerbe rather than a U(1)-fibration.

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Lüst, D., Malek, E. & Szabo, R.J. Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds.
*J. High Energ. Phys.* **2017**, 144 (2017). https://doi.org/10.1007/JHEP10(2017)144

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DOI: https://doi.org/10.1007/JHEP10(2017)144