Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds

Dieter Lüst, Emanuel Malek*, Richard J. Szabo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
20 Downloads (Pure)


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.

Original languageEnglish
Article number144
JournalJournal of High Energy Physics
Issue number10
Early online date20 Oct 2017
Publication statusPublished - 20 Oct 2017


  • Flux compactifications
  • M-Theory
  • Non-Commutative Geometry
  • p-branes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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