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

Journal of High Energy Physics

Dieter Lüst¹  Emanuel Malek¹  Richard J. Szabo² 

[1] Arnold Sommerfeld Center for Theoretical Physics, Department für Physik, Ludwig-Maximilians-Universität München;Department of Mathematics, Heriot-Watt University;

关键词: Flux compactifications;    M-Theory;    Non-Commutative Geometry;    p-branes;   

DOI  :  10.1007/JHEP10(2017)144

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown