Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds
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-algeb...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2017)144 |
| _version_ | 1819117241050857472 |
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| author | Dieter Lüst Emanuel Malek Richard J. Szabo |
| author_facet | Dieter Lüst Emanuel Malek Richard J. Szabo |
| author_sort | Dieter Lüst |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T05:29:51Z |
| format | Article |
| id | doaj.art-cb1f2cb3f21642dcaea86f7c19774bb2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T05:29:51Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-cb1f2cb3f21642dcaea86f7c19774bb22022-12-21T18:37:29ZengSpringerOpenJournal of High Energy Physics1029-84792017-10-0120171012210.1007/JHEP10(2017)144Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgroundsDieter Lüst0Emanuel Malek1Richard J. Szabo2Arnold Sommerfeld Center for Theoretical Physics, Department für Physik, Ludwig-Maximilians-Universität MünchenArnold Sommerfeld Center for Theoretical Physics, Department für Physik, Ludwig-Maximilians-Universität MünchenDepartment of Mathematics, Heriot-Watt UniversityAbstract 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.http://link.springer.com/article/10.1007/JHEP10(2017)144Flux compactificationsM-TheoryNon-Commutative Geometryp-branes |
| spellingShingle | Dieter Lüst Emanuel Malek Richard J. Szabo Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds Journal of High Energy Physics Flux compactifications M-Theory Non-Commutative Geometry p-branes |
| title | Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds |
| title_full | Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds |
| title_fullStr | Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds |
| title_full_unstemmed | Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds |
| title_short | Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds |
| title_sort | non geometric kaluza klein monopoles and magnetic duals of m theory r flux backgrounds |
| topic | Flux compactifications M-Theory Non-Commutative Geometry p-branes |
| url | http://link.springer.com/article/10.1007/JHEP10(2017)144 |
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