Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
Abstract
We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginary octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant gs.
- Authors:
-
- Pennsylvania State Univ., University Park, PA (United States). Physics Dept. Inst. for Gravitation and the Cosmos
- Ludwig Maximilian Univ., Munich (Germany). Dept. of Physics. Arnold Sommerfeld Center for Theoretical Physics; Max Planck Inst. for Physics, Munich (Germany). Werner Heisenberg Inst.
- Ludwig Maximilian Univ., Munich (Germany). Dept. of Physics. Arnold Sommerfeld Center for Theoretical Physics
- Publication Date:
- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States); Ludwig Maximilian Univ. of Munich, Munich (Germany)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); European Research Council (ERC)
- Contributing Org.:
- Max Planck Inst. for Physics, Munich (Germany)
- OSTI Identifier:
- 1368088
- Grant/Contract Number:
- SC0010534; 32004
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 11; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Flux compactifications; M-Theory; Non-Commutative Geometry; String Duality
Citation Formats
Günaydin, Murat, Lüst, Dieter, and Malek, Emanuel. Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes. United States: N. p., 2016.
Web. doi:10.1007/JHEP11(2016)027.
Günaydin, Murat, Lüst, Dieter, & Malek, Emanuel. Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes. United States. https://doi.org/10.1007/JHEP11(2016)027
Günaydin, Murat, Lüst, Dieter, and Malek, Emanuel. Mon .
"Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes". United States. https://doi.org/10.1007/JHEP11(2016)027. https://www.osti.gov/servlets/purl/1368088.
@article{osti_1368088,
title = {Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes},
author = {Günaydin, Murat and Lüst, Dieter and Malek, Emanuel},
abstractNote = {We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginary octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant gs.},
doi = {10.1007/JHEP11(2016)027},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2016,
place = {United States},
year = {Mon Nov 07 00:00:00 EST 2016},
month = {Mon Nov 07 00:00:00 EST 2016}
}
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