Nonassociativity in nongeometric string and Mtheory backgrounds, the algebra of octonions, and missing momentum modes
We propose a nonassociative phase space algebra for Mtheory backgrounds with locally nongeometric fluxes based on the nonassociative algebra of octonions. Our proposal is based on the observation that the nonassociative algebra of the nongeometric Rflux 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 fourdimensional locally nongeometric Mtheory background which is dual to a twisted torus, we show that the nongeometric background is “missing” a momentum mode. The resulting sevendimensional 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 Rflux algebra to Mtheory, with the contraction parameter playing the role of the string coupling constant g _{s}.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 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:
 Grant/Contract Number:
 SC0010534; 32004
 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 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Pennsylvania State Univ., University Park, PA (United States); Ludwig Maximilian Univ., Munich (Germany)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); European Research Council (ERC)
 Contributing Orgs:
 Max Planck Inst. for Physics, Munich (Germany)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Flux compactifications; MTheory; NonCommutative Geometry; String Duality
 OSTI Identifier:
 1368088
Günaydin, Murat, Lüst, Dieter, and Malek, Emanuel. Nonassociativity in nongeometric string and Mtheory backgrounds, the algebra of octonions, and missing momentum modes. United States: N. p.,
Web. doi:10.1007/JHEP11(2016)027.
Günaydin, Murat, Lüst, Dieter, & Malek, Emanuel. Nonassociativity in nongeometric string and Mtheory backgrounds, the algebra of octonions, and missing momentum modes. United States. doi:10.1007/JHEP11(2016)027.
Günaydin, Murat, Lüst, Dieter, and Malek, Emanuel. 2016.
"Nonassociativity in nongeometric string and Mtheory backgrounds, the algebra of octonions, and missing momentum modes". United States.
doi:10.1007/JHEP11(2016)027. https://www.osti.gov/servlets/purl/1368088.
@article{osti_1368088,
title = {Nonassociativity in nongeometric string and Mtheory backgrounds, the algebra of octonions, and missing momentum modes},
author = {Günaydin, Murat and Lüst, Dieter and Malek, Emanuel},
abstractNote = {We propose a nonassociative phase space algebra for Mtheory backgrounds with locally nongeometric fluxes based on the nonassociative algebra of octonions. Our proposal is based on the observation that the nonassociative algebra of the nongeometric Rflux 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 fourdimensional locally nongeometric Mtheory background which is dual to a twisted torus, we show that the nongeometric background is “missing” a momentum mode. The resulting sevendimensional 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 Rflux algebra to Mtheory, 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 = {2016},
month = {11}
}