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Title: Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

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 g s.
Authors:
 [1] ;  [2] ;  [3]
  1. Pennsylvania State Univ., University Park, PA (United States). Physics Dept. Inst. for Gravitation and the Cosmos
  2. Ludwig Maximilian Univ., Munich (Germany). Dept. of Physics. Arnold Sommerfeld Center for Theoretical Physics; Max Planck Inst. for Physics, Munich (Germany). Werner Heisenberg Inst.
  3. 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 1029-8479
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) (SC-25); 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; M-Theory; Non-Commutative Geometry; String Duality
OSTI Identifier:
1368088