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

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  • Published: 07 November 2016
  • Volume 2016, article number 27, (2016)
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Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
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  • Murat Günaydin1,
  • Dieter Lüst2,3 &
  • Emanuel Malek2 

  • 413 Accesses

  • 24 Citations

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A preprint version of the article is available at arXiv.

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 g s .

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Authors and Affiliations

  1. Institute for Gravitation and the Cosmos, Physics Department, Pennsylvania State University, University Park, PA, 16802, U.S.A.

    Murat Günaydin

  2. Arnold Sommerfeld Center for Theoretical Physics, Department für Physik, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333, München, Germany

    Dieter Lüst & Emanuel Malek

  3. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Föhringer Ring 6, 80805, München, Germany

    Dieter Lüst

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Correspondence to Emanuel Malek.

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ArXiv ePrint: 1607.06474

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Günaydin, M., Lüst, D. & Malek, E. Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes. J. High Energ. Phys. 2016, 27 (2016). https://doi.org/10.1007/JHEP11(2016)027

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  • Received: 29 July 2016

  • Revised: 08 September 2016

  • Accepted: 13 October 2016

  • Published: 07 November 2016

  • DOI: https://doi.org/10.1007/JHEP11(2016)027

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Keywords

  • Flux compactifications
  • M-Theory
  • Non-Commutative Geometry
  • String Duality
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