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(Non-)commutative closed string on T-dual toroidal backgrounds

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  • Published: 06 June 2013
  • Volume 2013, article number 21, (2013)
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(Non-)commutative closed string on T-dual toroidal backgrounds
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  • David Andriot1,2,
  • Magdalena Larfors3,
  • Dieter Lüst1,2,4 &
  • …
  • Peter Patalong1,2 

  • 555 Accesses

  • 63 Citations

  • 1 Altmetric

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Abstract

In this paper we investigate the connection between (non-)geometry and (non-)commutativity of the closed string. To this end, we solve the classical string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted torus and a non-geometric background with Q-flux. In all three situations we work under the assumption of a dilute flux and consider quantities to linear order in the flux density. Furthermore, we perform the first steps of a canonical quantization for the twisted torus, to derive commutators of the string expansion modes. We use them as well as T-duality to determine, in the non-geometric background, a commutator of two string coordinates, which turns out to be non-vanishing. We relate this non-commutativity to the closed string boundary conditions, and the non-geometric Q-flux.

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Author information

Authors and Affiliations

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

    David Andriot, Dieter Lüst & Peter Patalong

  2. Max-Planck-Institut für Physik, Föhringer Ring 6, 80805, München, Germany

    David Andriot, Dieter Lüst & Peter Patalong

  3. Mathematical Institute, Oxford University, 24-29 St Giles’, Oxford, OX1 3LB, England

    Magdalena Larfors

  4. Theory Group, CERN, 1211, Geneva 23, Switzerland

    Dieter Lüst

Authors
  1. David Andriot
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  2. Magdalena Larfors
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Corresponding author

Correspondence to Magdalena Larfors.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Andriot, D., Larfors, M., Lüst, D. et al. (Non-)commutative closed string on T-dual toroidal backgrounds. J. High Energ. Phys. 2013, 21 (2013). https://doi.org/10.1007/JHEP06(2013)021

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  • Received: 19 February 2013

  • Revised: 08 May 2013

  • Accepted: 23 May 2013

  • Published: 06 June 2013

  • DOI: https://doi.org/10.1007/JHEP06(2013)021

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Keywords

  • Flux compactifications
  • Non-Commutative Geometry
  • String Duality
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