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Double field theory and membrane sigma-models
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 03 July 2018

Double field theory and membrane sigma-models

  • Athanasios Chatzistavrakidis  ORCID: orcid.org/0000-0002-9326-98711,
  • Larisa Jonke1,
  • Fech Scen Khoo1 &
  • …
  • Richard J. Szabo2,3,4 

Journal of High Energy Physics volume 2018, Article number: 15 (2018) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

We investigate geometric aspects of double field theory (DFT) and its formulation as a doubled membrane sigma-model. Starting from the standard Courant algebroid over the phase space of an open membrane, we determine a splitting and a projection to a subbundle that sends the Courant algebroid operations to the corresponding operations in DFT. This describes precisely how the geometric structure of DFT lies in between two Courant algebroids and is reconciled with generalized geometry. We construct the membrane sigma-model that corresponds to DFT, and demonstrate how the standard T-duality orbit of geometric and non-geometric flux backgrounds is captured by its action functional in a unified way. This also clarifies the appearence of noncommutative and nonassociative deformations of geometry in non-geometric closed string theory. Gauge invariance of the DFT membrane sigma-model is compatible with the flux formulation of DFT and its strong constraint, whose geometric origin is explained. Our approach leads to a new generalization of a Courant algebroid, that we call a DFT algebroid and relate to other known generalizations, such as pre-Courant algebroids and symplectic nearly Lie 2-algebroids. We also describe the construction of a gauge-invariant doubled membrane sigma-model that does not require imposing the strong constraint.

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Authors and Affiliations

  1. Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia

    Athanasios Chatzistavrakidis, Larisa Jonke & Fech Scen Khoo

  2. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh, EH14 4AS, U.K.

    Richard J. Szabo

  3. Maxwell Institute for Mathematical Sciences, Edinburgh, U.K.

    Richard J. Szabo

  4. The Higgs Centre for Theoretical Physics, Edinburgh, U.K.

    Richard J. Szabo

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  1. Athanasios Chatzistavrakidis
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Chatzistavrakidis, A., Jonke, L., Khoo, F.S. et al. Double field theory and membrane sigma-models. J. High Energ. Phys. 2018, 15 (2018). https://doi.org/10.1007/JHEP07(2018)015

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  • Received: 08 March 2018

  • Revised: 28 May 2018

  • Accepted: 12 June 2018

  • Published: 03 July 2018

  • DOI: https://doi.org/10.1007/JHEP07(2018)015

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Keywords

  • Differential and Algebraic Geometry
  • Sigma Models
  • String Duality
  • Topological Field Theories
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