Journal of High Energy Physics

, 2018:36 | Cite as

Nonassociative differential geometry and gravity with non-geometric fluxes

  • Paolo Aschieri
  • Marija Dimitrijević Ćirić
  • Richard J. Szabo
Open Access
Regular Article - Theoretical Physics


We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct R-flux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in non-geometric string theory and double field theory.


Non-Commutative Geometry Flux compactifications Models of Quantum Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Dipartimento di Scienze e Innovazione TecnologicaUniversità del Piemonte OrientaleAlessandriaItaly
  2. 2.INFN, Sezione di TorinoTorinoItaly
  3. 3.Arnold-Regge CenterTorinoItaly
  4. 4.Faculty of PhysicsUniversity of BelgradeBeogradSerbia
  5. 5.Department of MathematicsHeriot-Watt UniversityEdinburghU.K.
  6. 6.Maxwell Institute for Mathematical SciencesEdinburghU.K.
  7. 7.The Higgs Centre for Theoretical PhysicsEdinburghU.K.

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