Extended Riemannian geometry III: global Double Field Theory with nilmanifolds

  • Andreas DeserEmail author
  • Christian Sämann
Open Access
Regular Article - Theoretical Physics


We describe the global geometry, symmetries and tensors for Double Field Theory over pairs of nilmanifolds with fluxes or gerbes. This is achieved by a rather straightforward application of a formalism we developed previously. This formalism constructs the analogue of a Courant algebroid over the correspondence space of a T-duality, using the language of graded manifolds, derived brackets and we use the description of nilmanifolds in terms of periodicity conditions rather than local patches. The strong section condition arises purely algebraically, and we show that for a particularly symmetric solution of this condition, we recover the Courant algebroids of both nilmanifolds with fluxes. We also discuss the finite, global symmetries of general local Double Field Theory and explain how this specializes to the case of T-duality between nilmanifolds.


Differential and Algebraic Geometry Flux compactifications String Duality 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic
  2. 2.Department of MathematicsHeriot-Watt UniversityEdinburghU.K.
  3. 3.Maxwell Institute for Mathematical SciencesEdinburghU.K.
  4. 4.Higgs Centre for Theoretical PhysicsEdinburghU.K.

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