Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds

Andreas Deser, Christian Saemann

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Abstract

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.
Original languageEnglish
Article number209
JournalJournal of High Energy Physics
Volume2019
Issue number5
Early online date31 May 2019
DOIs
Publication statusPublished - May 2019

Keywords

  • Differential and Algebraic Geometry
  • Flux compactifications
  • String Duality

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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