T-duality and non-geometric solutions from double geometry

Abstract

Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles in extended geometry. A proposal for solving this problem is given in the framework of double field theory. It is based on a clearly defined extension of the definition of gauge symmetry by isometries of an underlying pseudo-Riemannian manifold. The ensuing relation between transformations of coordinates and fields, which is now derived from first principles, differs from earlier proposals.

13 pp., plain tex

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Cited by in corpus (27)

• Exceptional field theory: $SL(5)$
• Exceptional field theory: $SO(5,5)$
• Branes are Waves and Monopoles
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• Fermions and Supersymmetry in ${\mathrm{E}}_{6(6)}$ Exceptional Field Theory
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Extended geometries
• $\mathbf{O}(D,D)$ Covariant Noether Currents and Global Charges in Double Field Theory
• Remarks on the non-Riemannian sector in Double Field Theory
• Type IIB flux vacua from G-theory II
• Double supergeometry
• Conserved Currents of Double Field Theory
• Type IIB flux vacua from G-theory I
• $L_{\infty }$ algebras for extended geometry from Borcherds superalgebras
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Patching DFT, T-duality and Gerbes
• A geometric formulation of exceptional field theory
• Teleparallelism in the algebraic approach to extended geometry
• Twistors and supertwistors for exceptional field theory
• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
• A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry
• The teleparallel complex
• Geometric U-folds in four dimensions
• $L_{\infty }$ algebras for extended geometry
• Algebraic structures in exceptional geometry