Towards an invariant geometry of double field theory

Abstract

We introduce a geometrical framework for double field theory in which generalized Riemann and torsion tensors are defined without reference to a particular basis. This invariant geometry provides a unifying framework for the frame-like and metric-like formulations developed before. We discuss the relation to generalized geometry and give an `index-free' proof of the algebraic Bianchi identity. Finally, we analyze to what extent the generalized Riemann tensor encodes the curvatures of Riemannian geometry. We show that it contains the conventional Ricci tensor and scalar curvature but not the full Riemann tensor, suggesting the possibility of a further extension of this framework.

44 pages, v2: refs. improved, minor corrections, to appear in J. Math. Phys

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• Generalized Geometry and M theory
• The gauge structure of generalised diffeomorphisms
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• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
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• Towards a double field theory on para-Hermitian manifolds
• Strings and Branes are Waves
• A Unique Connection for Born Geometry
• The geometry behind double geometry
• Generalised Kinematics for Double Field Theory
• Algebroid Structures on Para-Hermitian Manifolds
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• Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
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