Stringy differential geometry, beyond Riemann

Abstract

While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also O(D,D) T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry which is given by a direct product of two local Lorentz groups, SO(1,D-1) times SO(1,D-1). We comment that the notion of cosmological constant naturally changes.

7 pages, double column; References added

References in corpus (12)

• Double Field Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Differential geometry with a projection: Application to double field theory
• SO(5,5) duality in M-theory and generalized geometry
• Double Field Theory Formulation of Heterotic Strings
• Background Field Equations for the Duality Symmetric String
• Frame-like Geometry of Double Field Theory
• Double field formulation of Yang-Mills theory
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• On factorizations in perturbative quantum gravity

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