On the geometry of double field theory

Abstract

Double field theory was developed by theoretical physicists as a way to encompass $T$-duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms, in the framework of para-Kaehler manifolds. We define metric algebroids, which are vector bundles with a bracket of cross sections that has the same metric compatibility property as a Courant bracket. We show that a double field gives rise to two canonical connections, whose scalar curvatures can be integrated to obtain actions. Finally, in analogy with Dirac structures, we define and study para-Dirac structures on double manifolds.

The paper will appear in J. Math. Phys., 2012

References in corpus (5)

• Double Field Theory
• Differential geometry with a projection: Application to double field theory
• Stringy differential geometry, beyond Riemann
• Frame-like Geometry of Double Field Theory
• A construction of Courant algebroids on foliated manifolds

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