The geometry behind double geometry

Abstract

Generalised diffeomorphisms in double field theory rely on an O(d,d) structure defined on tangent space. We show that any (pseudo-)Riemannian metric on the doubled space defines such a structure, in the sense that the generalised diffeomorphisms defined using such a metric form an algebra, provided a covariant section condition is fulfilled. Consistent solutions of the section condition gives further restrictions. The case previously considered corresponds to a flat metric. The construction makes it possible to apply double geometry to a larger class of manifolds. Examples of curved defining metrics are given. We also comment on the role of the defining geometry for the symmetries of double field theory, and on the continuation of the present construction to the U-duality setting.

8 pp., plain tex. v2: Slightly expanded motivation and discussion parts

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• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
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• Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
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