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The geometry behind double geometry

A preprint version of the article is available at arXiv.

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 rôle of the defining geometry for the symmetries of double field theory, and on the continuation of the present construction to the U-duality setting.

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Correspondence to Martin Cederwall.

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ArXiv ePrint: 1402.2513

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Cederwall, M. The geometry behind double geometry. J. High Energ. Phys. 2014, 70 (2014). https://doi.org/10.1007/JHEP09(2014)070

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  • DOI: https://doi.org/10.1007/JHEP09(2014)070

Keywords

  • Differential and Algebraic Geometry
  • Space-Time Symmetries
  • String Duality