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 rôle of the defining geometry for the symmetries of double field theory, and on the continuation of the present construction to the Uduality setting.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2014
 DOI:
 10.1007/JHEP09(2014)070
 arXiv:
 arXiv:1402.2513
 Bibcode:
 2014JHEP...09..070C
 Keywords:

 Differential and Algebraic Geometry;
 SpaceTime Symmetries;
 String Duality;
 High Energy Physics  Theory
 EPrint:
 8 pp., plain tex. v2: Slightly expanded motivation and discussion parts