2004/06/30 by C M Hull · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.DG
paper · pdf · doi:10.1088/1126-6708/2005/10/065
published as JHEP0510:065,2005 · 28 Pages. Minor changes
arxiv created 2005/07/14 · arxiv updated 2009/12/01
A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirrors of flux compactifications, from reductions with duality twists and from asymmetric orbifolds. Strings in ` T-fold' backgrounds with a local n-torus fibration and T-duality transition functions in O(n,n;\Z) are formulated in an enlarged space with a T2n fibration which is geometric, with spacetime emerging locally from a choice of a Tn submanifold of each T2n fibre, so that it is a subspace or brane embedded in the enlarged space. T-duality acts by changing to a different Tn subspace of T2n. For a geometric background, the local choices of Tn fit together to give a spacetime which is a Tn bundle, while for non-geometric string backgrounds they do not fit together to form a manifold. In such cases spacetime geometry only makes sense locally, and the global structure involves the doubled geometry. For open strings, generalised D-branes wrap a Tn subspace of each T2n fibre and the physical D-brane is the part of the part of the physical space lying in the generalised D-brane subspace.