A geometry for non-geometric string backgrounds

A geometric string solution has background fields in overlapping coordinatepatches related by diffeomorphisms and gauge transformations, while for anon-geometric background this is generalised to allow transition functionsinvolving duality transformations. Non-geometric string backgrounds arise fromT-duals and mirrors of flux compactifications, from reductions with dualitytwists and from asymmetric orbifolds. Strings in ` T-fold' backgrounds with alocal $n$-torus fibration and T-duality transition functions in $O(n,n;\Z)$ areformulated in an enlarged space with a $T^{2n}$ fibration which is geometric,with spacetime emerging locally from a choice of a $T^n$ submanifold of each$T^{2n}$ fibre, so that it is a subspace or brane embedded in the enlargedspace. T-duality acts by changing to a different $T^n$ subspace of $T^{2n}$.For a geometric background, the local choices of $T^n$ fit together to give aspacetime which is a $T^n$ bundle, while for non-geometric string backgroundsthey do not fit together to form a manifold. In such cases spacetime geometryonly makes sense locally, and the global structure involves the doubledgeometry. For open strings, generalised D-branes wrap a $T^n$ subspace of each$T^{2n}$ fibre and the physical D-brane is the part of the part of the physicalspace lying in the generalised D-brane subspace.Comment: 28 Pages. Minor change