A geometry for non-geometric string backgrounds

Abstract

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 physical space lying in the generalised D-brane subspace. © SISSA 2005.