The compactification of the internal manifold is a natural way to get from higher dimensional
string theory to the observable 4-dimensional spacetime. An extension of this process, which usually assumes empty target space, is to incorporate electric/magnetic fluxes. This leads to a change of the properties of the manifold. In order to treat the complications that arise from a back-reaction of the fluxes a different geometrical description, the so-called generalised complex geometry or doubled geometry, needs to be introduced. These give rise to a more general picture and may lead to a new mathematical framework of string theory.
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