Non-geometric fluxes versus (non)-geometry

Abstract: Non-geometry has been introduced when considering a new type of string backgrounds, for which stringy symmetries serve as transition functions between patches of the target space. Then, some terms in the potential of four-dimensional gauged supergravities, generated by so-called non-geometric fluxes, have been argued to find a higher-dimensional origin in these backgrounds, even if a standard compactification on those cannot be made. We present here recent results clarifying the relation between these two settings. Thanks to a field redefinition, we reformulate the NSNS Lagrangian in such a way that the non-geometric fluxes appear in ten dimensions. In addition, if an NSNS field configuration is non-geometric, its reformulation in terms of the new fields can restore a standard geometry. A dimensional reduction is then possible, and leads to the non-geometric terms in the four-dimensional potential. Reformulating similarly doubled field theory, we get a better understanding of the role of the non-geometric fluxes, and rewrite the Lagrangian in a manifestly diffeomorphism-covariant manner. We finally discuss the relevance of the field redefinition and the non-geometric fluxes when studying the non-commutativity of string coordinates.