Beyond twisted tori

Exploiting the fact that Kaluza-Klein monopoles and the associated generalized orbifold planes are sources for geometrical fluxes, ω, we show that the standard constraint ωω=0, valid for superstring compactifications on twisted tori, can be consistently relaxed. This leads to novel possibilities for constructing superstring models with fluxes and localized sources, as well as for stabilizing moduli. This also explains the ten-dimensional origin of a family of N=4 gauged supergravities, whose interpretation in type-IIA orientifold compactifications was lacking.