Geometric non-geometry

We consider a class of (orbifolds of) M-theory compactifications on $S^{d} \times T^{7-d}$ with gauge fluxes yielding minimally supersymmetric STU-models in 4D. We present a group-theoretical derivation of the corresponding flux-induced superpotentials and argue that the aforementioned backgrounds provide a (globally) geometric origin for 4D theories that only look locally geometric from the perspective of twisted tori. In particular, we show that Q-flux can be used to generate compactifications on $S^4\times T^3$. We thus conclude that the effect of turning on non-geometric fluxes, at least when the section condition is solved, may be recovered by considering reductions on different topologies other than toroidal.