Geometric non-geometry

TL;DR

This work investigates how M-theory compactifications on manifolds with nontrivial topology, specifically $S^{d} imes T^{7-d}$, generate 4D STU-models via flux-induced superpotentials and how non-geometric flux effects can acquire a globally geometric origin when viewed through different internal topologies. Using a group-theoretical embedding-tensor framework and an SO(3) × Z2 truncation of maximal supergravity, the authors derive flux-induced superpotentials for backgrounds on twisted $T^{7}$, $S^{7}$, and $S^{4} imes T^{3}$, revealing a progression from quadratic to quartic and cubic couplings in the STU scalars $S,T,U$. They show that higher-degree terms, typically associated with non-geometric fluxes, can arise in globally geometric reductions on non-toroidal spaces, provided the section condition is respected; in particular, $Q$-flux can be realized in $S^{4} imes T^{3}$. The results illuminate how non-geometric backgrounds may have a physically meaningful eleven-dimensional origin and guide future model-building beyond toroidal reductions, with implications for de Sitter physics and possible connections to exotic differentiable structures on spheres. Overall, the paper provides a concrete geometric reinterpretation of certain non-geometric flux effects within M-theory compactifications and EFT techniques.

Abstract

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.