Geometric non-geometry

TL;DR

This paper explores how non-geometric fluxes in string theory compactifications can be understood through geometric backgrounds with different topologies, providing a new perspective on the origin of certain 4D theories.

Contribution

It offers a group-theoretical derivation of flux-induced superpotentials and demonstrates that non-geometric flux effects can be realized via geometric compactifications on alternative topologies.

Findings

Q-flux enables compactifications on $S^{4} imes T^{3}$

Non-geometric fluxes can be interpreted through geometric backgrounds with different topologies

The approach recovers non-geometric effects when the section condition is solved.

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.