Flux Compactifications of M-Theory on Twisted Tori

TL;DR

This work analyzes how eleven-dimensional supergravity with Scherk-Schwarz twists and flux on twisted tori can be consistently reduced to D-dimensional gauged supergravities, and under what conditions these reductions lift to full M-theory compactifications. It derives the reduction ansatz, the resulting Lagrangian with geometry and flux contributions, and the gauge algebra, including Chern-Simons-induced field dependence and symmetry breaking patterns. The authors embed these gaugings into duality-covariant frameworks (O(d,d), O(d,d+16), and E_{d(d)}) via universal Lagrangians and the embedding tensor formalism, revealing a unified view of geometric and non-geometric flux compactifications. They show that many flux/twist gaugings fit within the duality-covariant program, while emphasizing that non-geometric backgrounds (U-folds) arise naturally under duality actions, highlighting the deep role of U-duality in connecting different compactification scenarios in M-theory.

Abstract

We find the bosonic sector of the gauged supergravities that are obtained from 11-dimensional supergravity by Scherk-Schwarz dimensional reduction with flux to any dimension D. We show that, if certain obstructions are absent, the Scherk-Schwarz ansatz for a finite set of D-dimensional fields can be extended to a full compactification of M-theory, including an infinite tower of Kaluza-Klein fields. The internal space is obtained from a group manifold (which may be non-compact) by a discrete identification. We discuss the symmetry algebra and the symmetry breaking patterns and illustrate these with particular examples. We discuss the action of U-duality on these theories in terms of symmetries of the D-dimensional supergravity, and argue that in general it will take geometric flux compactifications to M-theory on non-geometric backgrounds, such as U-folds with U-duality transition functions.