Flux Compactifications of M-Theory on Twisted Tori

TL;DR

This paper explores how M-theory can be compactified on twisted tori using Scherk-Schwarz reduction, leading to gauged supergravities with potential non-geometric backgrounds like U-folds.

Contribution

It extends the Scherk-Schwarz ansatz to full M-theory compactifications on group manifolds, including infinite Kaluza-Klein towers, and discusses the role of U-duality in these settings.

Findings

Derivation of bosonic sectors of gauged supergravities from 11D supergravity.

Extension of Scherk-Schwarz reduction to full M-theory including infinite KK modes.

Identification of non-geometric backgrounds arising from U-duality transformations.

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.