The Scherk-Schwarz mechanism as a flux compactification with internal torsion

TL;DR

This paper advances understanding of Scherk-Schwarz dimensional reduction by linking it to flux compactifications with internal torsion, introducing a new duality approach and interpreting torsion flux as T-dual to NS flux.

Contribution

It presents a novel perspective on Scherk-Schwarz reduction involving background torsion and fluxes, and introduces a new method to study dualities in flux/torsion compactifications.

Findings

General E6(6) Scherk-Schwarz phase obtained via background torsion and fluxes.

New four-dimensional approach to dualities in flux/torsion compactifications.

Torsion flux interpreted as T-dual of NS three-form flux.

Abstract

The aim of this paper is to make progress in the understanding of the Scherk-Schwarz dimensional reduction in terms of a compactification in the presence of background fluxes and torsion. From the eleven dimensional supergravity point of view, we find that a general E6(6) S-S phase may be obtained by turning on an appropriate background torsion, together with suitable fluxes, some of which can be directly identified with certain components of the four-form field-strength. Furthermore, we introduce a novel (four dimensional) approach to the study of dualities between flux/torsion compactifications of Type II/M-theory. This approach defines the action that duality should have on the background quantities, in order for the E7(7) invariance of the field equations and Bianchi identities to be restored also in the presence of fluxes/torsion. This analysis further implies the interpretation of the torsion flux as the T-dual of the NS three-form flux.