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

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/torsion. From the eleven dimensional supergravity point of view, we find that a general E_{6(6)} S-S phase may by obtained by turning on an appropriate background torsion flux, together with suitable fluxes, some of which can be identified with certain components of the four-form field-strength. Our analysis also suggests the interpretation of the torsion flux as the T-dual of the NS three-form flux.