The quantization problem in Scherk-Schwarz compactifications

Understand

We re-examine the quantization of structure constants, or equivalently the choice of lattice in the so-called flat group reductions, introduced originally by Scherk and Schwarz.

• Depending on this choice, the vacuum either breaks supersymmetry and lifts certain moduli, or preserves all supercharges and is identical to the one obtained from the torus reduction.
• Nonetheless the low-energy effective theory proposed originally by Scherk and Schwarz is a gauged supergravity that describes supersymmetry breaking and moduli lifting for all values of the structure constants.
• When the vacuum does not break supersymmetry, such a description turns out to be an artifact of the consistent truncation to left-invariant forms as illustrated for the example of ISO(2).