Supersymmetric gauged double field theory: systematic derivation by virtue of twist

In a completely systematic and geometric way, we derive maximal and half:maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the D = 10 ungauged maximal and half-maximal supersymmetric double field theories constructed previously within the so-called semi-covariant formalism. The twisting ansatz may not satisfy the section condition. Nonetheless, all the features of the semi-covariant formalism, including its complete co-variantizability, are still valid after the twist under alternative consistency conditions. The twist allows gaugings as supersymmetry preserving deformations of the D = 10 untwisted theories after Scherk-Schwarz-type dimensional reductions. The maximal supersymmetric twist requires an extra condition to ensure both the Ramond-Ramond gauge symmetry and the 32 supersymmetries unbroken.