Electric-magnetic deformations of D=4 gauged supergravities

We discuss duality orbits and symplectic deformations of D=4 gauged supergravity theories, with focus on N$\ge$2. We provide a general constructive framework for computing symplectic deformations starting from a reference gauging, and apply it to many interesting examples. We prove that no continuous deformations are allowed for Fayet-Iliopoulos gaugings of the N=2 STU model and in particular that any $\omega$ deformation is classically trivial. We further show that although in the N=6 truncation of SO(8) maximal supergravity the $\omega$ parameter can be dualized away, in the 'twin' N=2 truncation $\omega$ is preserved and a second, new deformation appears. We further provide a full classification and appropriate duality orbits of certain N=4 gauged supergravities, including all inequivalent SO(4)$^2$ gaugings and several non-compact forms.