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 >= 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 w deformation is classically trivial. We further show that although in the N = 6 truncation of SO(8) maximal supergravity the w parameter can be dualized away, in the 'twin' N = 2 truncation w 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.