Gauged N=4 Supergravities

We present the complete gauged N = 4 (half-maximal) supergravities in four and five spacetime dimensions coupled to an arbitrary number of vector mul-tiplets. The gaugings are parameterized by a set of appropriately constrained constant tensors, which transform covariantly under the global symmetry groups SL(2) × SO(6, n) and SO(1, 1) × SO(5, n), respectively. In terms of these tensors the universal Lagrangian and the Killing Spinor equations are given. The known gaugings, in particular those originating from flux compact-ifications, are incorporated in the formulation, but also new classes of gaugings are found. Finally, we present the embedding chain of the five dimensional into the four dimensional into the three dimensional gaugings, thereby showing how the deformation parameters organize under the respectively larger duality groups.