Axionic symmetry gaugings in N = 4 supergravities and their higher-dimensional origin

We study the class of four-dimensional N = 4 supergravities obtained by gauging the axionic shift and axionic rescaling symmetries. We formulate these theories using the machinery of embedding tensors, characterize the full gauge algebras and discuss several specific features of this family of gauged supergravities. We exhibit in particular a generalized duality between massive vectors and massive two-forms in four dimensions, inherited from the gauging of the shift symmetry. We show that these theories can be deduced from higher dimensions by a Scherk-Schwarz reduction, where a twist with respect to a non-compact symmetry is required. The four-dimensional generalized duality plays a crucial role in identifying the higher-dimensional ascendent.