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

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