Using superspace techniques we construct the general theory describing D = 4, N = 2 supergravity coupled to an arbitrary number of vector and scalar-tensor multiplets. The scalar manifold of the theory is the direct product of a special Kähler and a reduction of a Quaternionic-Kähler manifold. We perform the electric gauging of a subgroup of the isometries of such manifold as well as "magnetic" deformations of the theory discussing the consistency conditions arising in this process. The resulting scalar potential is the sum of a symplectic invariant part (which in some instances can be recast into the standard form of the gauged N = 2 theory) and of a non-invariant part, both giving new deformations. We also show the relation of such theories to flux compactifications of type II string theories.As a next step we perform the gauging of the theory. After dualization, not all of the isometries of the original manifold remain isometries of the final scalar manifold. Moreover, some of these act non-trivially on the tensor fields and therefore cannot become local symmetries without leading to non-linear couplings for the tensor fields. We then discuss which isometries can be made local and therefore "gauged". Always using the superspace formalism we compute the fermion shifts which restore the supersymmetry of the theory and give rise to a potential satisfying the supersymmetry Ward identities.The appearance of tensor fields allows to redefine the gauge field strengths with a shift proportional to the tensor fields F Λ → F Λ + m IΛ B I without breaking supersymmetry, provided we redefine appropriately the fermion transformation laws. Here m IΛ are real constants which can be thought as mass parameters for the tensors. This kind of extension 2 of the theory was first obtained in [13] for six-dimensional supergravity, further extended in [14] and shown in Calabi-Yau compactification of Type II theories in [7].Indeed the gauging we perform after dualization of some of the hypermultiplets scalars is a standard electric gauging, but the appearance of the mass parameters m IΛ in the definition of the new gauge field strengths implies the existence of extended solutions. The shifts of the supersymmetry transformations indeed acquire some extra terms depending on such parameters so that the gravitino's and hyperino's shifts are symplectic invariants. This latter can be interpreted also as a "magnetic" gauging, though its definition is not related to the appearance of magnetic gauge fields. These would lead to the construction of [4] whose consistency is problematic, as explained in [6,7].The scalar potential of the theory follows as usual from the square of the fermionic shifts by using a known Ward identity of N-extended gauged supergravities [15]. Being the square of symplectic invariant quantities, but for a term coming from the gaugino shift when non-Abelian isometries of the Special Kähler manifold are gauged, the potential shows symplectic invariance for Abelian gaugings where such gaugino contribution does not appear. T...

We construct the so far unknown Lagrangian of D = 6, N = 2 F (4) Supergravity coupled to an arbitrary number of vector multiplets whose scalars span the coset manifold SO(4,n) SO(4)×SO(n) . This is done first in the ungauged case and then extended to the compact gauging of SU (2) × G, where SU (2) is the R-symmetry diagonal subgroup of SU (2) L × SU (2) R ≃ SO(4) and G is a compact subgroup of SO(n), n being the number of vector multiplets, and such that dim(G) = n. The knowledge of the Lagrangian allows in principle to refine the AdS 6 /CF T 5 correspondence already discussed, as far as supersymmetric multiplets are concerned, in a previous related paper. With respect to the latter we also give a more exaustive treatment of the construction of the theory at the level of superspace Bianchi identities and in particular of the scalar potential.

We analyze the properties of a spontaneously broken D = 4, N = 4 supergravity without cosmological constant, obtained by gauging translational isometries of its classical scalar manifold. This theory offers a suitable low energy description of the super-Higgs phases of certain Type-IIB orientifold compactifications with 3-form fluxes turned on. We study its N = 3, 2, 1, 0 phases and their classical moduli spaces and we show that this theory is an example of no-scale extended supergravity.