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 derive the full N = 2 supergravity Lagrangian which contains a symplectic invariant scalar potential in terms of electric and magnetic charges. As shown in reference [1], the appearance of magnetic charges is allowed only if tensor multiplets are present and a suitable FayetIliopoulos term is included in the fermion transformation laws. We generalize the procedure in the quoted reference by adding further a Fayet-Iliopoulos term which allows the introduction of electric charges in such a way that the potential and the equations of motion of the theory are symplectic invariant. The theory is further generalized to include an ordinary electric gauging and the form of the resulting scalar potential is given.
We discuss the relation between standard N = 2 supergravity with translational gauging and N = 2 supergravities with scalar-tensor multiplets with massive tensors and Abelian electric charges. We point out that a symplectic covariant formulation of N = 2 supergravity can be achieved just in the presence of tensor multiplets. As a consequence one can see that the formulation of the N = 2 theory as it comes from IIB flux compactification, which is included in these models, is equivalent to a non perturbative phase of standard N = 2 supergravity. It is also shown that the IIB tadpole cancellation condition is imposed by supersymmetry in four dimensions.
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