We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kähler modulus, T , of a Calabi-Yau 4-cycle gets charged under the anomalous U (1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the question of U (1)-gauge invariance of the (Tdependent) non-perturbative superpotential arises. In this case an index theorem guarantees that strings, stretching between the two stacks, yield additional charged chiral fields which also appear in the superpotential from gaugino condensation. We check that the charges work out to make this superpotential gauge invariant, and we argue that the mechanism survives the inclusion of higher curvature corrections to the D7-brane action.

We study cosmological properties of type IIA compactifications on orientifolds of SU(3)-structure manifolds with non-vanishing geometric flux. These compactifications give rise to effective 4D N = 1 supergravity theories that do not fall under some recentlyproven no-go theorems against de Sitter vacua and slow-roll inflation. Focusing on a wellunderstood class of models based on coset spaces, however, we can use a refined no-go theorem that rules out de Sitter vacua and slow-roll inflation in all but one case. The refined no-go theorem uses the dilaton and a specific linear combination of the Kähler moduli, which is different from the overall volume modulus. It puts a lower bound on the first slow-roll parameter: ǫ ≥ 2. The only case not ruled out is the manifold SU(2)×SU(2), for which we indeed find critical points with ǫ numerically zero. However, all the points we could find have a tachyon corresponding to an eta-parameter η −2.4.

We consider string theory compactifications of the form AdS 4 ×M 6 with orientifold six-planes, where M 6 is a six-dimensional compact space that is either a nilmanifold or a coset. For all known solutions of this type we obtain the four-dimensional N = 1 low energy effective theory by computing the superpotential, the Kähler potential and the mass spectrum for the light moduli. For the nilmanifold examples we perform a cross-check on the result for the mass spectrum by calculating it alternatively from a direct Kaluza-Klein reduction and find perfect agreement. We show that in all but one of the coset models all moduli are stabilized at the classical level. As an application we show that all but one of the coset models can potentially be used to bypass a recent no-go theorem against inflation in type IIA theory.

We study the general gaugings of N = 2 Maxwell-Einstein supergravity theories (MESGT) in five dimensions, extending and generalizing previous work. The global symmetries of these theories are of the form SU (2) R ×G, where SU (2) R is the R-symmetry group of the N = 2 Poincaré superalgebra and G is the group of isometries of the scalar manifold that extend to symmetries of the full action. We first gauge a subgroup K of G by turning some of the vector fields into gauge fields of K while dualizing the remaining vector fields into tensor fields transforming in a non-trivial representation of K. Surprisingly, we find that the presence of tensor fields transforming non-trivially under the Yang-Mills gauge group leads to the introduction of a potential which does not admit an AdS ground state. Next we give the simultaneous gauging of the U (1) R subgroup of SU (2) R and a subgroup K of G in the presence of K-charged tensor multiplets. The potential introduced by the simultaneous gauging is the sum of the potentials introduced by gauging K and U (1) R separately. We present a list of possible gauge groups K and the corresponding representations of tensor fields. For the exceptional supergravity we find that one can gauge the SO * (6) subgroup of the isometry group E 6(−26) of the scalar manifold if one dualizes 12 of the vector fields to tensor fields just as in the gauged N = 8 supergravity.

We investigate whether vacuum solutions in flux compactifications that are obtained with smeared sources (orientifolds or D-branes) still survive when the sources are localised. This seems to rely on whether the solutions are BPS or not. First we consider two sets of BPS solutions that both relate to the GKP solution through T-dualities: (p + 1)-dimensional solutions from spacetime-filling Op-planes with a conformally Ricci-flat internal space, and p-dimensional solutions with Op-planes that wrap a 1-cycle inside an everywhere negatively curved twisted torus. The relation between the solution with smeared orientifolds and the localised version is worked out in detail. We then demonstrate that a class of non-BPS AdS 4 solutions that exist for IASD fluxes and with smeared D3-branes (or analogously for ISD fluxes with anti-D3-branes) does not survive the localisation of the (anti) D3-branes. This casts doubts on the stringy consistency of non-BPS solutions that are obtained in the limit of smeared sources.