We compute the flux-induced F-term potential in 4d F-theory compactifications at large complex structure. In this regime, each complex structure field splits as an axionic field plus its saxionic partner, and the classical F-term potential takes the form V = ZABρAρB up to exponentially-suppressed terms, with ρ depending on the fluxes and axions and Z on the saxions. We provide explicit, general expressions for Z and ρ, and from there analyse the set of flux vacua for an arbitrary number of fields. We identify two families of vacua with all complex structure fields fixed and a flux contribution to the tad- pole Nflux which is bounded. In the first and most generic one, the saxion vevs are bounded from above by a power of Nflux. In the second their vevs may be unbounded and Nflux is a product of two arbitrary integers, unlike what is claimed by the Tadpole Conjecture. We specialise to type IIB orientifolds, where both families of vacua are present, and link our analysis with previous results in the literature. We illustrate our findings with several examples.

We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.

We study 4d membranes in type IIA flux compactifications of the form AdS4× X6, where X6 admits a Calabi-Yau metric. These models feature scale separation and D6-branes/O6-planes on three-cycles of X6. When the latter are treated as localised sources, explicit solutions to the 10d equations of motion and Bianchi identities are known in 4d $$ \mathcal{N} $$ N = 1 settings, valid at first order in an expansion parameter related to the AdS4 cosmological constant. We extend such solutions to a family of perturbatively stable $$ \mathcal{N} $$ N = 0 vacua, and analyse their non-perturbative stability by looking at 4d membranes. Up to the accuracy of the solution, we find that either D4-branes or anti-D4-branes on holomorphic curves feel no force in both $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 0 AdS4. Differently, D8-branes wrapping X6 and with D6-branes ending on them can be superextremal 4d membranes attracted towards the $$ \mathcal{N} $$ N = 0 AdS4 boundary. The sources of imbalance are the curvature of X6 and the D8/D6 BIon profile, with both comparable terms as can be checked for X6 a (blown-up) toroidal orbifold. We then show that simple $$ \mathcal{N} $$ N = 0 vacua with space-time filling D6-branes are unstable against bubble nucleation, decaying to $$ \mathcal{N} $$ N = 0 vacua with less D6-branes and larger Romans mass.