New instabilities for non-supersymmetric AdS$_4$ orientifold vacua

We consider massive type IIA orientifold compactifications of the form AdS$_4 \times X_6$, where $X_6$ admits a Calabi-Yau metric and is threaded by background fluxes. From a 4d viewpoint, fluxes generate a potential whose vacua have been classified, including one $\mathcal{N}=1$ and three perturbatively stable $\mathcal{N}=0$ branches. We reproduce this result from a 10d viewpoint, by solving the type IIA equations at the same level of detail as previously done for the $\mathcal{N}=1$ branch. All solutions exhibit localised sources and parametric scale separation. We then analyse the non-perturbative stability of the $\mathcal{N}=0$ branches. We consider new 4d membranes, obtained from wrapping D8-branes on $X_6$ or D6-branes on its divisors, threaded by non-diluted worldvolume fluxes. Using them we show that all branches are compatible with the Weak Gravity Conjecture for membranes. In fact, most vacua satisfy the sharpened conjecture that predicts superextremal membranes in $\mathcal{N}=0$ settings, except for a subset whose non-perturbative stability remains an open problem.