BIonic membranes and AdS instabilities

Abstract

We study 4d membranes in type IIA flux compactifications of the form AdS${}_4\times X_6$, where $X_6$ admits a Calabi--Yau metric. These models feature scale separation and D6-branes/O6-planes on three-cycles of $X_6$. When the latter are treated as localised sources, explicit solutions to the 10d equations of motion and Bianchi identities are known in 4d $\mathcal{N}=1$ settings, valid at first order in an expansion parameter related to the AdS${}_4$ cosmological constant. We extend such solutions to a family of perturbatively stable $\mathcal{N}=0$ 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 $\mathcal{N}=1$ and $\mathcal{N}=0$ AdS${}_4$. Differently, D8-branes wrapping $X_6$ and with D6-branes ending on them can be superextremal 4d membranes attracted towards the $\mathcal{N}=0$ AdS${}_4$ boundary. The sources of imbalance are the curvature of $X_6$ and the D8/D6 BIon profile, with both comparable terms as can be checked for $X_6$ a (blown-up) toroidal orbifold. We then show that simple $\mathcal{N}=0$ vacua with space-time filling D6-branes are unstable against bubble nucleation, decaying to $\mathcal{N}=0$ vacua with less D6-branes and larger Romans mass.

v4: Minor corrections, references added; v1:30 pages + appendices, 2 figures

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• On the Stability of String Theory Vacua
• New instabilities for non-supersymmetric AdS${}_4$ orientifold vacua
• Membranes in AdS4 orientifold vacua and their Weak Gravity Conjecture
• Relative scale separation in orbifolds of $S^2$ and $S^5$
• A domain wall bound on anti-de Sitter vacua