Membranes in AdS4 orientifold vacua and their Weak Gravity Conjecture

TL;DR

This paper investigates non-supersymmetric AdS4 vacua in type IIA string theory with fluxes, analyzing membrane instabilities and their relation to the Weak Gravity Conjecture, highlighting how geometric effects influence stability.

Contribution

It provides a detailed analysis of membrane instabilities in non-supersymmetric AdS4 vacua, incorporating curvature and backreaction effects to test the Weak Gravity Conjecture.

Findings

Membrane charge-to-tension mismatch depends on 3-cycle geometry.

Certain 3-cycle configurations can violate the Weak Gravity Conjecture.

Explicit expressions for backreaction effects in toroidal orientifolds.

Abstract

We study type IIA orientifold compactifications with fluxes that give rise to perturbatively stable, non-supersymmetric AdS$_4$ vacua with D6-brane gauge sectors. Non-perturbative instabilities can be mediated by D8-branes wrapped on the six internal dimensions $X_6$, if they reduce to 4d membranes with a charge $Q$ larger than its tension $T$. The mismatch $Q \neq T$ arises due to i) curvature corrections and ii) the BIon backreaction of D6-branes wrapping 3-cycles of $X_6$. We give a simple expression for the second effect in toroidal orientifolds, and find that only pairs of 3-cycles at SU(2) angles contribute to it. They either contribute towards $Q>T$ or $Q<T$ depending on the 3-cycles separation, allowing to engineer 4d $\mathcal{N}=0$ vacua in tension with the Weak Gravity Conjecture for membranes.