A Barren Landscape?

We consider the generation of a non-perturbative superpotential in F-theory compactifications with flux. We derive a necessary condition for the generation of such a superpotential in F-theory. For models with a single volume modulus, we show that the volume modulus is never stabilized by either abelian instantons or gaugino condensation. We then comment on how our analysis extends to a larger class of compactifications. From our results, it appears that among large volume string compactifications, metastable de Sitter vacua (should any exist) are non-generic.