A Barren Landscape?

TL;DR

The paper investigates non-perturbative superpotential generation in F-theory flux vacua by deriving a necessary arithmetic-genus condition and analyzing its implications for volume-modulus stabilization. It shows that in models with a single Kähler modulus, neither abelian M5-instantons nor gaugino condensation stabilize the volume in the presence of flux, due to constraints like $\chi_D=1$ and F-theory base conditions (e.g., $c_1[C]^2=-2$). Extending the analysis to more general multic modulus settings suggests that metastable de Sitter vacua, if they exist, are non-generic in large-volume string compactifications. Overall, the work provides a framework to assess non-perturbative stabilization across broad F-theory/M-theory setups and highlights the persistent challenge of achieving complete moduli stabilization.

Abstract

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.