Type IIA Moduli Stabilization

TL;DR

This work shows that flux compactifications in massive type IIA string theory can classically stabilize all geometric moduli in a controlled, large-volume, weak-coupling regime, yielding infinite families of AdS vacua. By analyzing a concrete $T^6/\mathbb{Z}_3^2$ orientifold both in 10D supergravity and in the 4D ${\cal N}=1$ effective theory, the authors derive explicit flux configurations and moduli solutions, including the stabilization of blow-up modes, and demonstrate perturbative stability against BF-bound tachyons. They further develop a 4D supergravity framework to express the conditions for supersymmetric vacua, decoupling the Kähler and complex-structure sectors, and discuss the resulting landscape statistics, showing a tendency towards large volume and small cosmological constant within SUSY ensembles. The results provide a transparent, parametric mechanism for moduli stabilization with potential avenues for de Sitter uplifts and a comparative perspective on flux vacua across string theory frameworks.

Abstract

We demonstrate that flux compactifications of type IIA string theory can classically stabilize all geometric moduli. For a particular orientifold background, we explicitly construct an infinite family of supersymmetric vacua with all moduli stabilized at arbitrarily large volume, weak coupling, and small negative cosmological constant. We obtain these solutions from both ten-dimensional and four-dimensional perspectives. For more general backgrounds, we study the equations for supersymmetric vacua coming from the effective superpotential and show that all geometric moduli can be stabilized by fluxes. We comment on the resulting picture of statistics on the landscape of vacua.

Figures (2)

• Figure 1: The potential $\frac{1}{\lambda}\,V(r, g)$ on solutions for $g$ as a function of $r$.
• Figure 2: The potential $\frac{1}{\lambda}\,V(r, g)$ on solutions for $r$ as a function of $g$.