Minimal Simple de Sitter Solutions

TL;DR

This work identifies the minimal, tree-level ingredients needed to realize metastable de Sitter vacua in massive IIA string theory: O6-planes, a nonzero Romans mass, RR/NSNS fluxes, and negative internal curvature. By performing a dimensional reduction on a simple hyperbolic compactification, the authors derive a 4D scalar potential depending on two moduli $\rho$ (volume) and $\tau$ (dilaton combination) and show that de Sitter vacua arise when negative curvature uplifts a previously AdS minimum, with the amplitudes captured by the $a(\rho)$, $b(\rho)$, and $c(\rho)$ components satisfying $4ac/b^2 \approx 1$. A concrete example yields a metastable de Sitter minimum with $V_{dS}/M_p^4 \sim 10^{-4}$, $\rho_{dS} \sim 90$, and $g_s \sim 0.56$, but the model exhibits no parametric separation between KK and moduli masses, highlighting limitations for a fully realistic vacuum. The analysis is extended to twisted 3-tori, where moduli-dependence of the uplift coefficients generally prevents stable de Sitter vacua with the minimal ingredients, suggesting that additional ingredients (e.g., KK5-branes) may be required for stabilization in more general metric-flux backgrounds. Overall, the paper clarifies the precise minimal ingredients needed for tree-level de Sitter constructions and delineates the challenges and directions for achieving fully controlled vacua and potential phenomenological applications.

Abstract

We show that the minimal set of necessary ingredients to construct explicit, four-dimensional de Sitter solutions from IIA string theory at tree-level are O6-planes, non-zero Romans mass parameter, form fluxes, and negative internal curvature. To illustrate our general results, we construct such minimal simple de Sitter solutions from an orientifold compactification of compact hyperbolic spaces. In this case there are only two moduli and we demonstrate that they are stabilized to a sufficiently weakly coupled and large volume regime. We also discuss generalizations of the scenario to more general metric flux constructions.

Figures (2)

• Figure 1: Simple stable de Sitter solutions (solid line) can be constructed by uplifting a stable AdS minimum (dotted line) by negative curvature (dashed line).
• Figure 2: Stable de Sitter vacua with small cosmological constant can be obtained with minimal tree-level ingredients when compactified on spaces of negative curvature.