A sufficient condition for de Sitter vacua in type IIB string theory

TL;DR

This work provides a rigorous analytical framework for realizing meta-stable de Sitter vacua in type IIB flux compactifications via the Kähler uplifting mechanism, relying on an interplay between non-perturbative superpotential corrections and the leading α' correction at parametrically large volume. It derives a concrete sufficient condition on microscopic parameters, expressed through flux-dependent quantities like $W_0$, the Euler characteristic via $\hat{\xi}$, and geometric data such as intersection numbers, which guarantees a dS minimum in the Kähler modulus, while stabilizing the dilaton and complex-structure moduli. The analysis generalizes from a single Kähler modulus to swiss-cheese Calabi-Yau manifolds with multiple Kähler moduli and extends to arbitrary numbers of complex structure moduli, showing that moduli stabilization remains perturbatively controlled and that backreaction from stabilized sectors on the volume is suppressed by inverse powers of the volume. An explicit F-theory interpretation ties the condition to purely geometric/topological data of an elliptically fibered Calabi-Yau fourfold, reinforcing the mechanism’s applicability across a broad class of compactifications and underscoring its potential relevance for string cosmology and landscape studies.

Abstract

We derive a sufficient condition for realizing meta-stable de Sitter vacua with small positive cosmological constant within type IIB string theory flux compactifications with spontaneously broken supersymmetry. There are a number of `lamp post' constructions of de Sitter vacua in type IIB string theory and supergravity. We show that one of them -- the method of `Kähler uplifting' by F-terms from an interplay between non-perturbative effects and the leading $α'$-correction -- allows for a more general parametric understanding of the existence of de Sitter vacua. The result is a condition on the values of the flux induced superpotential and the topological data of the Calabi-Yau compactification, which guarantees the existence of a meta-stable de Sitter vacuum if met. Our analysis explicitly includes the stabilization of all moduli, i.e. the Kähler, dilaton and complex structure moduli, by the interplay of the leading perturbative and non-perturbative effects at parametrically large volume.

Figures (5)

• Figure 1: The approximate 2-term scalar potential $V(x)$ from eq. \ref{['VFt2termx']} for different values of $C$.
• Figure 2: Dashed curve: the exact potential with parameters $W_0 = -32.35$. Solid curve: the approximate potential with parameters $W_0 = -37.73$, $C=3.652$.
• Figure 3: The approximate potential as a function of $t$ and $s$. Parameter choice were $C_1 = -13.926$, $C_2=1.4$.
• Figure 4: $(2\,u)^{h^{2,1}} \cdot m_2^2$ as a function of $h^{2,1}$ for $s=10$ and three different VEVs of the complex structure moduli.
• Figure 5: $\Delta$ for different values of $s$.