Small Cosmological Constants in String Theory

TL;DR

This paper constructs explicit supersymmetric AdS4 vacua in type IIB string theory with very small cosmological constants, demonstrating controlled moduli stabilization and hierarchical scale separation.

Contribution

It provides explicit Calabi-Yau orientifold compactifications with stabilized moduli and extremely small cosmological constants, advancing understanding of string vacua with hierarchical scales.

Findings

Cosmological constant < 10^{-123} in Planck units.

Moduli stabilized at weak string coupling.

Hierarchical scale separation with AdS length much larger than Kaluza-Klein length.

Abstract

We construct supersymmetric $\mathrm{AdS}_4$ vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the $\alpha'$ expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude $ < 10^{-123}$ in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.