Small cosmological constants in string theory

A bstract We construct supersymmetric AdS 4 vacua of type IIB string theory in compactifications on orientifolds Calabi-Yau threefold hypersurfaces. first find explicit and quantized fluxes for which the superpotential takes form proposed by Kachru, Kallosh, Linde, Trivedi. Given very mild assumptions numerical values Pfaffians, these admit all moduli are stabilized at weak coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that ? ? expansion is likewise well-controlled. extremely small cosmological constants, with magnitude < 10 ? 123 Planck units. The large, but not exponentially so, hence manifest hierarchical scale-separation, length exceeding Kaluza-Klein a factor googol.