Small cosmological constants in string theory

We construct supersymmetric 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.

Automated summary

By constructing supersymmetric AdS(4) vacua in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces, we have found that with mild assumptions on numerical values, all moduli can be stabilized at weak string coupling. Furthermore, high-degree Gopakumar-Vafa invariants provide strong evidence that the compactifications are well-controlled, resulting in extremely small cosmological constants. The hierarchical scale-separation in these large but not exponentially compactifications is manifested by the AdS length exceeding the Kaluza-Klein length by a googol factor.