On the Explicit Construction and Statistics of Calabi-Yau Flux Vacua

We explicitly construct and study the statistics of flux vacua for type IIBstring theory on an orientifold of the Calabi-Yau hypersurface$P^4_{[1,1,2,2,6]}$, parametrised by two relevant complex structure moduli. Wesolve for these moduli and the dilaton field in terms of the set of integersdefining the 3-form fluxes and examine the distribution of vacua. We compareour numerical results with the predictions of the Ashok-Douglas density $\det(-R - \omega)$, finding good overall agreement in different regions of modulispace. The number of vacua are found to scale with the distance in flux space.Vacua cluster in the region close to the conifold singularity. Largesupersymmetry breaking is more generic but supersymmetric and hierarchicalsupersymmetry breaking vacua can also be obtained. In particular, the smallsuperpotentials and large dilaton VEVs needed to obtain de Sitter space in acontrollable approximation are possible but not generic. We argue that in ageneral flux compactification, the rank of the gauge group coming from D3branes could be statistically preferred to be very small.Comment: 26 pages, 9 figures; v2: references adde