On the Taxonomy of Flux Vacua

We investigate several predictions about the properties of IIB flux vacua on Calabi-Yau orientifolds, by constructing and characterizing a very large set of vacua in a specific example, an orientifold of the Calabi-Yau hypersurface in $W{P}_{1,1,1,1,4}^4$. We find support for the prediction of Ashok and Douglas that the density of vacua on moduli space is governed by ${\rm det}(-R - \omega)$where$R$and$\omega$ are curvature and K"ahler forms on the moduli space. The conifold point $\psi =1$ on moduli space therefore serves as an attractor, with a significant fraction of the flux vacua contained in a small neighborhood surrounding $\psi =1$. We also study the functional dependence of the number of flux vacua on the D3 charge in the fluxes, finding simple power law growth.