On the Taxonomy of Flux Vacua

We investigate several predictions about the properties of IIB flux vacua onCalabi-Yau orientifolds, by constructing and characterizing a very large set ofvacua in a specific example, an orientifold of the Calabi-Yau hypersurface in$WP^{4}_{1,1,1,1,4}$. We find support for the prediction of Ashok and Douglasthat 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 modulispace. The conifold point $\psi=1$ on moduli space therefore serves as anattractor, with a significant fraction of the flux vacua contained in a smallneighborhood surrounding $\psi=1$. We also study the functional dependence ofthe number of flux vacua on the D3 charge in the fluxes, finding simple powerlaw growth.Comment: 22 pages, harvmac; v2 typos corrected, refs added; v3 minor error correcte