On the Taxonomy of Flux Vacua

TL;DR

This paper constructs a large set of IIB flux vacua on a specific Calabi-Yau orientifold to test predictions about their distribution, revealing a concentration near the conifold point and a power law relation with D3 charge.

Contribution

It provides a detailed characterization of flux vacua distribution on a Calabi-Yau orientifold, supporting theoretical predictions and analyzing their dependence on flux parameters.

Findings

Vacua density governed by ${ m det}(-R - \omega)$

Significant clustering of vacua near the conifold point

Number of vacua scales as a power law with D3 charge

Abstract

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 $WP^{4}_{1,1,1,1,4}$. 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.