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

TL;DR

This paper explicitly constructs and analyzes the distribution of flux vacua in type IIB string theory on a specific Calabi-Yau manifold, comparing numerical results with theoretical predictions and exploring implications for supersymmetry breaking and gauge groups.

Contribution

It provides a detailed explicit construction of flux vacua on a Calabi-Yau hypersurface and compares statistical distributions with theoretical density predictions.

Findings

Vacua cluster near conifold points.

Number of vacua scales with flux space distance.

Large supersymmetry breaking is common, but supersymmetric vacua are also possible.

Abstract

We explicitly construct and study the statistics of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau hypersurface $P^4_{[1,1,2,2,6]}$, parametrised by two relevant complex structure moduli. We solve for these moduli and the dilaton field in terms of the set of integers defining the 3-form fluxes and examine the distribution of vacua. We compare our numerical results with the predictions of the Ashok-Douglas density $\det (-R - \omega)$, finding good overall agreement in different regions of moduli space. The number of vacua are found to scale with the distance in flux space. Vacua cluster in the region close to the conifold singularity. Large supersymmetry breaking is more generic but supersymmetric and hierarchical supersymmetry breaking vacua can also be obtained. In particular, the small superpotentials and large dilaton VEVs needed to obtain de Sitter space in a controllable approximation are possible but not generic. We argue that in a general flux compactification, the rank of the gauge group coming from D3 branes could be statistically preferred to be very small.