Flux Vacua Statistics for Two-Parameter Calabi-Yau's

TL;DR

This paper analyzes the distribution of flux vacua in a specific Calabi-Yau compactification, revealing a power-law behavior away from singularities and the conifold locus acting as an attractor, with insights into supersymmetric solutions.

Contribution

It provides a detailed evaluation of flux vacua statistics for a two-parameter Calabi-Yau, including behavior near the conifold locus and the nature of supersymmetric solutions.

Findings

Flux vacua follow a power law away from the conifold locus.

The conifold locus acts as an attractor in moduli space.

Supersymmetric solutions near the conifold do not support fluxes.

Abstract

We study the number of flux vacua for type IIB string theory on an orientifold of the Calabi-Yau expressed as a hypersurface in WCP^4[1,1,2,2,6] by evaluating a suitable integral over the complex-structure moduli space as per the conjecture of Douglas and Ashok. We show that away from the singular conifold locus, one gets a power law, and that the (neighborhood) of the conifold locus indeed acts as an attractor in the (complex structure) moduli space. We also study (non)supersymmetric solutions near the conifold locus.In the process, we evaluate the periods near the conifold locus. We also study (non)supersymmetric solutions near the conifold locus, and show that supersymmetric solutions near the conifold locus do not support fluxes.