Warped Vacuum Statistics

TL;DR

This paper analyzes how warping influences the distribution of type IIB flux vacua in Calabi-Yau orientifolds, deriving an analytical distribution and comparing it with numerical results, revealing significant dilution effects near the conifold point.

Contribution

It provides the first analytical form of flux vacuum distribution that includes warping effects, validated by Monte Carlo simulations.

Findings

Warping causes a steep drop in vacuum density near the conifold point.

Analytical distribution closely matches Monte Carlo enumeration results.

Vacuum density is highly diluted close to the conifold point due to warping.

Abstract

We consider the effect of warping on the distribution of type IIB flux vacua constructed with Calabi-Yau orientifolds. We derive an analytical form of the distribution that incorporates warping and find close agreement with the results of a Monte Carlo enumeration of vacua. Compared with calculations that neglect warping, we find that for any finite volume compactification, the density of vacua is highly diluted in close proximity to the conifold point, with a steep drop-off within a critical distance.