Distribution of the Number of Generations in Flux Compactifications

TL;DR

This paper analyzes the statistical distribution of the number of generations in flux compactifications of F-theory, revealing a Gaussian distribution for small numbers and discussing gauge group costs.

Contribution

It provides a detailed statistical analysis of the distribution of generations in F-theory flux compactifications, linking gauge groups and couplings.

Findings

Distribution of N_gen is approximately Gaussian for |N_gen| ≤ 10

Distribution factorizes into gauge group, generations, and couplings

Higher-rank gauge groups have a higher statistical cost

Abstract

Flux compactification of string theory generates an ensemble with a large number of vacua called the landscape. By using the statistics of various properties of low-energy effective theories in the string landscape, one can therefore hope to provide a scientific foundation to the notion of naturalness. This article discusses how to answer such questions of practical interest by using flux compactification of F-theory. It is found that the distribution is approximately in a factorized form given by the distribution of the choice of 7-brane gauge group, that of the number of generations $N_{\rm gen}$ and that of effective coupling constants. The distribution of $N_{\rm gen}$ is approximately Gaussian for the range $|N_{\rm gen}| \lesssim 10$. The statistical cost of higher-rank gauge groups is also discussed.