Statistics of Flux Vacua for Particle Physics

TL;DR

This paper studies the statistical distribution of flux vacua in F-theory compactifications, focusing on the prevalence of U(1) symmetries and their implications for particle physics models.

Contribution

It estimates the fraction of flux vacua with specific symmetries and analyzes how the choice of unbroken gauge groups affects the number of vacua, providing new insights into flux vacua statistics.

Findings

Vacua with unbroken U(1) symmetries are less numerous when U(1)_Y arises from a non-trivial Mordell--Weil group.

Vacua with approximate U(1) symmetries tend to cluster as accumulation points.

The number of flux vacua is significantly reduced when U(1)_Y is from Mordell--Weil group, but not in SU(5) unification.

Abstract

Supersymmetric flux compactification of F-theory in the geometric phase yields numerous vacua, and provides an ensemble of low-energy effective theories with different symmetry, matter multiplicity and Lagrangian parameters. Theoretical tools have already been developed so that we can study how the statistics of flux vacua depend on the choice of symmetry and some of Lagrangian parameters. In this article, we estimate the fraction of i) vacua that have a U(1) symmetry for spontaneous R-parity violation, and ii) those that realise ideas which achieve hierarchical eigenvalues of the Yukawa matrices. We also learn a lesson that the number of flux vacua is reduced very much when the unbroken $U(1)_Y$ symmetry is obtained from a non-trivial Mordell--Weil group, while it is not when $U(1)_Y$ is in SU(5) unification. It also turns out that vacua with an approximate U(1) symmetry forms a locus of accumulation points of the flux vacua distribution.