Algorithmic universality in F-theory compactifications

Abstract

We study universality of geometric gauge sectors in the string landscape in the context of F-theory compactifications. A finite time construction algorithm is presented for $\frac{4}{3}\ifmmode\times\else\texttimes\fi{}2.96\ifmmode\times\else\texttimes\fi{}{10}^{755}$ F-theory geometries that are connected by a network of topological transitions in a connected moduli space. High probability geometric assumptions uncover universal structures in the ensemble without explicitly constructing it. For example, non-Higgsable clusters of seven-branes with intricate gauge sectors occur with a probability above $1--1.01\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}755}$, and the geometric gauge group rank is above 160 with probability 0.999995. In the latter case there are at least 10 ${E}_{8}$ factors, the structure of which fixes the gauge groups on certain nearby seven-branes. Visible sectors may arise from ${E}_{6}$ or $SU(3)$ seven-branes, which occur in certain random samples with probability $\ensuremath{\simeq}1/200$.