From Local to Global in F-Theory Model Building

TL;DR

This paper explores the limitations of local F-theory model building by examining how global constraints and singularities influence the structure and consistency of the models, especially in SU(5) scenarios.

Contribution

It analyzes the global aspects of F-theory models, highlighting how local assumptions are affected by global D7-brane dependencies and intrinsic singularities.

Findings

Global D7-branes are not independent locally assumed

Unavoidable intrinsic singularities occur on D7-branes

Global constraints impact tadpole cancellation in SU(5) models

Abstract

When locally engineering F-theory models some D7-branes for the gauge group factors are specified and matter is localized on the intersection curves of the compact parts of the world-volumes. In this note we discuss to what extent one can draw conclusions about F-theory models by just restricting the attention locally to a particular seven-brane. Globally the possible D7-branes are not independent from each other and the (compact part of the) D7-brane can have unavoidable intrinsic singularities. Many special intersecting loci which were not chosen by hand occur inevitably, notably codimension three loci which are not intersections of matter curves. We describe these complications specifically in a global SU(5) model and also their impact on the tadpole cancellation condition.