String Junctions and Non-Simply Connected Gauge Groups

TL;DR

This paper explores the relationship between the global structure of gauge groups in elliptic F-theory compactifications, fractional string junctions, and the Mordell-Weil lattice, extending previous results to more complex geometries.

Contribution

It provides a method to determine the full gauge group structure, including U(1) factors, beyond rational elliptic surfaces to K3 and Calabi-Yau three-folds.

Findings

Derived pi^1(G) for semi-simple gauge groups

Established methods to include U(1) factors in gauge group analysis

Extended results to elliptic K3 and Calabi-Yau three-folds

Abstract

Relations between the global structure of the gauge group in elliptic F-theory compactifications, fractional null string junctions, and the Mordell-Weil lattice of rational sections are discussed. We extend results in the literature, which pertain primarily to rational elliptic surfaces and obtain pi^1(G) where G is the semi-simple part of the gauge group. We show how to obtain the full global structure of the gauge group, including all U(1) factors. Our methods are not restricted to rational elliptic surfaces. We also consider elliptic K3's and K3-fibered Calabi-Yau three-folds.