Extended Gauge Symmetries in F-theory

TL;DR

This paper explores the global aspects of gauge symmetry in F-theory, analyzing how complete gauge groups, matter localization, and anomaly constraints influence unification, with insights from dual heterotic string vacua.

Contribution

It introduces a comprehensive analysis of global gauge groups in F-theory, including semi-simple and Abelian factors, and elucidates their matter content and unification constraints.

Findings

Complete gauge groups can be derived from discriminant decomposition.

Global constraints enforce a unified gauge group structure.

Matter curves and embeddings into exceptional groups are explicitly characterized.

Abstract

We study gauge symmetry in F-theory in light of global aspects. For this, we consider not only a simple (local) group, but also a semi-simple group with Abelian factors. Once we specify the complete gauge group by decomposing the discriminant, analogous to arranging 7-branes, we can derive the matter contents, their localization and the relation to enhanced groups. Global constraints coming from Calabi--Yau conditions and anomaly cancellations imply a unified group. The semisiple group shows explicit formation of matter curves and nontriviality of its embedding into exceptional group. Also the dual heterotic string vacua with line bundles provide a guide on the unification.