Extended Gauge Symmetries in F-theory

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.