Tate Trees for Elliptic Fibrations with Rank one Mordell-Weil group

Understand

U(1) symmetries play a central role in constructing phenomenologically viable F-theory compactifications that realize Grand Unified Theories (GUTs).

• In F-theory, gauge symmetries with abelian gauge factors are modeled by singular elliptic fibrations with additional rational sections, i.e.
• a non-trivial Mordell-Weil rank.
• To determine the full scope of possible low energy theories with abelian gauge factors, which allow for an F-theory realization, it is central to obtain a comprehensive list of all singular elliptic fibrations with extra sections.