The origin of discrete symmetries in F-theory models

TL;DR

This paper reviews how discrete and abelian symmetries originate in F-theory GUT models, emphasizing the role of Mordell-Weil groups and singularities in shaping phenomenologically relevant symmetries.

Contribution

It provides an overview of the origin of discrete symmetries in F-theory, focusing on models with rank-one Mordell-Weil groups and their phenomenological implications.

Findings

Discrete symmetries can arise from Mordell-Weil groups in F-theory.

Rank-one Mordell-Weil groups are key to understanding abelian symmetries.

The structure of singularities influences the emergence of discrete symmetries.

Abstract

While non-abelian groups are undoubtedly the cornerstone of Grand Unified Theories (GUTs), phenomenology shows that the role of abelian and discrete symmetries is equally important in model building. The latter are the appropriate tool to suppress undesired proton decay operators and various flavour violating interactions, to generate a hierarchical fermion mass spectrum, etc. In F-theory, GUT symmetries are linked to the singularities of the elliptically fibred K3 manifolds; they are of ADE type and have been extensively discussed in recent literature. In this context, abelian and discrete symmetries usually arise either as a subgroup of the non-abelian symmetry or from a non-trivial Mordell-Weil group associated to rational sections of the elliptic fibration. In this note we give a short overview of the current status and focus in models with rank-one Mordell-Weil group.