Yukawas and discrete symmetries in F-theory compactifications without section

TL;DR

This paper explores how discrete symmetries in F-theory compactifications without sections influence Yukawa couplings, highlighting the role of instanton effects in superpotential generation within SU(5) GUT models.

Contribution

It demonstrates the association of discrete symmetries with massive U(1)s and their impact on Yukawa coupling selection rules in genus-one fibrations without sections.

Findings

Discrete symmetries induce non-trivial Yukawa coupling restrictions.

M2 instantons are crucial for superpotential terms near phase transitions.

Concrete SU(5) GUT model exemplifies the theoretical concepts.

Abstract

In the case of F-theory compactifications on genus-one fibrations without section there are naturally appearing discrete symmetries, which we argue to be associated to geometrically massive U(1) gauge symmetries. These discrete symmetries are shown to induce non-trivial selection rules for the allowed Yukawa couplings in SU(N) gauge theories. The general discussion is exemplified using a concrete Calabi-Yau fourfold realizing an SU(5) GUT model. We observe that M2 instanton effects appear to play a key role in the generation of new superpotential terms and in the dynamics close to phase transition loci.