Yukawas and discrete symmetries in F-theory compactifications without section

TL;DR

This paper investigates Yukawa couplings in F-theory on genus-one fibrations without a section, where discrete symmetries arise as remnants of geometrically massive $U(1)$ gauge fields. It develops both closed-string (Stückelberg) and open-string (singlet Higgsing) pictures and constructs a class of elliptically fibered Calabi–Yau fourfolds without section realizing an $SU(5)$ GUT with a residual $\mathbb{Z}_2$ symmetry distinguishing matter curves. The authors show that the discrete symmetry forbids certain Yukawa couplings that would be allowed by the continuous symmetry, and that conifold transitions and M2-instanton effects encode the associated dynamics. Together, the results provide concrete geometric mechanisms for discrete selection rules in F-theory with implications for global models and phenomenology and illuminate the open/closed string duality in Higgsed setups.

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.