Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications

TL;DR

This paper explores how discrete gauge symmetries emerge in four-dimensional F-Theory compactifications through Higgsing, providing geometric and field-theoretic insights, and analyzing their implications on matter charges and fluxes.

Contribution

It offers a geometric prescription for discrete charge calculation and maps the Higgsing process between field theory and geometry in F-Theory.

Findings

Discrete symmetries arise from deforming elliptic fibrations to genus-one fibrations.

The paper provides a method to compute induced discrete charges on matter curves.

Higgsing U(1) induces G-flux that preserves the D3 tadpole.

Abstract

We study F-Theory compactifications to four dimensions that exhibit discrete gauge symmetries. Geometrically these arise by deforming elliptic fibrations with two sections to a genus-one fibration with a bi-section. From a four-dimensional field-theory perspective they are remnant symmetries from a Higgsed U(1) gauge symmetry. We implement such symmetries in the presence of an additional SU(5) symmetry and associated matter fields, giving a geometric prescription for calculating the induced discrete charge for the matter curves and showing the absence of Yukawa couplings that are forbidden by this charge. We present a detailed map between the field theory and the geometry, including an identification of the Higgs field and the massless states before and after the Higgsing. Finally we show that the Higgsing of the U(1) induces a G-flux which precisely accounts for the change in the Calabi-Yau Euler number so as to leave the D3 tadpole invariant.