General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry

Abstract

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with $U(1)$ gauge symmetry and charges $q\le 4$ previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetič, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an $\mathrm{SU}(5)$ unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group $G$ and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here.

36 pages, LaTeX