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

Nikhil Raghuram; Washington Taylor; Andrew P. Turner

doi:10.1007/JHEP04(2020)008

paper

General F-theory models with tuned $(SU (3) \times SU (2) \times U (1)) / Z_{6}$ symmetry

arXiv:1912.10991 · doi:10.1007/JHEP04(2020)008

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 $(SU (3) \times SU (2) \times U (1)) / Z_{6}$ 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 $q \leq 4$ 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 $SU (5)$ 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.

arXiv comment36 pages, LaTeX

General F-theory models with tuned $(SU (3) \times SU (2) \times U (1)) / Z_{6}$ symmetry

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General F-theory models with tuned (SU(3)×SU(2)×U(1))/Z6​ symmetry

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General F-theory models with tuned $(SU (3) \times SU (2) \times U (1)) / Z_{6}$ symmetry