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

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arXiv · 1912.10991

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

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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 $(\operatorname{SU}(3) \times \operatorname{SU}(2) \times \operatorname{U}(1)) / \mathbb{Z}_6$ and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with $\operatorname{U}(1)$ 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 Cveti\v{c}, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an $\operatorname{SU}(5)$ 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.

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Nikhil Raghuram, Washington Taylor, Andrew P. Turner. 2019-12-23. General F-theory models with tuned $(\operatorname{SU}(3) \times \operatorname{SU}(2) \times \operatorname{U}(1)) / \mathbb{Z}_6$ symmetry. https://doi.org/10.1007/jhep04(2020)008

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