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) × SU(2) × U(1))/ℤ6 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 ≤ 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.
Highlights
A primary goal of string theory is to understand how the observed physics of the standard model of particle physics can arise in a UV complete quantum theory of gravity
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) × SU(2) × U(1))/Z6 and generic associated matter, which includes the matter content of the standard model
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 and confirm that this holds for the models constructed here
Summary
A primary goal of string theory is to understand how the observed physics of the standard model of particle physics can arise in a UV complete quantum theory of gravity. We address the most straightforward approach, in which the standard model gauge group is directly tuned in the Weierstrass model describing the axiodilaton in the IIB/F-theory framework Such constructions of theories with the standard model gauge group have been considered in [7,8,9,10]; recently, Cvetic, Halverson, Lin, Liu, and Tian (CHLLT) [3], building on a toric construction identified in [11] and aspects of global group structure studied in [12,13,14], considered one class of such models that can be realized over any weak Fano base, giving a large number of possible standard model-like constructions in F-theory.
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