# Generic construction of the Standard Model gauge group and matter representations in F-theory

## TL;DR

This paper constructs and classifies F-theory models with the Standard Model gauge group and matter content, proving their completeness for certain 6D supergravity theories and suggesting their generality.

## Contribution

It provides a comprehensive geometric construction of F-theory models with the Standard Model gauge group, establishing their completeness in specific 6D supergravity contexts.

## Key findings

- Classifies all consistent 6D supergravity models with the gauge group and matter representations.
- Constructs models from deforming geometries with larger gauge symmetries.
- Suggests these models are generic for 4D and other 6D theories.

## Abstract

We describe general classes of 6D and 4D F-theory models with gauge group $(\operatorname{SU}(3) \times \operatorname{SU}(2) \times \operatorname{U}(1)) / \mathbb{Z}_6$. We prove that this set of constructions gives all possible consistent 6D supergravity theories with no tensor multiplets having this gauge group and the corresponding generic matter representations, which include those of the MSSM. We expect, though do not prove, that these models are similarly generic for 6D theories with tensor multiplets and for 4D $\mathcal{N} = 1$ supergravity theories. The largest class of these constructions comes from deforming an underlying geometry with gauge symmetry $\operatorname{SU}(4) \times \operatorname{SU}(3) \times \operatorname{SU}(2)$.