# Geometrically Engineering the Standard Model: Locally Unfolding Three Families out of E8

## TL;DR

This paper demonstrates how to geometrically unfold a single E8 singularity to produce the three Standard Model families, reducing arbitrariness in model building and linking singularity positions to physical matter content.

## Contribution

It extends previous work by explicitly showing how a single E8 singularity can be unfolded into the Standard Model with three families, providing a geometric framework for matter generation.

## Key findings

- Three Standard Model families emerge from a single E8 singularity.
- The geometric unfolding process relates singularity positions to matter content.
- The framework reduces arbitrariness in geometrically engineered models.

## Abstract

This paper extends and builds upon the results of an earlier paper, in which we described how to use the tools of geometrical engineering to deform geometrically-engineered grand unified models into ones with lower symmetry. This top-down unfolding has the advantage that the relative positions of singularities giving rise to the many `low energy' matter fields are related by only a few parameters which deform the geometry of the unified model. And because the relative positions of singularities are necessary to compute the superpotential, for example, this is a framework in which the arbitrariness of geometrically engineered models can be greatly reduced. In our earlier paper, this picture was made concrete for the case of deforming the representations of an SU(5) model into their Standard Model content. In this paper we continue that discussion to show how a geometrically engineered 16 of SO(10) can be unfolded into the Standard Model, and how the three families of the Standard Model uniquely emerge from the unfolding of a single, isolated E8 singularity.