# Multiple Unfoldings of Orbifold Singularities: Engineering Geometric Analogies to Unification

## TL;DR

This paper explores how deforming orbifold singularities in string compactifications can naturally produce Standard Model physics from grand unified theories, reducing arbitrary parameters in model building.

## Contribution

It introduces a method to deform compactification manifolds to transition from GUT models to the Standard Model, simplifying the geometric engineering process.

## Key findings

- Deformation of a GUT manifold into a Standard Model manifold.
- Reduced arbitrariness in the relative positions of Standard Model fields.
- Explicit realization of Standard Model from geometric deformations.

## Abstract

Katz and Vafa showed how charged matter can arise geometrically by the deformation of ADE-type orbifold singularities in type IIa, M-theory, and F-theory compactifications. In this paper we use those same basic ingredients, used there to geometrically engineer specific matter representations, here to deform the compactification manifold itself in a way which naturally compliments many features of unified model building. We realize this idea explicitly by deforming a manifold engineered to give rise to an $SU_5$ grand unified model into a one giving rise to the Standard Model. In this framework, the relative local positions of the singularities giving rise to Standard Model fields are specified in terms of the values of a small number of complex structure moduli which deform the original manifold, greatly reducing the arbitrariness of their relative positions.