Yukawa Unification in Heterotic String Theory

TL;DR

This paper investigates Yukawa unification within heterotic string models, revealing that traditional GUT symmetry does not enforce unification, but certain additional symmetries in specific models can enable it.

Contribution

It provides a detailed analysis of Yukawa unification in heterotic models and presents an explicit line bundle model demonstrating scenarios where unification occurs due to extra symmetries.

Findings

GUT symmetry alone does not enforce Yukawa unification in heterotic models.

Additional symmetries can lead to Yukawa unification in specific heterotic constructions.

An explicit heterotic line bundle model illustrating these scenarios.

Abstract

We analyze Yukawa unification in the the context of $E_8\times E_8$ heterotic Calabi-Yau models which rely on breaking to a GUT theory via a non-flat gauge bundle and subsequent Wilson line breaking to the standard model. Our focus is on underlying GUT theories with gauge group $SU(5)$ or $SO(10)$. We provide a detailed analysis of the fact that, in contrast to traditional field theory GUTs, the underlying GUT symmetry of these models does not enforce Yukawa unification. Using this formalism, we present various scenarios where Yukawa unification can occur as a consequence of additional symmetries. These additional symmetries arise naturally in some heterotic constructions and we present an explicit heterotic line bundle model which realizes one of these scenarios.