Classification of Non-Supersymmetric Pati-Salam Heterotic String Models

TL;DR

This paper classifies non-supersymmetric Pati-Salam heterotic string models, develops methods to find tachyon-free configurations, and analyzes their phenomenological viability and particle content.

Contribution

It extends the classification to non-supersymmetric models, introduces a systematic method for tachyon-free model extraction, and assesses their phenomenological features.

Findings

Tachyon-free configurations occur with probabilities of ~0.002 and ~0.01.

Pati-Salam -models lack necessary Higgs representations for symmetry breaking.

Identified three-generation models with balanced bosonic and fermionic degrees of freedom.

Abstract

We extend the classification of fermionic $\mathbb{Z}_2\times\mathbb{Z}_2$ heterotic string orbifolds to non--supersymmetric Pati--Salam (PS) models in two classes of vacua, that we dub $\tilde S$--models and $S$--models. The first correspond to compactifications of a tachyonic ten--dimensional vacuum, whereas the second correspond to compactifications of the ten--dimensional tachyon--free $SO(16)\times SO(16)$ heterotic string. In both cases we develop a systematic method to extract tachyon--free four--dimensional models. We show that tachyon--free configurations arise with probability $\sim0.002$ and $\sim0.01$ in the first and second case, respectively. We adapt the `fertility methodology' that facilitates the extraction of phenomenological models. We show that Pati--Salam $\tilde S$--models do not contain heavy Higgs scalar representations that are required to break the PS symmetry to the Standard Model and are therefore not phenomenologically viable. Hence, we argue that in $\tilde S$--models the $SO(10)$ GUT symmetry must be broken at the string scale to the Standard--like Model subgroup. We extract tachyon--free three generation models in both cases that contain an equal number of massless bosonic and fermionic degrees of freedom, ${\it i.e.}$ with $a_{00}=N_b^0-N_f^0=0$, and analyse their one--loop partition function.