Type 0 $\mathbb{Z}_2\times \mathbb{Z}_2$ Heterotic String Orbifolds and Misaligned Supersymmetry

TL;DR

This paper investigates the existence and properties of type 0 heterotic string orbifolds with $ ext{Z}_2 imes ext{Z}_2$ symmetry, revealing their instability due to tachyons but also their potential for exploring string dynamics in cosmology, and demonstrating a form of misaligned supersymmetry.

Contribution

It demonstrates the existence of type 0 $ ext{Z}_2 imes ext{Z}_2$ heterotic orbifolds, analyzes their uniqueness, and explores their properties including tachyonic instabilities and misaligned supersymmetry.

Findings

Existence of type 0 models in $ ext{Z}_2 imes ext{Z}_2$ heterotic orbifolds.

Identification of a unique configuration among many GGSO choices.

Presence of physical tachyons indicating instability, but with finite amplitudes after removal of tachyons, showing misaligned supersymmetry.

Abstract

The $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic string orbifold yielded a large space of phenomenological three generation models and serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. In this paper we explore the existence of type 0 models in this class of string compactifications. We demonstrate the existence of type 0 $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic string orbifolds, and show that there exist a large degree of redundancy in the space of GGSO projection coefficients when the type 0 restrictions are implemented. We explore the existence of such configurations in several constructions. The first correspond to essentially a unique configuration out of a priori $2^{21}$ discrete GGSO choices. We demonstrate this uniqueness analytically, as well as by the corresponding analysis of the partition function. A wider classification is performed in $\tilde S$--models and $S$--models, where the first class correspond to compactifications of a tachyonic ten dimensional heterotic string vacuum, whereas the second correspond to compactifications of the ten dimensional non--tachyonic $SO(16)\times SO(16)$. We show that the type 0 models in both cases contain physical tachyons at the free fermionic point in the moduli space. These vacua are therefore necessarily unstable, but may be instrumental in exploring the string dynamics in cosmological scenarios. we analyse the properties of the string one--loop amplitude. Naturally, these are divergent due to the existence of tachyonic states. We show that once the tachyonic states are removed by hand the amplitudes are finite and exhibit a form of misaligned supersymmetry.