Flat Directions in $Z_{2n}$ Orbifold Models

TL;DR

This paper analyzes $Z_{2n}$ orbifold models, revealing their matter content and flat directions, especially focusing on conjugate pairs that lead to D-flatness, and classifying models based on twisted sector features.

Contribution

It introduces a classification of $Z_{2n}$ orbifold models based on the presence of conjugate pairs and demonstrates that certain flat directions are realized through these pairs.

Findings

$Z_{2n}$ orbifold models contain massless conjugate pairs in specific sectors.

Conjugate pairs induce D-flat directions with non-zero VEVs.

The study classifies models into two types based on twisted sector features.

Abstract

We study generic features related to matter contents and flat directions in $Z_{2n}$ orbifold models. It is shown that $Z_{2n}$ orbifold models have massless conjugate pairs, $R$ and $\overline R$, in certain twisted sectors as well as one of untwisted subsectors. Using these twisted sectors, $Z_{2n}$ orbifold models are classified into two types. Conjugate pairs, $R$ and $\overline R$, lead to $D$-flatness as $\langle R \rangle = \langle \overline R \rangle \neq 0$. We investigate generic superpotentials derived from orbifold models so as to show that this direction is indeed a flat direction.