The $Z_2\times Z_2$ heterotic string orbifold gives rise to a large space of phenomenological three generation models that serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. Recently, we demonstrated the existence of type 0 $Z_2\times Z_2$ heterotic string orbifolds in which there are no massless fermionic states. In this paper we demonstrate the existence of non--supersymmetric tachyon--free $Z_2\times Z_2$ heterotic string orbifolds that do not contain any massless bosonic states from the twisted sectors. We dub these configurations type ${\bar 0}$ models. They necessarily contain untwisted bosonic states, producing the gravitational, gauge and scalar moduli degrees of freedom, but possess an excess of massless fermionic states over bosonic ones, hence producing a positive cosmological constant. Such configurations may be instrumental when trying to understand the string dynamics in the early universe.

中文翻译：

---

0¯型杂优势串orbifolds

$Z_2\times Z_2$ 异质弦orbifold 产生了大量的现象学三代模型空间，作为探索粒子物理学标准模型如何被纳入量子引力理论的试验场。最近，我们证明了 0 型 $Z_2\times Z_2$ 异质弦 orbifolds 的存在，其中没有无质量的费米子态。在本文中，我们证明了非超对称快子的存在 - 无 $Z_2\times Z_2$ 异质弦 orbifolds，不包含来自扭曲扇区的任何无质量玻色子态。我们将这些配置类型称为 ${\bar 0}$ 模型。它们必然包含未扭曲的玻色子态，产生引力、规范和标量模自由度，但拥有比玻色子态更多的无质量费米子态，因此产生一个正的宇宙常数。当试图理解早期宇宙中的弦动力学时，这种配置可能会有所帮助。