Type \(\mathbf{\bar{0}}\) Heterotic String Orbifolds

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.