Towards the Classification of Tachyon-Free Models From Tachyonic Ten-Dimensional Heterotic String Vacua

Recently it was proposed that ten-dimensional tachyonic string vacua may serve as starting points for the construction of viable four dimensional phenomenological string models which are tachyon free. This is achieved by projecting out the tachyons in the four-dimensional models using projectors other than the projector which is utilised in the supersymmetric models and those of the \(SO(16)\times SO(16)\) heterotic string. We continue the exploration of this class of models by developing systematic computerised tools for their classification, the analysis of their tachyonic and massless spectra, as well as analysis of their partition functions and vacuum energy. We explore a randomly generated space of \(2\times10^9\) string vacua in this class and find that tachyon--free models occur with \(\sim 5\times 10^{-3}\) probability, and of those, phenomenologically inclined \(SO(10)\) vacua with \(a_{00}=N_b^0-N_f^0=0\), i.e. equal number of fermionic and bosonic massless states, occur with frequency \(\sim 2\times 10^{-6}\). Extracting larger numbers of phenomenological vacua therefore requires adaptation of fertility conditions that we discuss, and significantly increase the frequency of tachyon--free models. Our results suggest that spacetime supersymmetry may not be a necessary ingredient in phenomenological string models, even at the Planck scale.