Vacuum energy in non-supersymmetric quasi-realistic heterotic-string vacua with fixed moduli

Recently, Baykara et al. (The Quasicrystalline string landscape, 2024; New non-supersymmetric tachyon-free strings, 2024) discussed the existence of quasicrystalline string vacua that contain a single neutral moduli, the dilaton, and studied compactifications of the non-supersymmetric $$ heterotic-string on these spaces. We discuss a specific class of quasi-realistic string vacua with similar properties that has been known since the late eighties and analyse the vacuum energy in several non-supersymmetric examples that correspond to compactifications of tachyon free ten dimensional vacua as well as compactifications of tachyonic ten dimensional vacua. Our analysis uses the Free Fermionic Formalism of the heterotic-string in four dimensions and employs asymmetric boundary conditions that project all the geometrical moduli by Generalised GSO projections. This methodology produces models with both positive and negative spacetime potential at one-loop.