Non-supersymmetric non-tachyonic heterotic vacua with reduced rank in various dimensions

We construct rigid non-supersymmetric heterotic vacua with reduced rank and no tachyons in six and four dimensions. These configurations are based on asymmetric orbifold compactifications which do not admit deformation moduli and represent, to the best of our knowledge, the first instances of non-tachyonic non-supersymmetric heterotic vacua with reduced rank.