Non-supersymmetric heterotic strings and chiral CFTs

Non-supersymmetric heterotic strings share various properties with their supersymmetric counterparts. Torus compactifications of the latter live in a component of the moduli space of string vacua with 16 supercharges, and various asymmetric orbifolds thereof realize vacua in other components, exhibiting qualitative differences such as rank reduction. We set out to study the analogous problem for non-supersymmetric heterotic strings, framing it in relation to chiral fermionic CFTs with central charge 24, which were classified recently. We find that for the case analogous to the so-called CHL string, which has gauge group rank reduced by 8, there are in total four non-supersymmetric versions. These include the well known $E_8$ string and three other constructions a la CHL, which can be distinguished qualitatively by how tachyons appear in their classical moduli spaces. We also discuss the classification problem for lower rank theories and the relationship between MSDS models and Scherk-Schwarz reductions.