New non-supersymmetric heterotic string theory with reduced rank and exponential suppression of the cosmological constant

We study the heterotic asymmetric orbifold model in which supersymmetry is broken by the stringy Schark-Schwarz mechanism. This model is a natural non-supersymmetric extension of CHL strings and can also be interpreted as the interpolating model between the $E_{8}\times E'_{8}$ theory and the non-supersymmetric $E_{8}$ theory. The enhancement of gauge groups, of which the rank is reduced to $8+d$, is explored. In particular, the enhancement to non-simply-laced groups is possible with $d\geq 2$, as well as in the CHL model. We also give the conditions that the massless matter spectrum must satisfy. Moreover, the one-loop cosmological constant is evaluated in the regime where supersymmetry is asymptotically restored, and we show that the exponential suppression can occur unless $d=1$.