Interpolation and Exponentially Suppressed Cosmological Constant in Non-Supersymmetric Heterotic Strings with General ${\mathbb{Z}}_2$ Twists

We study general non-supersymmetric heterotic string models, including so-called interpolating models, $d$-dimensionally compactified with the arbitrary number of freely acting ${\mathbb{Z}}_2$ twisted directions. Taking the limits of the compactified radii to zero and infinity (the endpoint limits), we show some examples of the various interpolation patterns in the $d=2$ (8-dimensional) case. In the region where supersymmetry is asymptotically restored, we derive the formula for the one-loop cosmological constant of $(10-d)$ dimensional non-supersymmetric heterotic string models with general ${\mathbb{Z}}_2$ twists, which does not depend on all the other endpoints and find out the points in the moduli space where the cosmological constant is exponentially suppressed. The moduli stability of the cosmological constant is also analyzed.