Non-SUSY heterotic string vacua of Gepner models with vanishing cosmological constant

Abstract We study a natural generalization of the results given in K. Aoyama and Y. Sugawara, Prog. Theor. Exp. Phys. 2020, 103B01 (2020) to heterotic strings. Namely, starting from the generic Gepner models for Calabi –Yau three-folds, we construct non-SUSY heterotic string vacua with vanishing cosmological constant at the one-loop level. We especially focus on asymmetric orbifolding based on some discrete subgroup of the chiral $U(1)$ action which acts on both the Gepner model and the $SO(32)$ or $E_8\times E_8$ sector. We present a classification of the relevant orbifold models leading to the string vacua with the properties mentioned above. In some cases, the desired vacua can be constructed in a manner quite similar to those given in the previous paper for the type II string, in which the orbifold groups contain two generators with discrete torsions. On the other hand, we also have simpler models that are just realized as asymmetric orbifolds of cyclic groups with only one generator.