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

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.

PERTURBATIVE DEFORMATIONS OF CONFORMAL FIELD THEORIES REVISITED

The purpose of this paper is to revisit the theory of perturbative deformations of conformal field theory from a mathematically rigorous, purely worldsheet point of view. We specifically include the case of N = (2,2) conformal field theories. From this point of view, we find certain surprising obstructions, which appear to indicate that contrary to previous findings, not all deformations along marginal fields exist perturbatively. This includes the case of deformation of the Gepner model of the Fermat quintic along certain cc fields. In other cases, including Gepner models of K3-surfaces and the free field theory, our results coincides with known predictions. We give partial interpretation of our results via renormalization and mirror symmetry.

PHENOMENOLOGICAL DISCUSSION OF THE THREE-GENERATION GEPNER MODEL

We discuss in detail if the three-generation Gepner model in string theory and some variants can lead to a low energy theory with phenomenological attractive features. Starting from an SU(3)3 gauge theory obtained at the compactification scale by Wilson line breaking from the E6, extensive use of (numerical) renormalization group methods allows for a detailed search for further symmetry breakings and the final low energy massless particle content. In most cases the 273 Yukawa couplings are kept as from the Gepner construction, but we allow for a variation of the other couplings related to radial variations of the corresponding Calabi-Yau manifold of Schimmrigk. The parametrization of soft supersymmetry breaking also induces some freedom. Nevertheless we have not found a parametrization of one of the model variants which simultaneously evades proton decay, has only the standard spectrum of light particles, a reasonable Weinberg angle and a heavy top.