Moduli fixing in semirealistic string compactifications

Heterotic orbifold compactifications yield a myriad of models that reproduce many properties of the supersymmetric extension of the standard model and provide potential solutions to persisting problems of high energy physics, such as the origin of the neutrino masses and the strong CP problem. However, the details of the phenomenology in these scenarios rely on the assumption of a stable vacuum, characterized by moduli fields. In this note, we drop this assumption and address the problem of moduli stabilization in realistic orbifold models. We study their qualities and their 4D effective action, and discuss how nonperturbative effects indeed lift all bulk moduli directions. The resulting vacua, although still unstable, are typically de Sitter and there are generically some quasi-flat directions which can help to deal with cosmological challenges, such as inflation.