Abstract

Gauged Linear Sigma Models (GLSMs) provide a framework for studying different phases of compactification spaces for heterotic string theories. Among them are toroidal orbifolds and smooth Calabi-Yau constructions, both of which are very popular among string model builders. Up to now, quite a few MSSM -like string models have been constructed based on these compactification spaces. We describe the construction of toroidal orbifolds and describe how to obtain their smooth Calabi-Yau counterparts in the GLSM framework. The two regimes lie at different regions in Kahler moduli space, which can be accessed by tuning the Fayet-Iliopoulos GLSM parameters. However, upon probing the entire moduli space, also other phases are encountered which do not have a geometric interpretation as straightforward as the previously mentioned ones. Furthermore, there can be flop and flop-like transitions which further subdivide the different phases.