Exploring the Web of Heterotic String Theories using Anomalies

Abstract

We investigate how anomalies can be used to infer relations among different descriptions of heterotic string theory. Starting from the observation that the construction mechanism of heterotic orbifold compactifications considered up to now prevents them from being resolved into fully smooth Calabi-Yau compactification manifolds, we use a new mechanism to obtain an orbifold which does not suffer from the aforementioned limitations. We explain in general how to resolve orbifolds into smooth Calabi-Yaus using toric geometry and gauged linear sigma models. The latter allow for studying the theory in various other regions of the string moduli space as well, which unveils interesting intermediate geometries. By following anomalies through the different regimes, we can match the orbifold theories to their smooth Calabi-Yau counterparts. In the process, we investigate discrete R and non-R orbifold symmetries and propose a mechanism for studying their fate in other regions of the moduli space. Finally, we introduce a novel anomaly cancelation mechanism in gauged linear sigma models, which manifests itself in target space as a description of compactification geometries with torsion and Neveu-Schwarz five branes.