Vacuum Varieties, Holomorphic Bundles and Complex Structure Stabilization in Heterotic Theories

Understand

We discuss the use of gauge fields to stabilize complex structure moduli in Calabi-Yau three-fold compactifications of heterotic string and M-theory.

• The requirement that the gauge fields in such models preserve supersymmetry leads to a complicated landscape of vacua in complex structure moduli space.
• We develop methods to systematically map out this multi-branched vacuum space, in a computable and explicit manner.
• In analyzing the resulting vacua, it is found that the associated Calabi-Yau three-folds are sometimes stabilized at a value of complex structure resulting in a singular compactification manifold.