Heterotic Calabi-Yau compactification

Compactification of a heterotic string on a Calabi-Yau threefold with a consistent holomorphic vector bundle. Suitable bundle and geometry choices preserve four-dimensional N=1 supersymmetry and generate chiral matter from internal Dirac zero modes. The index controls net chirality. In the standard embedding, the net generation index is half the internal Euler characteristic, up to chirality orientation conventions.