Heterotic string

A string theory combining a bosonic left-moving system with a supersymmetric right-moving system. Ten target coordinates leave sixteen left-moving internal degrees of freedom for gauge currents. Modular consistency allows the familiar gauge algebras ${\mathfrak{e}}_8\oplus {\mathfrak{e}}_8$ and $\mathfrak{so}(32)$. Suitable compactification can produce spacetime supersymmetry and chiral gauge matter.

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.