An Abundance of Heterotic Vacua

We explicitly construct the largest dataset to date of heterotic vacua arising from stable vector bundles on Calabi-Yau threefolds. Focusing on elliptically fibered Calabi-Yau manifolds with spectral cover bundles, we show that the number of heterotic models with non-zero number of generations is finite. We classify these models according to the complex base of their Calabi-Yau threefold and to the unification gauge group that they preserve in four dimensions. This database of the order of $10^7$ models, which includes potential Standard Model candidates, is subjected to some preliminary statistical analyses. The additional constraint that there should be three net generations of particles gives a dramatic reduction of the number of vacua.