Gut particle spectrum from heterotic compactification

This reviews intends to introduce the reader to the general methodology of computing GUT particle spectrum from compactifying the E-8 x E-8 heterotic string on smooth Calabi-Yau threefolds endowed with stable vector bundles. We use the spectral construction for the bundle and show, with illustrative examples, how one computes the requisite cohomology groups that determine the spectrum. Moreover, physical constraints lead to an algorithmic classification scheme. Finally, we will see the fascinating moduli-dependence, a so-called jumping phenomenon, of the particle spectra.