  In a previous paper, we introduced a heterotic standard model and discussed
its basic properties. This vacuum has the spectrum of the MSSM with one
additional pair of Higgs-Higgs conjugate fields and a small number of uncharged
moduli. In this paper, the requisite vector bundles are formulated;
specifically, stable, holomorphic bundles with structure group SU(N) on smooth
Calabi-Yau threefolds with Z_3 x Z_3 fundamental group. A method for computing
bundle cohomology is presented and used to evaluate the cohomology groups of
the standard model bundles. It is shown how to determine the Z_3 x Z_3 action
on these groups. Finally, using an explicit method of "doublet-triplet
splitting", the low-energy particle spectrum is computed.
