Deformations of bundles and the Standard Model

We modify a recently proposed heterotic model hep-th/0703210, giving three net-generations of Standard Model fermions, to get rid of an additional U(1) factor in the gauge group. The method employs a stable SU(5) bundle on a Calabi-Yau threefold admitting a free involution. The bundle has to be built as a deformation of the direct sum of a stable SU(4) bundle and the trivial line bundle.