  A holomorphic vector bundle on a Calabi-Yau threefold, X, with h^{1,1}(X)>1
can have regions of its Kahler cone where it is slope-stable, that is, where
the four-dimensional theory is N=1 supersymmetric, bounded by "walls of
stability". On these walls the bundle becomes poly-stable, decomposing into a
direct sum, and the low energy gauge group is enhanced by at least one
anomalous U(1) gauge factor. In this paper, we show that these additional
symmetries can strongly constrain the superpotential in the stable region,
leading to non-trivial textures of Yukawa interactions and restrictions on
allowed masses for vector-like pairs of matter multiplets. The Yukawa textures
exhibit a hierarchy; large couplings arise on the stability wall and some
suppressed interactions "grow back" off the wall, where the extended U(1)
symmetries are spontaneously broken. A number of explicit examples are
presented involving both one and two stability walls, with different
decompositions of the bundle structure group. A three family standard-like
model with no vector-like pairs is given as an example of a class of SU(4)
bundles that has a naturally heavy third quark/lepton family. Finally, we
present the complete set of Yukawa textures that can arise for any holomorphic
bundle with one stability wall where the structure group breaks into two
factors.

High Energy Physics - Theory