We present a class of N = 1 supersymmetric models of particle physics, derived directly
from heterotic M-theory, that contain three families of chiral quarks and leptons
coupled to the gauge group SU(3)C×SU(2)L×U(1)Y. These models are a fundamental
form of “brane-world” theories, with an observable and hidden sector each confined,
after compactification on a Calabi–Yau threefold, to a BPS threebrane separated by a
five-dimensional bulk space with size of the order of the intermediate scale. The requirement
of three families, coupled to the fundamental conditions of anomaly freedom
and supersymmetry, constrains these models to contain additional fivebranes wrapped
around holomorphic curves in the Calabi–Yau threefold. These fivebranes “live” in
the bulk space and represent new, non-perturbative aspects of these particle physics
vacua. We discuss, in detail, the relevant mathematical structure of a class of torus-
fibered Calabi–Yau threefolds with non-trivial first homotopy groups and construct
holomorphic vector bundles over such threefolds, which, by including Wilson lines,
break the gauge symmetry to the standard model gauge group. Rules for constructing
phenomenological particle physics models in this context are presented and we give a
number of explicit examples.